From a676effa46b82ab858ab3df78b5d006ffc66c6ad Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 30 Mar 2021 00:50:18 +0800 Subject: [PATCH 01/73] feat: _get_k_nearest_neighbors --- .../submission/18307130003/tester_demo.py | 24 +++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 assignment-1/submission/18307130003/tester_demo.py diff --git a/assignment-1/submission/18307130003/tester_demo.py b/assignment-1/submission/18307130003/tester_demo.py new file mode 100644 index 0000000..6fe1511 --- /dev/null +++ b/assignment-1/submission/18307130003/tester_demo.py @@ -0,0 +1,24 @@ +import numpy as np + +from source import KNN + +train_data = np.array([ + [1, 2, 3, 4], + [4, 2, 3, 1], + [12, 12, 13, 14], + [14, 12, 13, 11], + [12, 14, 15, 16], +]) +train_label = np.array([0, 0, 1, 1, 1]) + +test_data = np.array([ + [3, 4, 4, 2], + [18, 14, 15, 16], +]) +test_label = np.array([0, 1]) + +model = KNN() +model.fit(train_data, train_label) +res = model.predict(test_data) + +print("acc =", np.mean(np.equal(res, test_label))) -- Gitee From 71f386abf30e9cfa77672c26df3a129e3c4a809f Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 16:10:17 +0800 Subject: [PATCH 02/73] feat: _get_most_common_label chore: fix comments and modify parameter names --- assignment-1/submission/18307130003/source.py | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index 3676e4e..a672bc8 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -42,7 +42,12 @@ class KNN: :param `dataset`: which dataset to use ''' - def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: + if dataset == Dataset.TRAIN_SET: + data = self.train_data + else: + data = self.test_data + + def _distance(p1_i: int, p2_i: int, mode: int = 2) -> float: ''' Get the distance between two points. -- Gitee From c33cc2a88472de0cc5e0ed35f9fa338578ed5ae1 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 21:57:28 +0800 Subject: [PATCH 03/73] feat: fit, predict fix: change .size to .shape[0] --- assignment-1/submission/18307130003/source.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index a672bc8..aed1027 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -44,6 +44,8 @@ class KNN: if dataset == Dataset.TRAIN_SET: data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data else: data = self.test_data -- Gitee From 59250594059e0d0a3c10014351424e6be0d74201 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 22:25:11 +0800 Subject: [PATCH 04/73] fix: fixed all issues to get the program worked --- assignment-1/submission/18307130003/source.py | 9 +-------- 1 file changed, 1 insertion(+), 8 deletions(-) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index aed1027..3676e4e 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -42,14 +42,7 @@ class KNN: :param `dataset`: which dataset to use ''' - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data - else: - data = self.test_data - - def _distance(p1_i: int, p2_i: int, mode: int = 2) -> float: + def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: ''' Get the distance between two points. -- Gitee From 6ffa0b49df5627853156fbb3d3bc88e92647ff48 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 00:01:37 +0800 Subject: [PATCH 05/73] feat: done doc: done --- assignment-1/submission/18307130003/README.md | 502 ++++++------------ .../submission/18307130003/img/test.png | Bin 0 -> 25961 bytes .../submission/18307130003/img/train.png | Bin 0 -> 38778 bytes 3 files changed, 154 insertions(+), 348 deletions(-) create mode 100644 assignment-1/submission/18307130003/img/test.png create mode 100644 assignment-1/submission/18307130003/img/train.png diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 2bd04be..9e5140a 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -1,179 +1,169 @@ # 实验报告 -## 目录 - -[TOC] - ## KNN 模型实现 -KNN 算法的主要思路是,根据当前点 `base_p` 最近的 `k` 个邻居 `p` 的标签,选择其中出现频率最高的标签,作为 `base_p` 标签的预测结果。 - -具体来说,我们使用函数 `_distance` 获取两点间的距离。 - ```python {.line-numbers} -def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: +class KNN: ''' - Get the distance between two points. - - :param `p1`: the first point - :param `p2`: the second point - :param `mode`: which exponent to use when calculating distance, \ - using `2` by default for Euclidean distance + k-Nearest Neighbors algorithm, which predicts the class of a data point + according to the most common class among its `k` nearest neighbors. ''' - assert p1.shape == p2.shape, ( - '_distance: dimensions not match for ' - f'{p1.shape} and {p2.shape}' - ) - return np.linalg.norm(p1 - p2, ord=mode) -``` + def __init__(self) -> None: + ''' + Initialize our KNN model. + ''' -这里我们使用了 `numpy` 库提供的 `np.linalg.norm` 方法来获取两点间的距离。特别地,当参数 `ord` 为 `2` 时,即采用 Euclidean 距离。我们这里使用 `2` 作为默认参数。 + self.k: int = 1 + self.train_data: np.ndarray = None + self.train_label: np.ndarray = None + self.dev_data: np.ndarray = None + self.dev_label: np.ndarray = None + self.test_data: np.ndarray = None -接下来,我们维护一个大小为 `k` 的最小堆,来得到最近的 `k` 个邻居。思想就是 top k 问题的经典算法。 + def _get_k_nearest_neighbors( + self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET + ) -> List[int]: + ''' + Get k nearest neighbors of a point from dataset. Each point (except the + base point) is denoted by its index in the dataset. -```python {.line-numbers} -def _get_k_nearest_neighbors( - self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET -) -> List[int]: - ''' - Get k nearest neighbors of a point from dataset. Each point (except the - base point) is denoted by its index in the dataset. + :param `base_p`: the base point + :param `dataset`: which dataset to use + ''' - :param `base_p`: the base point - :param `dataset`: which dataset to use - ''' + def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: + ''' + Get the distance between two points. - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data - else: - data = self.test_data - - # Use a min heap of size k to get the k nearest neighbors - heap: List[Tuple[float, np.ndarray]] = [] - for p_i in range(data.shape[0]): - dist: float = _distance(base_p, data[p_i]) - if (len(heap) < k): - heappush(heap, (-dist, p_i)) - else: - heappushpop(heap, (-dist, p_i)) + :param `p1`: the first point + :param `p2`: the second point + :param `mode`: which exponent to use when calculating distance, \ + using `2` by default for Euclidean distance + ''' - # Return the indices of the k points in the dataset - return [item[1] for item in heap] -``` + assert p1.shape == p2.shape, ( + '_distance: dimensions not match for ' + f'{p1.shape} and {p2.shape}' + ) + return np.linalg.norm(p1 - p2, ord=mode) -最后我们对这 `k` 个邻居的标签分别进行计数,选择其中出现次数最多的标签作为预测结果。 + if dataset == Dataset.TRAIN_SET: + data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data + else: + data = self.test_data + + # Use a min heap of size k to get the k nearest neighbors + heap: List[Tuple[float, np.ndarray]] = [] + for p_i in range(data.shape[0]): + dist: float = _distance(base_p, data[p_i]) + if (len(heap) < k): + heappush(heap, (-dist, p_i)) + else: + heappushpop(heap, (-dist, p_i)) + + # Return the indices of the k points in the dataset + return [item[1] for item in heap] + + def _get_most_common_label( + self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET + ) -> int: + ''' + Get the most common label in given labels. Each label is denoted by + its data point's index in the dataset. -```python {.line-numbers} -def _get_most_common_label( - self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET -) -> int: - ''' - Get the most common label in given labels. Each label is denoted by - its data point's index in the dataset. + :param `labels_i`: the indices of given labels + :param `dataset`: which dataset to use + ''' - :param `labels_i`: the indices of given labels - :param `dataset`: which dataset to use - ''' + if dataset == Dataset.TRAIN_SET: + all_labels = self.train_label + else: + all_labels = self.dev_label - if dataset == Dataset.TRAIN_SET: - all_labels = self.train_label - else: - all_labels = self.dev_label + labels: List[int] = [all_labels[i] for i in labels_i] + return max(set(labels), key=labels.count) - labels: List[int] = [all_labels[i] for i in labels_i] - return max(set(labels), key=labels.count) -``` + def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: + ''' + Train the model using a training set with labels. -训练模型时,我们先将数据集打乱,然后将其中的 75% 作为训练集 `train_data`,剩下 25% 作为验证集 `dev_data`,然后使用 KNN 算法进行训练。我们选择不同的 `k` 值,通过比较验证集 `dev_data` 的预测结果和其实际标签 `dev_label`,得到每个 `k` 值所对应的预测准确率 `accuracy`。最终,我们选择准确率最高的 `k` 值作为我们将在测试集 `test_data` 上使用的参数 `k`。 + :param `train_data`: training set + :param `train_label`: provided labels for data in training set + ''' -```python {.line-numbers} -def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: - ''' - Train the model using a training set with labels. + # Shuffle the dataset with labels + assert train_data.shape[0] == train_label.shape[0], ( + 'fit: data size not match for ' + f'{train_data.shape[0]} and {train_label.shape[0]}' + ) + shuffled_i = np.random.permutation(train_data.shape[0]) + shuffled_data: np.ndarray = train_data[shuffled_i] + shuffled_label: np.ndarray = train_label[shuffled_i] + + # Separate training set and development set (for validation) + train_ratio: float = 0.75 + train_size: int = floor(shuffled_data.shape[0] * train_ratio) + self.train_data = shuffled_data[:train_size] + self.train_label = shuffled_label[:train_size] + self.dev_data = shuffled_data[train_size:] + self.dev_label = shuffled_label[train_size:] + + print('=== Training ===') + + # Compare the predicted and expected results, calculate the accuracy + # for each parameter k, and find out the best k for prediction. + k_threshold: int = train_size if train_size < 20 else 20 + accuracy_table: List[float] = [0.0] + max_accuracy: float = 0.0 + + for k in range(1, k_threshold): + predicted_labels: List[int] = [] + for p in self.dev_data: + k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( + k, p, Dataset.TRAIN_SET + ) + predicted_label: int = self._get_most_common_label( + k_nearest_neighbors, Dataset.TRAIN_SET + ) + predicted_labels.append(predicted_label) + prediction: np.ndarray = np.array(predicted_labels) + + accuracy: float = np.mean(np.equal(prediction, self.dev_label)) + accuracy_table.append(accuracy) + print(f'k = {k}, train_acc = {accuracy * 100} %') + if accuracy > max_accuracy: + max_accuracy, self.k = accuracy, k + + print(f'best k = {self.k}\n') + + def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the label of a point using our model. - :param `train_data`: training set - :param `train_label`: provided labels for data in training set - ''' + :param `test_data`: testing set + ''' + + self.test_data = test_data - # Shuffle the dataset with labels - assert train_data.shape[0] == train_label.shape[0], ( - 'fit: data size not match for ' - f'{train_data.shape[0]} and {train_label.shape[0]}' - ) - shuffled_i = np.random.permutation(train_data.shape[0]) - shuffled_data: np.ndarray = train_data[shuffled_i] - shuffled_label: np.ndarray = train_label[shuffled_i] - - # Separate training set and development set (for validation) - train_ratio: float = 0.75 - train_size: int = floor(shuffled_data.shape[0] * train_ratio) - self.train_data = shuffled_data[:train_size] - self.train_label = shuffled_label[:train_size] - self.dev_data = shuffled_data[train_size:] - self.dev_label = shuffled_label[train_size:] - - print('=== Training ===') - - # Compare the predicted and expected results, calculate the accuracy - # for each parameter k, and find out the best k for prediction. - k_threshold: int = train_size if train_size < 20 else 20 - accuracy_table: List[float] = [0.0] - max_accuracy: float = 0.0 - - for k in range(1, k_threshold): predicted_labels: List[int] = [] - for p in self.dev_data: + for p in self.test_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - k, p, Dataset.TRAIN_SET + self.k, p, Dataset.TRAIN_SET ) predicted_label: int = self._get_most_common_label( k_nearest_neighbors, Dataset.TRAIN_SET ) predicted_labels.append(predicted_label) prediction: np.ndarray = np.array(predicted_labels) - - accuracy: float = np.mean(np.equal(prediction, self.dev_label)) - accuracy_table.append(accuracy) - print(f'k = {k}, train_acc = {accuracy * 100} %') - if accuracy > max_accuracy: - max_accuracy, self.k = accuracy, k - - print(f'best k = {self.k}\n') -``` - -对测试集进行预测时,我们就使用之前得到的最优的参数 `k` 进行预测,同样使用 KNN 算法。 - -```python {.line-numbers} -def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the label of a point using our model. - - :param `test_data`: testing set - ''' - - self.test_data = test_data - - print('=== Predicting ===') - - predicted_labels: List[int] = [] - for p in self.test_data: - k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - self.k, p, Dataset.TRAIN_SET - ) - predicted_label: int = self._get_most_common_label( - k_nearest_neighbors, Dataset.TRAIN_SET - ) - predicted_labels.append(predicted_label) - prediction: np.ndarray = np.array(predicted_labels) - return prediction + return prediction ``` -## 生成数据 +## 实验探究部分 -我们使用不同的参数生成数据集,并保存到文件 `data.npy`。这里由于时间有限,为了方便起见,我们直接在函数 `generate` 的 `parameters` 变量中对相应参数进行修改。 +生成数据集,并保存到文件: ```python {.line-numbers} def generate() -> None: @@ -190,7 +180,7 @@ def generate() -> None: def _generate_with_parameters(param: Parameter) -> np.ndarray: ''' - Generate a dataset using given parameters. + Generate a dataset using given parameters :param `param`: a tuple of `mean`, `cov`, `size` `mean`: the mean of the dataset @@ -248,34 +238,27 @@ def generate() -> None: )) ``` -为了直观起见,我们提供了函数 `display` 用于将当前使用的数据集可视化,并将图片保存到 `./img` 目录下。 +作图: ```python {.line-numbers} -def display(data: np.ndarray, label: np.ndarray, name: str) -> None: +def display(data, label, name): ''' - Visualize dataset with labels using `matplotlib.pyplot`. - - :param `data`: dataset - :param `label`: labels for data in the dataset - :param `name`: file name when saving to file + Visualize data and labels using `matplotlib.pyplot`. ''' - datasets_with_label: List[List[np.ndarray]] = [[], [], []] - for i in range(data.shape[0]): - datasets_with_label[label[i]].append(data[i]) - - for dataset_with_label in datasets_with_label: - dataset_with_label_: np.ndarray = np.array(dataset_with_label) - plt.scatter(dataset_with_label_[:, 0], dataset_with_label_[:, 1]) + datas = [[], [], []] + for i in range(len(data)): + datas[label[i]].append(data[i]) + for each in datas: + each = np.array(each) + plt.scatter(each[:, 0], each[:, 1]) plt.savefig(f'img/{name}') plt.show() ``` ## 运行代码 -在当前目录下,我们可以使用以下参数执行代码 `source.py`,具体功能参见注释。 - ```bash # 训练模型及预测 python ./source.py g @@ -284,40 +267,9 @@ python ./source.py g python ./source.py d ``` -### 输出样例 - -```text -=== Training === -k = 1, train_acc = 67.5 % -k = 2, train_acc = 67.75 % -k = 3, train_acc = 70.5 % -k = 4, train_acc = 72.5 % -k = 5, train_acc = 72.75 % -k = 6, train_acc = 73.25 % -k = 7, train_acc = 74.25 % -k = 8, train_acc = 74.0 % -k = 9, train_acc = 75.75 % -k = 10, train_acc = 75.5 % -k = 11, train_acc = 75.75 % -k = 12, train_acc = 75.5 % -k = 13, train_acc = 75.75 % -k = 14, train_acc = 75.5 % -k = 15, train_acc = 75.5 % -k = 16, train_acc = 74.5 % -k = 17, train_acc = 75.0 % -k = 18, train_acc = 75.0 % -k = 19, train_acc = 75.25 % -best k = 9 - -=== Predicting === -k = 9, predict_acc = 71.5 % -``` - -## 实验探究 +## 数据集 -### 1. 实验 1 - -#### 1.1 参数 +数据生成使用的参数: ```python {.line-numbers} mean = (1, 2) @@ -337,27 +289,21 @@ cov = [[10, 5], [5, 10]] size = 1000 ``` -其中: - -- `mean` 表示数据集的均值 -- `cov` 表示数据集的协方差 -- `size` 表示数据集的大小 +其中,`mean` 表示数据集的均值、`cov` 表示数据集的协方差、`size` 表示数据集的大小。 -下同。 +### 训练集 -#### 1.2 数据集 +![训练集](./img/train.png) -训练集: +在训练时,我们随机选取 80% 作为训练集、20% 作为验证集。 -![训练集](./img/train_1.png) +### 测试集 -测试集: +![测试集](./img/test.png) -![测试集](./img/test_1.png) +## 参数 -#### 1.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示: +训练时使用的参数 `k` 及相应的准确率: ```text k = 1, train_acc = 95.75 % @@ -381,146 +327,6 @@ k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % ``` -预测时使用的参数 `k` 及相应的准确率如下所示: - -```text -k = 3, predict_acc = 96.0 % -``` - -可见,对于此数据集,最优的参数 `k` 为 `3`,其对测试集的预测准确率为 96.0 %。 - -### 2. 实验 2 - -这次,我们调大数据集之间的距离,观察预测准确率的变化。 - -#### 2.1 参数 - -```python {.line-numbers} -mean = (-5, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (30, -10) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (20, 40) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -#### 2.2 数据集 - -训练集: - -![训练集](./img/train_2.png) - -测试集: - -![测试集](./img/test_2.png) - -#### 2.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示: - -```text -k = 1, train_acc = 100.0 % -k = 2, train_acc = 100.0 % -k = 3, train_acc = 100.0 % -k = 4, train_acc = 100.0 % -k = 5, train_acc = 100.0 % -k = 6, train_acc = 100.0 % -k = 7, train_acc = 100.0 % -k = 8, train_acc = 100.0 % -k = 9, train_acc = 100.0 % -k = 10, train_acc = 100.0 % -k = 11, train_acc = 100.0 % -k = 12, train_acc = 100.0 % -k = 13, train_acc = 100.0 % -k = 14, train_acc = 100.0 % -k = 15, train_acc = 100.0 % -k = 16, train_acc = 100.0 % -k = 17, train_acc = 100.0 % -k = 18, train_acc = 100.0 % -k = 19, train_acc = 100.0 % -``` - -预测时使用的参数 `k` 及相应的准确率如下所示: - -```text -k = 1, predict_acc = 100.0 % -``` - -可见,对于不同标签区分度较大(即彼此间距离较远)的数据集,所有 `k` 的预测准确率均为 100.0 %。这说明 KNN 算法对于较分散的数据有着很高的准确率。 - -### 3. 实验 3 - -我们再试试减小数据集间的距离,观察预测准确率的变化。 - -#### 3.1 参数 - -```python {.line-numbers} -mean = (1, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (3, -2) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (-5, 4) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -#### 3.2 数据集 - -训练集: - -![训练集](./img/train_3.png) - -测试集: - -![测试集](./img/test_3.png) - -#### 3.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示: - -```text -k = 1, train_acc = 65.0 % -k = 2, train_acc = 65.75 % -k = 3, train_acc = 69.25 % -k = 4, train_acc = 68.25 % -k = 5, train_acc = 72.5 % -k = 6, train_acc = 71.5 % -k = 7, train_acc = 73.75 % -k = 8, train_acc = 75.0 % -k = 9, train_acc = 76.0 % -k = 10, train_acc = 75.75 % -k = 11, train_acc = 76.0 % -k = 12, train_acc = 74.5 % -k = 13, train_acc = 75.25 % -k = 14, train_acc = 75.0 % -k = 15, train_acc = 74.75 % -k = 16, train_acc = 75.5 % -k = 17, train_acc = 75.0 % -k = 18, train_acc = 75.0 % -k = 19, train_acc = 74.5 % -``` - -预测时使用的参数 `k` 及相应的准确率如下所示: - -```text -k = 9, predict_acc = 76.0 % -``` +可见,对于此数据集,最优的参数 `k` 为 `3`。 -此时,最优的参数 `k` 为 `9`,其对测试集的预测准确率为 76.0 %。可见,当数据集间的区分度较低时,较高的 `k` 值有着相对较高的准确率。这是可以理解的,因为提高可参考的邻居数量可以尽可能地减少噪声的影响。 +相应的准确率为 96%。 diff --git a/assignment-1/submission/18307130003/img/test.png b/assignment-1/submission/18307130003/img/test.png new file mode 100644 index 0000000000000000000000000000000000000000..77b898ff8a239b7338b029c2b7e1f76c0fd149f2 GIT binary patch literal 25961 zcmeFZWmJ_>+cmlY0i{EvLy+$7P`bNg)3xdDlrBL+T9EEeX$eW`?(S}c@7_M&dEYbM zGrsfl{5lLp2YcP?UU9{o^ID4tB?U=TBmyK52!tvvC8h!b!3KapFl(<7fS+)VFKq$; 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z&^cWk7zkmOhqp~04@9}7q5zfaqfoZtRY!P0fF|k|d3lNO`Q*pAc(knCeo?yBWMg72F59?m=aJ~ zw5rzm-3zdXtYUdJ-u<=sqDCBhT|&<-4_rempY`-f(9yC zBE1zwNfdT#H=N{|1_cIE%FXk@x^?XA?ARc&;r*?oW&%^ifg+R1a4|74*NR*g#E&I@ zpcet5btkTH@nK$G*{Ahkv%RkH*X7lKcUpaEJ;|B3h~v$u@_x)w**%v#W6v89|@_NPyjSFGc(JBN?uCIs4*E1UMBs*Kh21qwU$i)euylEGwt=2Z_uroM!5Evu zgDw+)tu*nbEc5hZ#_EU%?mDW2Bp?5CeDOQs$N&G~>&r?ai;DHQ_bT-$`1yGIp({O) GWc>rO%;R$a literal 0 HcmV?d00001 -- Gitee From 7f50ad02fcaf88362bbd89a0e2276114b1823bc5 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:04:01 +0800 Subject: [PATCH 06/73] doc: improve report --- assignment-1/submission/18307130003/README.md | 437 ++++++++++++------ .../submission/18307130003/img/test.png | Bin 25961 -> 0 bytes .../submission/18307130003/img/train.png | Bin 38778 -> 0 bytes .../submission/18307130003/tester_demo.py | 24 - 4 files changed, 292 insertions(+), 169 deletions(-) delete mode 100644 assignment-1/submission/18307130003/img/test.png delete mode 100644 assignment-1/submission/18307130003/img/train.png delete mode 100644 assignment-1/submission/18307130003/tester_demo.py diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 9e5140a..21cd813 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -1,169 +1,177 @@ # 实验报告 +## 目录 + +[TOC] + ## KNN 模型实现 +KNN 算法的主要思路是,根据当前点 `base_p` 最近的 `k` 个邻居 `p` 的标签,选择其中出现频率最高的标签,作为 `base_p` 标签的预测结果。 + +具体来说,我们使用函数 `_distance` 获取两点间的距离。 + ```python {.line-numbers} -class KNN: +def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: ''' - k-Nearest Neighbors algorithm, which predicts the class of a data point - according to the most common class among its `k` nearest neighbors. - ''' - - def __init__(self) -> None: - ''' - Initialize our KNN model. - ''' + Get the distance between two points. - self.k: int = 1 - self.train_data: np.ndarray = None - self.train_label: np.ndarray = None - self.dev_data: np.ndarray = None - self.dev_label: np.ndarray = None - self.test_data: np.ndarray = None + :param `p1`: the first point + :param `p2`: the second point + :param `mode`: which exponent to use when calculating distance, \ + using `2` by default for Euclidean distance + ''' - def _get_k_nearest_neighbors( - self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET - ) -> List[int]: - ''' - Get k nearest neighbors of a point from dataset. Each point (except the - base point) is denoted by its index in the dataset. + assert p1.shape == p2.shape, ( + '_distance: dimensions not match for ' + f'{p1.shape} and {p2.shape}' + ) + return np.linalg.norm(p1 - p2, ord=mode) +``` - :param `base_p`: the base point - :param `dataset`: which dataset to use - ''' +这里我们使用了 `numpy` 库提供的 `np.linalg.norm` 方法来获取两点间的距离。特别地,当参数 `ord` 为 `2` 时,即采用 Euclidean 距离。我们这里使用 `2` 作为默认参数。 - def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: - ''' - Get the distance between two points. +接下来,我们维护一个大小为 `k` 的最小堆,来得到最近的 `k` 个邻居。思想就是 top k 问题的经典算法。 - :param `p1`: the first point - :param `p2`: the second point - :param `mode`: which exponent to use when calculating distance, \ - using `2` by default for Euclidean distance - ''' +```python {.line-numbers} +def _get_k_nearest_neighbors( + self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET +) -> List[int]: + ''' + Get k nearest neighbors of a point from dataset. Each point (except the + base point) is denoted by its index in the dataset. - assert p1.shape == p2.shape, ( - '_distance: dimensions not match for ' - f'{p1.shape} and {p2.shape}' - ) - return np.linalg.norm(p1 - p2, ord=mode) + :param `base_p`: the base point + :param `dataset`: which dataset to use + ''' - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data + if dataset == Dataset.TRAIN_SET: + data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data + else: + data = self.test_data + + # Use a min heap of size k to get the k nearest neighbors + heap: List[Tuple[float, np.ndarray]] = [] + for p_i in range(data.shape[0]): + dist: float = _distance(base_p, data[p_i]) + if (len(heap) < k): + heappush(heap, (-dist, p_i)) else: - data = self.test_data - - # Use a min heap of size k to get the k nearest neighbors - heap: List[Tuple[float, np.ndarray]] = [] - for p_i in range(data.shape[0]): - dist: float = _distance(base_p, data[p_i]) - if (len(heap) < k): - heappush(heap, (-dist, p_i)) - else: - heappushpop(heap, (-dist, p_i)) - - # Return the indices of the k points in the dataset - return [item[1] for item in heap] - - def _get_most_common_label( - self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET - ) -> int: - ''' - Get the most common label in given labels. Each label is denoted by - its data point's index in the dataset. + heappushpop(heap, (-dist, p_i)) - :param `labels_i`: the indices of given labels - :param `dataset`: which dataset to use - ''' + # Return the indices of the k points in the dataset + return [item[1] for item in heap] +``` - if dataset == Dataset.TRAIN_SET: - all_labels = self.train_label - else: - all_labels = self.dev_label +最后我们对这 k 个邻居的标签分别进行计数,选择其中出现次数最多的标签作为预测结果。 - labels: List[int] = [all_labels[i] for i in labels_i] - return max(set(labels), key=labels.count) +```python {.line-numbers} +def _get_most_common_label( + self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET +) -> int: + ''' + Get the most common label in given labels. Each label is denoted by + its data point's index in the dataset. - def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: - ''' - Train the model using a training set with labels. + :param `labels_i`: the indices of given labels + :param `dataset`: which dataset to use + ''' - :param `train_data`: training set - :param `train_label`: provided labels for data in training set - ''' + if dataset == Dataset.TRAIN_SET: + all_labels = self.train_label + else: + all_labels = self.dev_label - # Shuffle the dataset with labels - assert train_data.shape[0] == train_label.shape[0], ( - 'fit: data size not match for ' - f'{train_data.shape[0]} and {train_label.shape[0]}' - ) - shuffled_i = np.random.permutation(train_data.shape[0]) - shuffled_data: np.ndarray = train_data[shuffled_i] - shuffled_label: np.ndarray = train_label[shuffled_i] - - # Separate training set and development set (for validation) - train_ratio: float = 0.75 - train_size: int = floor(shuffled_data.shape[0] * train_ratio) - self.train_data = shuffled_data[:train_size] - self.train_label = shuffled_label[:train_size] - self.dev_data = shuffled_data[train_size:] - self.dev_label = shuffled_label[train_size:] - - print('=== Training ===') - - # Compare the predicted and expected results, calculate the accuracy - # for each parameter k, and find out the best k for prediction. - k_threshold: int = train_size if train_size < 20 else 20 - accuracy_table: List[float] = [0.0] - max_accuracy: float = 0.0 - - for k in range(1, k_threshold): - predicted_labels: List[int] = [] - for p in self.dev_data: - k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - k, p, Dataset.TRAIN_SET - ) - predicted_label: int = self._get_most_common_label( - k_nearest_neighbors, Dataset.TRAIN_SET - ) - predicted_labels.append(predicted_label) - prediction: np.ndarray = np.array(predicted_labels) - - accuracy: float = np.mean(np.equal(prediction, self.dev_label)) - accuracy_table.append(accuracy) - print(f'k = {k}, train_acc = {accuracy * 100} %') - if accuracy > max_accuracy: - max_accuracy, self.k = accuracy, k - - print(f'best k = {self.k}\n') - - def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the label of a point using our model. + labels: List[int] = [all_labels[i] for i in labels_i] + return max(set(labels), key=labels.count) +``` - :param `test_data`: testing set - ''' +训练模型时,我们先将数据集打乱,然后将其中的 75% 作为训练集 `train_data`,剩下 25% 作为验证集 `dev_data`,然后使用 KNN 算法进行训练。我们选择不同的 `k` 值,通过比较验证集 `dev_data` 的预测结果和其实际标签 `dev_label`,得到每个 `k` 值所对应的预测准确率 `accuracy`。最终,我们选择准确率最高的 `k` 值作为我们将在测试集 `test_data` 上使用的参数 `k`。 - self.test_data = test_data +```python {.line-numbers} +def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: + ''' + Train the model using a training set with labels. + :param `train_data`: training set + :param `train_label`: provided labels for data in training set + ''' + + # Shuffle the dataset with labels + assert train_data.shape[0] == train_label.shape[0], ( + 'fit: data size not match for ' + f'{train_data.shape[0]} and {train_label.shape[0]}' + ) + shuffled_i = np.random.permutation(train_data.shape[0]) + shuffled_data: np.ndarray = train_data[shuffled_i] + shuffled_label: np.ndarray = train_label[shuffled_i] + + # Separate training set and development set (for validation) + train_ratio: float = 0.75 + train_size: int = floor(shuffled_data.shape[0] * train_ratio) + self.train_data = shuffled_data[:train_size] + self.train_label = shuffled_label[:train_size] + self.dev_data = shuffled_data[train_size:] + self.dev_label = shuffled_label[train_size:] + + print('=== Training ===') + + # Compare the predicted and expected results, calculate the accuracy + # for each parameter k, and find out the best k for prediction. + k_threshold: int = train_size if train_size < 20 else 20 + accuracy_table: List[float] = [0.0] + max_accuracy: float = 0.0 + + for k in range(1, k_threshold): predicted_labels: List[int] = [] - for p in self.test_data: + for p in self.dev_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - self.k, p, Dataset.TRAIN_SET + k, p, Dataset.TRAIN_SET ) predicted_label: int = self._get_most_common_label( k_nearest_neighbors, Dataset.TRAIN_SET ) predicted_labels.append(predicted_label) prediction: np.ndarray = np.array(predicted_labels) - return prediction + + accuracy: float = np.mean(np.equal(prediction, self.dev_label)) + accuracy_table.append(accuracy) + print(f'k = {k}, train_acc = {accuracy * 100} %') + if accuracy > max_accuracy: + max_accuracy, self.k = accuracy, k + + print(f'best k = {self.k}\n') ``` -## 实验探究部分 +对测试集进行预测时,我们就使用之前得到的最优的参数 `k` 进行预测,同样使用 KNN 算法。 -生成数据集,并保存到文件: +```python {.line-numbers} +def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the label of a point using our model. + + :param `test_data`: testing set + ''' + + self.test_data = test_data + + predicted_labels: List[int] = [] + for p in self.test_data: + k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( + self.k, p, Dataset.TRAIN_SET + ) + predicted_label: int = self._get_most_common_label( + k_nearest_neighbors, Dataset.TRAIN_SET + ) + predicted_labels.append(predicted_label) + prediction: np.ndarray = np.array(predicted_labels) + return prediction +``` + +## 生成数据 + +我们使用不同的参数生成数据集,并保存到文件 `data.npy`。这里由于时间有限,为了方便起见,我们直接在函数 `generate` 的 `parameters` 变量中对相应参数进行修改。 ```python {.line-numbers} def generate() -> None: @@ -238,7 +246,7 @@ def generate() -> None: )) ``` -作图: +为了直观起见,我们提供了函数 `display` 用于将当前使用的数据集可视化,并将图片保存到 `./img` 目录下。 ```python {.line-numbers} def display(data, label, name): @@ -259,6 +267,8 @@ def display(data, label, name): ## 运行代码 +在当前目录下,我们可以使用以下参数执行代码 `source.py`,具体功能参见注释。 + ```bash # 训练模型及预测 python ./source.py g @@ -267,9 +277,11 @@ python ./source.py g python ./source.py d ``` -## 数据集 +## 实验探究 + +### 1. 实验 1 -数据生成使用的参数: +#### 1.1 参数 ```python {.line-numbers} mean = (1, 2) @@ -289,21 +301,27 @@ cov = [[10, 5], [5, 10]] size = 1000 ``` -其中,`mean` 表示数据集的均值、`cov` 表示数据集的协方差、`size` 表示数据集的大小。 +其中: -### 训练集 +- `mean` 表示数据集的均值 +- `cov` 表示数据集的协方差 +- `size` 表示数据集的大小 -![训练集](./img/train.png) +下同。 -在训练时,我们随机选取 80% 作为训练集、20% 作为验证集。 +#### 1.2 数据集 -### 测试集 +训练集: -![测试集](./img/test.png) +![训练集](./img/train_1.png) -## 参数 +测试集: -训练时使用的参数 `k` 及相应的准确率: +![测试集](./img/test_1.png) + +#### 1.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示: ```text k = 1, train_acc = 95.75 % @@ -325,8 +343,137 @@ k = 16, train_acc = 96.75 % k = 17, train_acc = 96.75 % k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % +best k = 3 + +acc = 0.96 +``` + +可见,对于此数据集,最优的参数 `k` 为 `3`,其对测试集的预测准确率为 96%。 + +### 2. 实验 2 + +这次,我们调大数据之间的距离,观察预测准确率的变化。 + +#### 2.1 参数 + +```python {.line-numbers} +mean = (-5, 2) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (30, -10) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (20, 40) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +#### 2.2 数据集 + +训练集: + +![训练集](./img/train_2.png) + +测试集: + +![测试集](./img/test_2.png) + +#### 2.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示: + +```text +k = 1, train_acc = 100.0 % +k = 2, train_acc = 100.0 % +k = 3, train_acc = 100.0 % +k = 4, train_acc = 100.0 % +k = 5, train_acc = 100.0 % +k = 6, train_acc = 100.0 % +k = 7, train_acc = 100.0 % +k = 8, train_acc = 100.0 % +k = 9, train_acc = 100.0 % +k = 10, train_acc = 100.0 % +k = 11, train_acc = 100.0 % +k = 12, train_acc = 100.0 % +k = 13, train_acc = 100.0 % +k = 14, train_acc = 100.0 % +k = 15, train_acc = 100.0 % +k = 16, train_acc = 100.0 % +k = 17, train_acc = 100.0 % +k = 18, train_acc = 100.0 % +k = 19, train_acc = 100.0 % +best k = 1 + +acc = 1.0 +``` + +可见,对于不同标签区分度较大(即彼此间距离较远)的数据集,所有 `k` 的预测准确率均为 100%。这说明 KNN 算法对于较分散的数据有着很高的准确率。 + +### 3. 实验 3 + +#### 3.1 参数 + +```python {.line-numbers} +mean = (1, 2) +cov = [[73, 0], [0, 22]] +size = 800 ``` -可见,对于此数据集,最优的参数 `k` 为 `3`。 +```python {.line-numbers} +mean = (3, -2) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (-5, 4) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +#### 3.2 数据集 + +训练集: + +![训练集](./img/train_3.png) + +测试集: + +![测试集](./img/test_3.png) + +#### 3.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示: + +```text +k = 1, train_acc = 65.0 % +k = 2, train_acc = 65.75 % +k = 3, train_acc = 69.25 % +k = 4, train_acc = 68.25 % +k = 5, train_acc = 72.5 % +k = 6, train_acc = 71.5 % +k = 7, train_acc = 73.75 % +k = 8, train_acc = 75.0 % +k = 9, train_acc = 76.0 % +k = 10, train_acc = 75.75 % +k = 11, train_acc = 76.0 % +k = 12, train_acc = 74.5 % +k = 13, train_acc = 75.25 % +k = 14, train_acc = 75.0 % +k = 15, train_acc = 74.75 % +k = 16, train_acc = 75.5 % +k = 17, train_acc = 75.0 % +k = 18, train_acc = 75.0 % +k = 19, train_acc = 74.5 % +best k = 9 + +acc = 0.76 +``` -相应的准确率为 96%。 +此时,最优的参数 `k` 为 `9`,其对测试集的预测准确率为 76%。可见,当数据集间的区分度较低时,较高的 `k` 值有着相对较高的准确率。这是可以理解的,因为这样可以尽可能地减少噪声的影响。 diff --git a/assignment-1/submission/18307130003/img/test.png 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a/assignment-1/submission/18307130003/tester_demo.py +++ /dev/null @@ -1,24 +0,0 @@ -import numpy as np - -from source import KNN - -train_data = np.array([ - [1, 2, 3, 4], - [4, 2, 3, 1], - [12, 12, 13, 14], - [14, 12, 13, 11], - [12, 14, 15, 16], -]) -train_label = np.array([0, 0, 1, 1, 1]) - -test_data = np.array([ - [3, 4, 4, 2], - [18, 14, 15, 16], -]) -test_label = np.array([0, 1]) - -model = KNN() -model.fit(train_data, train_label) -res = model.predict(test_data) - -print("acc =", np.mean(np.equal(res, test_label))) -- Gitee From f063fce6362d085d450d51cc45db4da4d59c6bb8 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:09:56 +0800 Subject: [PATCH 07/73] doc: minor fix --- assignment-1/submission/18307130003/README.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 21cd813..511563b 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -64,7 +64,7 @@ def _get_k_nearest_neighbors( return [item[1] for item in heap] ``` -最后我们对这 k 个邻居的标签分别进行计数,选择其中出现次数最多的标签作为预测结果。 +最后我们对这 `k` 个邻居的标签分别进行计数,选择其中出现次数最多的标签作为预测结果。 ```python {.line-numbers} def _get_most_common_label( @@ -352,7 +352,7 @@ acc = 0.96 ### 2. 实验 2 -这次,我们调大数据之间的距离,观察预测准确率的变化。 +这次,我们调大数据集之间的距离,观察预测准确率的变化。 #### 2.1 参数 @@ -417,6 +417,8 @@ acc = 1.0 ### 3. 实验 3 +我们再试试减小数据集间的距离,观察预测准确率的变化。 + #### 3.1 参数 ```python {.line-numbers} -- Gitee From d7cb18c4e4e3172e63857e313b74f78c6efce653 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:50:03 +0800 Subject: [PATCH 08/73] style: type annotations --- assignment-1/submission/18307130003/README.md | 81 ++++++++++++++----- 1 file changed, 63 insertions(+), 18 deletions(-) diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 511563b..2bd04be 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -156,6 +156,8 @@ def predict(self, test_data: np.ndarray) -> np.ndarray: self.test_data = test_data + print('=== Predicting ===') + predicted_labels: List[int] = [] for p in self.test_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( @@ -188,7 +190,7 @@ def generate() -> None: def _generate_with_parameters(param: Parameter) -> np.ndarray: ''' - Generate a dataset using given parameters + Generate a dataset using given parameters. :param `param`: a tuple of `mean`, `cov`, `size` `mean`: the mean of the dataset @@ -249,18 +251,23 @@ def generate() -> None: 为了直观起见,我们提供了函数 `display` 用于将当前使用的数据集可视化,并将图片保存到 `./img` 目录下。 ```python {.line-numbers} -def display(data, label, name): +def display(data: np.ndarray, label: np.ndarray, name: str) -> None: ''' - Visualize data and labels using `matplotlib.pyplot`. + Visualize dataset with labels using `matplotlib.pyplot`. + + :param `data`: dataset + :param `label`: labels for data in the dataset + :param `name`: file name when saving to file ''' - datas = [[], [], []] - for i in range(len(data)): - datas[label[i]].append(data[i]) + datasets_with_label: List[List[np.ndarray]] = [[], [], []] + for i in range(data.shape[0]): + datasets_with_label[label[i]].append(data[i]) + + for dataset_with_label in datasets_with_label: + dataset_with_label_: np.ndarray = np.array(dataset_with_label) + plt.scatter(dataset_with_label_[:, 0], dataset_with_label_[:, 1]) - for each in datas: - each = np.array(each) - plt.scatter(each[:, 0], each[:, 1]) plt.savefig(f'img/{name}') plt.show() ``` @@ -277,6 +284,35 @@ python ./source.py g python ./source.py d ``` +### 输出样例 + +```text +=== Training === +k = 1, train_acc = 67.5 % +k = 2, train_acc = 67.75 % +k = 3, train_acc = 70.5 % +k = 4, train_acc = 72.5 % +k = 5, train_acc = 72.75 % +k = 6, train_acc = 73.25 % +k = 7, train_acc = 74.25 % +k = 8, train_acc = 74.0 % +k = 9, train_acc = 75.75 % +k = 10, train_acc = 75.5 % +k = 11, train_acc = 75.75 % +k = 12, train_acc = 75.5 % +k = 13, train_acc = 75.75 % +k = 14, train_acc = 75.5 % +k = 15, train_acc = 75.5 % +k = 16, train_acc = 74.5 % +k = 17, train_acc = 75.0 % +k = 18, train_acc = 75.0 % +k = 19, train_acc = 75.25 % +best k = 9 + +=== Predicting === +k = 9, predict_acc = 71.5 % +``` + ## 实验探究 ### 1. 实验 1 @@ -343,12 +379,15 @@ k = 16, train_acc = 96.75 % k = 17, train_acc = 96.75 % k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % -best k = 3 +``` + +预测时使用的参数 `k` 及相应的准确率如下所示: -acc = 0.96 +```text +k = 3, predict_acc = 96.0 % ``` -可见,对于此数据集,最优的参数 `k` 为 `3`,其对测试集的预测准确率为 96%。 +可见,对于此数据集,最优的参数 `k` 为 `3`,其对测试集的预测准确率为 96.0 %。 ### 2. 实验 2 @@ -408,12 +447,15 @@ k = 16, train_acc = 100.0 % k = 17, train_acc = 100.0 % k = 18, train_acc = 100.0 % k = 19, train_acc = 100.0 % -best k = 1 +``` + +预测时使用的参数 `k` 及相应的准确率如下所示: -acc = 1.0 +```text +k = 1, predict_acc = 100.0 % ``` -可见,对于不同标签区分度较大(即彼此间距离较远)的数据集,所有 `k` 的预测准确率均为 100%。这说明 KNN 算法对于较分散的数据有着很高的准确率。 +可见,对于不同标签区分度较大(即彼此间距离较远)的数据集,所有 `k` 的预测准确率均为 100.0 %。这说明 KNN 算法对于较分散的数据有着很高的准确率。 ### 3. 实验 3 @@ -473,9 +515,12 @@ k = 16, train_acc = 75.5 % k = 17, train_acc = 75.0 % k = 18, train_acc = 75.0 % k = 19, train_acc = 74.5 % -best k = 9 +``` -acc = 0.76 +预测时使用的参数 `k` 及相应的准确率如下所示: + +```text +k = 9, predict_acc = 76.0 % ``` -此时,最优的参数 `k` 为 `9`,其对测试集的预测准确率为 76%。可见,当数据集间的区分度较低时,较高的 `k` 值有着相对较高的准确率。这是可以理解的,因为这样可以尽可能地减少噪声的影响。 +此时,最优的参数 `k` 为 `9`,其对测试集的预测准确率为 76.0 %。可见,当数据集间的区分度较低时,较高的 `k` 值有着相对较高的准确率。这是可以理解的,因为提高可参考的邻居数量可以尽可能地减少噪声的影响。 -- Gitee From a6f469f3cc063693e3d556354f29f8eac69275e1 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 20 Apr 2021 18:08:34 +0800 Subject: [PATCH 09/73] chore: initialize --- .../submission/18307130003/numpy_fnn.py | 292 +++++++----------- .../submission/18307130003/numpy_mnist.py | 81 ++--- .../submission/18307130003/tester_demo.py | 109 +++---- .../submission/18307130003/torch_mnist.py | 46 ++- assignment-2/submission/18307130003/utils.py | 18 +- 5 files changed, 209 insertions(+), 337 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 4331007..150ab17 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -1,213 +1,153 @@ -from typing import Tuple import numpy as np class NumpyOp: - ''' - The base class for Numpy operations. - ''' - + def __init__(self): self.memory = {} self.epsilon = 1e-12 class Matmul(NumpyOp): - ''' - Matrix multiplication unit. - ''' - - def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: - ''' - Args: - x: shape(N, d) - w: shape(d, d') - - Returns: - shape(N, d') - ''' - + + def forward(self, x, W): + """ + x: shape(N, d) + w: shape(d, d') + """ self.memory['x'] = x - self.memory['w'] = w - return np.matmul(x, w) - - def backward(self, grad_y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: - ''' - Args: - grad_y: shape(N, d') - - Returns: - grad_x: shape(N, d) - grad_w: shape(d, d') - ''' - - x: np.ndarray = self.memory['x'] - w: np.ndarray = self.memory['w'] - grad_x: np.ndarray = np.matmul(grad_y, w.T) - grad_w: np.ndarray = np.matmul(x.T, grad_y) - return grad_x, grad_w + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + #################### + + return grad_x, grad_W class Relu(NumpyOp): - ''' - Rectified Linear Unit. - ''' - - def forward(self, x: np.ndarray) -> np.ndarray: - ''' - Args: - x: shape(N, d) - - Returns: - shape(N, d) - ''' - + + def forward(self, x): self.memory['x'] = x - return np.where(x > 0, x, 0) - - def backward(self, grad_y: np.ndarray) -> np.ndarray: - ''' - Args: - grad_y: shape(N, d) - - Returns: - shape(N, d) - ''' - - x: np.ndarray = self.memory['x'] - return np.where(x > 0, grad_y, 0) + return np.where(x > 0, x, np.zeros_like(x)) + + def backward(self, grad_y): + """ + grad_y: same shape as x + """ + + #################### + # code 2 # + #################### + + return grad_x class Log(NumpyOp): - ''' - Natural logarithm unit. - ''' - - def forward(self, x: np.ndarray) -> np.ndarray: - ''' - Args: - x: shape(N, d) - - Returns: - shape(N, d) - ''' - + + def forward(self, x): + """ + x: shape(N, c) + """ + + out = np.log(x + self.epsilon) self.memory['x'] = x - return np.log(x + self.epsilon) - - def backward(self, grad_y: np.ndarray) -> np.ndarray: - ''' - Args: - grad_y: shape(N, d) - - Returns: - shape(N, d) - ''' - - x: np.ndarray = self.memory['x'] - return grad_y / x + + return out + + def backward(self, grad_y): + """ + grad_y: same shape as x + """ + + #################### + # code 3 # + #################### + + return grad_x class Softmax(NumpyOp): - ''' - Softmax over last dimension. - ''' - - def forward(self, x: np.ndarray) -> np.ndarray: - ''' - Args: - x: shape(N, d) - - Returns: - shape(N, d) - ''' - - y: np.ndarray = np.exp(x) / np.exp(x).sum(axis=1)[:, None] - self.memory['y'] = y - return y - - def backward(self, grad_y: np.ndarray) -> np.ndarray: - ''' - Args: - grad_y: shape(N, d) - - Returns: - shape(N, d) - ''' - - y: np.ndarray = self.memory['y'] - return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) - - -class NumpyLoss: - ''' - Loss function. - ''' - - def __init__(self): - self.target: np.ndarray = None - - def get_loss(self, pred: np.ndarray, target: np.ndarray) -> float: - self.target = target - return (-pred * target).sum(axis=1).mean() - - def backward(self) -> np.ndarray: - return -self.target / self.target.shape[0] + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + #################### + + return out + + def backward(self, grad_y): + """ + grad_y: same shape as x + """ + + #################### + # code 5 # + #################### + + return grad_x class NumpyModel: - ''' - An FNN model implemented in NumPy. - ''' - def __init__(self): - self.W1: np.ndarray = np.random.normal(size=(28 * 28, 256)) - self.W2: np.ndarray = np.random.normal(size=(256, 64)) - self.W3: np.ndarray = np.random.normal(size=(64, 10)) + self.W1 = np.random.normal(size=(28 * 28, 256)) + self.W2 = np.random.normal(size=(256, 64)) + self.W3 = np.random.normal(size=(64, 10)) + + # 以下算子会在 forward 和 backward 中使用 self.matmul_1 = Matmul() self.relu_1 = Relu() - self.matmul_2 = Matmul() self.relu_2 = Relu() - self.matmul_3 = Matmul() - self.softmax_3 = Softmax() - self.log_3 = Log() - - def forward(self, x: np.ndarray) -> np.ndarray: - ''' - Args: - x: shape(N, d) - - Returns: - shape(N, d) - ''' - + self.softmax = Softmax() + self.log = Log() + + # 以下变量需要在 backward 中更新 + self.x1_grad, self.W1_grad = None, None + self.relu_1_grad = None + self.x2_grad, self.W2_grad = None, None + self.relu_2_grad = None + self.x3_grad, self.W3_grad = None, None + self.softmax_grad = None + self.log_grad = None + + + def forward(self, x): x = x.reshape(-1, 28 * 28) - x = self.relu_1.forward(self.matmul_1.forward(x, self.W1)) - x = self.relu_2.forward(self.matmul_2.forward(x, self.W2)) - x = self.softmax_3.forward(self.matmul_3.forward(x, self.W3)) - x = self.log_3.forward(x) + + #################### + # code 6 # + #################### + return x - - def backward(self, y: np.ndarray) -> None: - ''' - Args: - y: shape(N, d) - ''' - - self.log_grad = self.log_3.backward(y) - self.softmax_grad = self.softmax_3.backward(self.log_grad) - self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) - - self.relu_2_grad = self.relu_2.backward(self.x3_grad) - self.x2_grad, self.W2_grad = self.matmul_2.backward(self.relu_2_grad) - - self.relu_1_grad = self.relu_1.backward(self.x2_grad) - self.x1_grad, self.W1_grad = self.matmul_1.backward(self.relu_1_grad) - - def optimize(self, learning_rate: float): + + def backward(self, y): + for size in y.shape: + y /= size + + #################### + # code 7 # + #################### + + pass + + def optimize(self, learning_rate): self.W1 -= learning_rate * self.W1_grad self.W2 -= learning_rate * self.W2_grad self.W3 -= learning_rate * self.W3_grad diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index f992979..903d7a7 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,77 +1,34 @@ -from typing import Any, List, Tuple import numpy as np -from numpy_fnn import NumpyModel, NumpyLoss -from utils import ( - download_mnist, - batch, - # mini_batch, - get_torch_initialization, - plot_curve, - one_hot, -) - - -def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: - ''' - Split the data and labels from the given dataset into batches. - - Args: - dataset: the given dataset - batch_size: the size of retrieved data - - Returns: - Batches of [data, labels] pair. - ''' - - data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) - labels: np.ndarray = np.array([pair[1] for pair in dataset]) - - # Shuffle the dataset - size: int = len(dataset) - indices: np.ndarray = np.arange(size) - np.random.shuffle(indices) - - batches: List[Tuple[np.ndarray, np.ndarray]] = [] - for i in range(0, size, batch_size): - chunk: np.ndarray = indices[i:i+batch_size] - batches.append((data[chunk], labels[chunk])) - return batches +from numpy_fnn import NumpyModel +from utils import download_mnist, batch, mini_batch, get_torch_initialization, plot_curve, one_hot def numpy_run(): - ''' - Train the FNN network on MNIST. - ''' - train_dataset, test_dataset = download_mnist() - + model = NumpyModel() - numpy_loss = NumpyLoss() model.W1, model.W2, model.W3 = get_torch_initialization() - - train_loss: List[float] = [] - - epoch_number = 10 - batch_size = 256 - learning_rate = 0.5 - + + train_loss = [] + + epoch_number = 3 + learning_rate = 0.1 + for epoch in range(epoch_number): - for x, y in mini_batch(train_dataset, batch_size=batch_size): - x: np.ndarray - y: np.ndarray = one_hot(y) - - y_pred = model.forward(x) - loss = numpy_loss.get_loss(y_pred, y) - - model.backward(numpy_loss.backward()) + for x, y in mini_batch(train_dataset): + y = one_hot(y) + + y_pred = model.forward(x.numpy()) + loss = (-y_pred * y).sum(axis=1).mean() + model.backward(y) model.optimize(learning_rate) - + train_loss.append(loss.item()) - + x, y = batch(test_dataset)[0] - accuracy: float = np.mean((model.forward(x).argmax(axis=1) == y)) + accuracy = np.mean((model.forward(x).argmax(axis=1) == y)) print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) - + plot_curve(train_loss) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 68874de..563de6b 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -1,17 +1,12 @@ import numpy as np import torch -from torch import ( - matmul as torch_matmul, - relu as torch_relu, - softmax as torch_softmax, - log as torch_log, -) - -from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel, NumpyLoss +from torch import matmul as torch_matmul, relu as torch_relu, softmax as torch_softmax, log as torch_log + +from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel from torch_mnist import TorchModel from utils import get_torch_initialization, one_hot -err_epsilon = 1e-6 +err_epsilon = 1e-3 err_p = 0.4 @@ -23,46 +18,42 @@ def check_result(numpy_result, torch_result=None): return flag T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() direction = T / torch_result.numel() < err_p - result = direction and ( - (torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon - ).item() - print(result) - return result + return direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() def case_1(): x = np.random.normal(size=[5, 6]) W = np.random.normal(size=[6, 4]) - + numpy_matmul = Matmul() numpy_out = numpy_matmul.forward(x, W) numpy_x_grad, numpy_W_grad = numpy_matmul.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() torch_W = torch.from_numpy(W).clone().requires_grad_() - + torch_out = torch_matmul(torch_x, torch_W) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), - (numpy_W_grad, torch_W.grad), + (numpy_W_grad, torch_W.grad) ]) def case_2(): x = np.random.normal(size=[5, 6]) - + numpy_relu = Relu() numpy_out = numpy_relu.forward(x) numpy_x_grad = numpy_relu.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_relu(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -71,16 +62,16 @@ def case_2(): def case_3(): x = np.random.uniform(low=0.0, high=1.0, size=[3, 4]) - + numpy_log = Log() numpy_out = numpy_log.forward(x) numpy_x_grad = numpy_log.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_log(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -89,29 +80,29 @@ def case_3(): def case_4(): x = np.random.normal(size=[4, 5]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) - + return check_result(numpy_out, torch_out) def case_5(): x = np.random.normal(size=[20, 25]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) numpy_x_grad = numpy_softmax.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -120,54 +111,52 @@ def case_5(): def test_model(): try: - numpy_loss = NumpyLoss() numpy_model = NumpyModel() torch_model = TorchModel() - torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = ( - get_torch_initialization(numpy=False) - ) + torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = get_torch_initialization(numpy=False) numpy_model.W1 = torch_model.W1.detach().clone().numpy() numpy_model.W2 = torch_model.W2.detach().clone().numpy() numpy_model.W3 = torch_model.W3.detach().clone().numpy() - + x = torch.randn((10000, 28, 28)) y = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 0] * 1000) - + y = one_hot(y, numpy=False) x2 = x.numpy() y_pred = torch_model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() - + y_pred_numpy = numpy_model.forward(x2) - numpy_loss.get_loss(y_pred_numpy, y.numpy()) - + y2 = y.numpy() + loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() + check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) - except Exception as err: - print("[Runtime Error in forward, error: {}]".format(err)) + except: + print("[Runtime Error in forward]") print("+ {:12} {}/{}".format("forward", 0, 10)) return 0 - + try: - numpy_model.backward(numpy_loss.backward()) - + + numpy_model.backward(y2) + check_flag_2 = [ - check_result(numpy_model.log_grad, torch_model.log_input.grad), - check_result(numpy_model.softmax_grad, - torch_model.softmax_input.grad), + check_result(numpy_model.log_grad, torch_model.log.grad), + check_result(numpy_model.softmax_grad, torch_model.softmax.grad), check_result(numpy_model.W3_grad, torch_model.W3.grad), check_result(numpy_model.W2_grad, torch_model.W2.grad), check_result(numpy_model.W1_grad, torch_model.W1.grad) ] - check_flag_2 = sum(check_flag_2) / 5 - print("+ {:12} {}/{}".format("backward", int(20 * check_flag_2), 20)) - except Exception as err: - print("[Runtime Error in backward, error: {}]".format(err)) + check_flag_2 = sum(check_flag_2) >= 4 + print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) + except: + print("[Runtime Error in backward]") print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False - - return int(10 * check_flag_1 + 20 * check_flag_2) + + return 10 * check_flag_1 + 20 * check_flag_2 if __name__ == "__main__": @@ -182,8 +171,8 @@ if __name__ == "__main__": for case in testcases: try: res = case[2] if case[1]() else 0 - except Exception as err: - print("[Runtime Error in {}, error: {}]".format(case[0], err)) + except: + print("[Runtime Error in {}]".format(case[0])) res = 0 score += res print("+ {:12} {}/{}".format(case[0], res, case[2])) diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py index dec6c89..6a5649b 100644 --- a/assignment-2/submission/18307130003/torch_mnist.py +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -3,38 +3,29 @@ from utils import mini_batch, batch, download_mnist, get_torch_initialization, o class TorchModel: - + def __init__(self): self.W1 = torch.randn((28 * 28, 256), requires_grad=True) self.W2 = torch.randn((256, 64), requires_grad=True) self.W3 = torch.randn((64, 10), requires_grad=True) - self.softmax_input = None - self.log_input = None - + def forward(self, x): x = x.reshape(-1, 28 * 28) x = torch.relu(torch.matmul(x, self.W1)) x = torch.relu(torch.matmul(x, self.W2)) x = torch.matmul(x, self.W3) - - self.softmax_input = x - self.softmax_input.retain_grad() - - x = torch.softmax(x, 1) - - self.log_input = x - self.log_input.retain_grad() - - x = torch.log(x) - - return x - + self.softmax = torch.softmax(x, 1) + self.log = torch.log(self.softmax) + self.softmax.retain_grad() # for test only + self.log.retain_grad() # for test only + return self.log + def optimize(self, learning_rate): with torch.no_grad(): self.W1 -= learning_rate * self.W1.grad self.W2 -= learning_rate * self.W2.grad self.W3 -= learning_rate * self.W3.grad - + self.W1.grad = None self.W2.grad = None self.W3.grad = None @@ -42,31 +33,30 @@ class TorchModel: def torch_run(): train_dataset, test_dataset = download_mnist() - + model = TorchModel() - model.W1.data, model.W2.data, model.W3.data = get_torch_initialization( - numpy=False) - + model.W1.data, model.W2.data, model.W3.data = get_torch_initialization(numpy=False) + train_loss = [] - + epoch_number = 3 learning_rate = 0.1 - + for epoch in range(epoch_number): for x, y in mini_batch(train_dataset, numpy=False): y = one_hot(y, numpy=False) - + y_pred = model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() model.optimize(learning_rate) - + train_loss.append(loss.item()) - + x, y = batch(test_dataset, numpy=False)[0] accuracy = model.forward(x).argmax(dim=1).eq(y).float().mean().item() print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) - + plot_curve(train_loss) diff --git a/assignment-2/submission/18307130003/utils.py b/assignment-2/submission/18307130003/utils.py index f471049..709220c 100644 --- a/assignment-2/submission/18307130003/utils.py +++ b/assignment-2/submission/18307130003/utils.py @@ -13,19 +13,15 @@ def plot_curve(data): def download_mnist(): from torchvision import datasets, transforms - + transform = transforms.Compose([ transforms.ToTensor(), transforms.Normalize(mean=(0.1307,), std=(0.3081,)) ]) - - train_dataset = datasets.MNIST( - root="./data/", transform=transform, train=True, download=True - ) - test_dataset = datasets.MNIST( - root="./data/", transform=transform, train=False, download=True - ) - + + train_dataset = datasets.MNIST(root="./data/", transform=transform, train=True, download=True) + test_dataset = datasets.MNIST(root="./data/", transform=transform, train=False, download=True) + return train_dataset, test_dataset @@ -62,7 +58,7 @@ def get_torch_initialization(numpy=True): fc1 = torch.nn.Linear(28 * 28, 256) fc2 = torch.nn.Linear(256, 64) fc3 = torch.nn.Linear(64, 10) - + if numpy: W1 = fc1.weight.T.detach().clone().numpy() W2 = fc2.weight.T.detach().clone().numpy() @@ -71,5 +67,5 @@ def get_torch_initialization(numpy=True): W1 = fc1.weight.T.detach().clone().data W2 = fc2.weight.T.detach().clone().data W3 = fc3.weight.T.detach().clone().data - + return W1, W2, W3 -- Gitee From 2361c86b7db3ffa51ecbf9d1d4e188c713735b16 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 20 Apr 2021 18:15:48 +0800 Subject: [PATCH 10/73] style: fix coding style --- .../submission/18307130003/numpy_fnn.py | 58 +++++++++--------- .../submission/18307130003/numpy_mnist.py | 16 ++--- .../submission/18307130003/tester_demo.py | 60 ++++++++++--------- .../submission/18307130003/torch_mnist.py | 28 +++++---- assignment-2/submission/18307130003/utils.py | 18 +++--- 5 files changed, 93 insertions(+), 87 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 150ab17..f50cb4c 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -2,14 +2,14 @@ import numpy as np class NumpyOp: - + def __init__(self): self.memory = {} self.epsilon = 1e-12 class Matmul(NumpyOp): - + def forward(self, x, W): """ x: shape(N, d) @@ -19,58 +19,58 @@ class Matmul(NumpyOp): self.memory['W'] = W h = np.matmul(x, W) return h - + def backward(self, grad_y): """ grad_y: shape(N, d') """ - + #################### # code 1 # #################### - + return grad_x, grad_W class Relu(NumpyOp): - + def forward(self, x): self.memory['x'] = x return np.where(x > 0, x, np.zeros_like(x)) - + def backward(self, grad_y): """ grad_y: same shape as x """ - + #################### # code 2 # #################### - + return grad_x class Log(NumpyOp): - + def forward(self, x): """ x: shape(N, c) """ - + out = np.log(x + self.epsilon) self.memory['x'] = x - + return out - + def backward(self, grad_y): """ grad_y: same shape as x """ - + #################### # code 3 # #################### - + return grad_x @@ -78,27 +78,27 @@ class Softmax(NumpyOp): """ softmax over last dimension """ - + def forward(self, x): """ x: shape(N, c) """ - + #################### # code 4 # #################### - + return out - + def backward(self, grad_y): """ grad_y: same shape as x """ - + #################### # code 5 # #################### - + return grad_x @@ -108,7 +108,6 @@ class NumpyModel: self.W2 = np.random.normal(size=(256, 64)) self.W3 = np.random.normal(size=(64, 10)) - # 以下算子会在 forward 和 backward 中使用 self.matmul_1 = Matmul() self.relu_1 = Relu() @@ -126,27 +125,26 @@ class NumpyModel: self.x3_grad, self.W3_grad = None, None self.softmax_grad = None self.log_grad = None - - + def forward(self, x): x = x.reshape(-1, 28 * 28) - + #################### # code 6 # #################### - + return x - + def backward(self, y): for size in y.shape: y /= size - + #################### # code 7 # #################### - + pass - + def optimize(self, learning_rate): self.W1 -= learning_rate * self.W1_grad self.W2 -= learning_rate * self.W2_grad diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index 903d7a7..c92e1a7 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -5,30 +5,30 @@ from utils import download_mnist, batch, mini_batch, get_torch_initialization, p def numpy_run(): train_dataset, test_dataset = download_mnist() - + model = NumpyModel() model.W1, model.W2, model.W3 = get_torch_initialization() - + train_loss = [] - + epoch_number = 3 learning_rate = 0.1 - + for epoch in range(epoch_number): for x, y in mini_batch(train_dataset): y = one_hot(y) - + y_pred = model.forward(x.numpy()) loss = (-y_pred * y).sum(axis=1).mean() model.backward(y) model.optimize(learning_rate) - + train_loss.append(loss.item()) - + x, y = batch(test_dataset)[0] accuracy = np.mean((model.forward(x).argmax(axis=1) == y)) print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) - + plot_curve(train_loss) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 563de6b..39e137c 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -24,17 +24,17 @@ def check_result(numpy_result, torch_result=None): def case_1(): x = np.random.normal(size=[5, 6]) W = np.random.normal(size=[6, 4]) - + numpy_matmul = Matmul() numpy_out = numpy_matmul.forward(x, W) numpy_x_grad, numpy_W_grad = numpy_matmul.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() torch_W = torch.from_numpy(W).clone().requires_grad_() - + torch_out = torch_matmul(torch_x, torch_W) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -44,16 +44,16 @@ def case_1(): def case_2(): x = np.random.normal(size=[5, 6]) - + numpy_relu = Relu() numpy_out = numpy_relu.forward(x) numpy_x_grad = numpy_relu.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_relu(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -62,16 +62,16 @@ def case_2(): def case_3(): x = np.random.uniform(low=0.0, high=1.0, size=[3, 4]) - + numpy_log = Log() numpy_out = numpy_log.forward(x) numpy_x_grad = numpy_log.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_log(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -80,29 +80,29 @@ def case_3(): def case_4(): x = np.random.normal(size=[4, 5]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) - + return check_result(numpy_out, torch_out) def case_5(): x = np.random.normal(size=[20, 25]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) numpy_x_grad = numpy_softmax.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -113,35 +113,37 @@ def test_model(): try: numpy_model = NumpyModel() torch_model = TorchModel() - torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = get_torch_initialization(numpy=False) + torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = ( + get_torch_initialization(numpy=False) + ) numpy_model.W1 = torch_model.W1.detach().clone().numpy() numpy_model.W2 = torch_model.W2.detach().clone().numpy() numpy_model.W3 = torch_model.W3.detach().clone().numpy() - + x = torch.randn((10000, 28, 28)) y = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 0] * 1000) - + y = one_hot(y, numpy=False) x2 = x.numpy() y_pred = torch_model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() - + y_pred_numpy = numpy_model.forward(x2) y2 = y.numpy() loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() - + check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) except: print("[Runtime Error in forward]") print("+ {:12} {}/{}".format("forward", 0, 10)) return 0 - + try: - + numpy_model.backward(y2) - + check_flag_2 = [ check_result(numpy_model.log_grad, torch_model.log.grad), check_result(numpy_model.softmax_grad, torch_model.softmax.grad), @@ -155,7 +157,7 @@ def test_model(): print("[Runtime Error in backward]") print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False - + return 10 * check_flag_1 + 20 * check_flag_2 diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py index 6a5649b..c1315f0 100644 --- a/assignment-2/submission/18307130003/torch_mnist.py +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -3,12 +3,12 @@ from utils import mini_batch, batch, download_mnist, get_torch_initialization, o class TorchModel: - + def __init__(self): self.W1 = torch.randn((28 * 28, 256), requires_grad=True) self.W2 = torch.randn((256, 64), requires_grad=True) self.W3 = torch.randn((64, 10), requires_grad=True) - + def forward(self, x): x = x.reshape(-1, 28 * 28) x = torch.relu(torch.matmul(x, self.W1)) @@ -19,13 +19,13 @@ class TorchModel: self.softmax.retain_grad() # for test only self.log.retain_grad() # for test only return self.log - + def optimize(self, learning_rate): with torch.no_grad(): self.W1 -= learning_rate * self.W1.grad self.W2 -= learning_rate * self.W2.grad self.W3 -= learning_rate * self.W3.grad - + self.W1.grad = None self.W2.grad = None self.W3.grad = None @@ -33,30 +33,32 @@ class TorchModel: def torch_run(): train_dataset, test_dataset = download_mnist() - + model = TorchModel() - model.W1.data, model.W2.data, model.W3.data = get_torch_initialization(numpy=False) - + model.W1.data, model.W2.data, model.W3.data = ( + get_torch_initialization(numpy=False) + ) + train_loss = [] - + epoch_number = 3 learning_rate = 0.1 - + for epoch in range(epoch_number): for x, y in mini_batch(train_dataset, numpy=False): y = one_hot(y, numpy=False) - + y_pred = model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() model.optimize(learning_rate) - + train_loss.append(loss.item()) - + x, y = batch(test_dataset, numpy=False)[0] accuracy = model.forward(x).argmax(dim=1).eq(y).float().mean().item() print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) - + plot_curve(train_loss) diff --git a/assignment-2/submission/18307130003/utils.py b/assignment-2/submission/18307130003/utils.py index 709220c..f471049 100644 --- a/assignment-2/submission/18307130003/utils.py +++ b/assignment-2/submission/18307130003/utils.py @@ -13,15 +13,19 @@ def plot_curve(data): def download_mnist(): from torchvision import datasets, transforms - + transform = transforms.Compose([ transforms.ToTensor(), transforms.Normalize(mean=(0.1307,), std=(0.3081,)) ]) - - train_dataset = datasets.MNIST(root="./data/", transform=transform, train=True, download=True) - test_dataset = datasets.MNIST(root="./data/", transform=transform, train=False, download=True) - + + train_dataset = datasets.MNIST( + root="./data/", transform=transform, train=True, download=True + ) + test_dataset = datasets.MNIST( + root="./data/", transform=transform, train=False, download=True + ) + return train_dataset, test_dataset @@ -58,7 +62,7 @@ def get_torch_initialization(numpy=True): fc1 = torch.nn.Linear(28 * 28, 256) fc2 = torch.nn.Linear(256, 64) fc3 = torch.nn.Linear(64, 10) - + if numpy: W1 = fc1.weight.T.detach().clone().numpy() W2 = fc2.weight.T.detach().clone().numpy() @@ -67,5 +71,5 @@ def get_torch_initialization(numpy=True): W1 = fc1.weight.T.detach().clone().data W2 = fc2.weight.T.detach().clone().data W3 = fc3.weight.T.detach().clone().data - + return W1, W2, W3 -- Gitee From 7ef7e86ec68bf9009d58ba5539dd21e4b1efde00 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Wed, 21 Apr 2021 03:04:08 +0800 Subject: [PATCH 11/73] feat: implement Matmul, Relu, Log style: fix coding style --- .../submission/18307130003/numpy_fnn.py | 133 +++++++++++------- .../submission/18307130003/tester_demo.py | 4 +- 2 files changed, 86 insertions(+), 51 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index f50cb4c..f17c5f3 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -1,7 +1,11 @@ +from typing import Tuple import numpy as np class NumpyOp: + ''' + The base class for Numpy operations. + ''' def __init__(self): self.memory = {} @@ -9,97 +13,128 @@ class NumpyOp: class Matmul(NumpyOp): + ''' + Matrix multiplication unit.. + ''' + + def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + w: shape(d, d') + + Returns: + shape(N, d') + ''' - def forward(self, x, W): - """ - x: shape(N, d) - w: shape(d, d') - """ self.memory['x'] = x - self.memory['W'] = W - h = np.matmul(x, W) - return h + self.memory['w'] = w + return np.matmul(x, w) - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ + def backward(self, grad_y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: + ''' + Args: + grad_y: shape(N, d') - #################### - # code 1 # - #################### + Returns: + grad_x: shape(N, d) + grad_w: shape(d, d') + ''' - return grad_x, grad_W + x: np.ndarray = self.memory['x'] + w: np.ndarray = self.memory['w'] + grad_x: np.ndarray = np.matmul(grad_y, w.T) + grad_w: np.ndarray = np.matmul(x.T, grad_y) + return grad_x, grad_w class Relu(NumpyOp): + ''' + Rectified Linear Unit. + ''' + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + + Returns: + shape(N, d) + ''' - def forward(self, x): self.memory['x'] = x - return np.where(x > 0, x, np.zeros_like(x)) + return np.where(x > 0, x, 0) - def backward(self, grad_y): - """ - grad_y: same shape as x - """ + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) - #################### - # code 2 # - #################### + Returns: + shape(N, d) + ''' - return grad_x + x: np.ndarray = self.memory['x'] + grad_y[x < 0] = 0 + return grad_y class Log(NumpyOp): + ''' + Natural logarithm unit. + ''' - def forward(self, x): - """ - x: shape(N, c) - """ + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) - out = np.log(x + self.epsilon) - self.memory['x'] = x + Returns: + shape(N, d) + ''' - return out + self.memory['x'] = x + return np.log(x + self.epsilon) - def backward(self, grad_y): - """ - grad_y: same shape as x - """ + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) - #################### - # code 3 # - #################### + Returns: + shape(N, d) + ''' - return grad_x + x: np.ndarray = self.memory['x'] + return grad_y / x class Softmax(NumpyOp): - """ + ''' softmax over last dimension - """ + ''' def forward(self, x): - """ + ''' x: shape(N, c) - """ + ''' #################### # code 4 # #################### - return out + # return out def backward(self, grad_y): - """ + ''' grad_y: same shape as x - """ + ''' #################### # code 5 # #################### - return grad_x + # return grad_x class NumpyModel: diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 39e137c..c2c9bc5 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -173,8 +173,8 @@ if __name__ == "__main__": for case in testcases: try: res = case[2] if case[1]() else 0 - except: - print("[Runtime Error in {}]".format(case[0])) + except Exception as err: + print("[Runtime Error in {}, error: {}]".format(case[0], err)) res = 0 score += res print("+ {:12} {}/{}".format(case[0], res, case[2])) -- Gitee From 9117d2993ae4a77a55ffb3130ad7f4a05b1bb0ec Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:08 +0800 Subject: [PATCH 12/73] feat: implement Softmax, NumpyModel --- .../submission/18307130003/numpy_fnn.py | 111 ++++++++++++------ 1 file changed, 72 insertions(+), 39 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index f17c5f3..dbb1d34 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -111,76 +111,109 @@ class Log(NumpyOp): class Softmax(NumpyOp): ''' - softmax over last dimension + Softmax over last dimension. ''' - def forward(self, x): - ''' - x: shape(N, c) + def forward(self, x: np.ndarray) -> np.ndarray: ''' + Args: + x: shape(N, d) - #################### - # code 4 # - #################### + Returns: + shape(N, d) + ''' - # return out + y: np.ndarray = np.exp(x) / np.exp(x).sum(axis=1)[:, None] + self.memory['y'] = y + return y - def backward(self, grad_y): - ''' - grad_y: same shape as x + def backward(self, grad_y: np.ndarray) -> np.ndarray: ''' + Args: + grad_y: shape(N, d) - #################### - # code 5 # - #################### + Returns: + shape(N, d) + ''' - # return grad_x + y: np.ndarray = self.memory['y'] + return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) class NumpyModel: + ''' + An FNN model implemented in NumPy. + ''' + def __init__(self): - self.W1 = np.random.normal(size=(28 * 28, 256)) - self.W2 = np.random.normal(size=(256, 64)) - self.W3 = np.random.normal(size=(64, 10)) + self.W1: np.ndarray = np.random.normal(size=(28 * 28, 256)) + self.W2: np.ndarray = np.random.normal(size=(256, 64)) + self.W3: np.ndarray = np.random.normal(size=(64, 10)) # 以下算子会在 forward 和 backward 中使用 + self.matmul_1 = Matmul() self.relu_1 = Relu() + self.matmul_2 = Matmul() self.relu_2 = Relu() + self.matmul_3 = Matmul() - self.softmax = Softmax() - self.log = Log() + self.softmax_3 = Softmax() + self.log_3 = Log() # 以下变量需要在 backward 中更新 - self.x1_grad, self.W1_grad = None, None - self.relu_1_grad = None - self.x2_grad, self.W2_grad = None, None - self.relu_2_grad = None - self.x3_grad, self.W3_grad = None, None - self.softmax_grad = None - self.log_grad = None - - def forward(self, x): - x = x.reshape(-1, 28 * 28) - #################### - # code 6 # - #################### + self.x1_grad: np.ndarray = None + self.W1_grad: np.ndarray = None + self.relu_1_grad: np.ndarray = None + + self.x2_grad: np.ndarray = None + self.W2_grad: np.ndarray = None + self.relu_2_grad: np.ndarray = None + + self.x3_grad: np.ndarray = None + self.W3_grad: np.ndarray = None + self.softmax_grad: np.ndarray = None + self.log_grad: np.ndarray = None + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + Returns: + shape(N, d) + ''' + + x = x.reshape(-1, 28 * 28) + x = self.relu_1.forward(self.matmul_1.forward(x, self.W1)) + x = self.relu_2.forward(self.matmul_2.forward(x, self.W2)) + x = self.softmax_3.forward(self.matmul_3.forward(x, self.W3)) + x = self.log_3.forward(x) return x - def backward(self, y): + def backward(self, y: np.ndarray) -> None: + ''' + Args: + y: shape(N, d) + ''' + for size in y.shape: + size: int y /= size - #################### - # code 7 # - #################### + self.log_grad = self.log_3.backward(y) + self.softmax_grad = self.softmax_3.backward(self.log_grad) + self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) + + self.relu_2_grad = self.relu_2.backward(self.x3_grad) + self.x2_grad, self.W2_grad = self.matmul_2.backward(self.relu_2_grad) - pass + self.relu_1_grad = self.relu_1.backward(self.x2_grad) + self.x1_grad, self.W1_grad = self.matmul_1.backward(self.relu_1_grad) - def optimize(self, learning_rate): + def optimize(self, learning_rate: float): self.W1 -= learning_rate * self.W1_grad self.W2 -= learning_rate * self.W2_grad self.W3 -= learning_rate * self.W3_grad -- Gitee From 34efa33d7c936e84f311b2058173ecef05f72537 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:26 +0800 Subject: [PATCH 13/73] feat: add more logs in tester --- .../submission/18307130003/tester_demo.py | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index c2c9bc5..c607208 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -18,7 +18,9 @@ def check_result(numpy_result, torch_result=None): return flag T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() direction = T / torch_result.numel() < err_p - return direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + result = direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + print(result) + return result def case_1(): @@ -135,13 +137,12 @@ def test_model(): check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) - except: - print("[Runtime Error in forward]") + except Exception as err: + print("[Runtime Error in forward, error: {}]".format(err)) print("+ {:12} {}/{}".format("forward", 0, 10)) return 0 try: - numpy_model.backward(y2) check_flag_2 = [ @@ -151,10 +152,10 @@ def test_model(): check_result(numpy_model.W2_grad, torch_model.W2.grad), check_result(numpy_model.W1_grad, torch_model.W1.grad) ] - check_flag_2 = sum(check_flag_2) >= 4 + check_flag_2 = sum(check_flag_2) / 5 print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) - except: - print("[Runtime Error in backward]") + except Exception as err: + print("[Runtime Error in backward, error: {}]".format(err)) print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False -- Gitee From 07a988a595c77a29108841c046b3b0f29d78fde3 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:29 +0800 Subject: [PATCH 14/73] fix: negative loss function issue --- .../submission/18307130003/numpy_fnn.py | 19 +------------------ .../submission/18307130003/tester_demo.py | 8 +++++--- 2 files changed, 6 insertions(+), 21 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index dbb1d34..ac9ee2f 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -150,8 +150,6 @@ class NumpyModel: self.W2: np.ndarray = np.random.normal(size=(256, 64)) self.W3: np.ndarray = np.random.normal(size=(64, 10)) - # 以下算子会在 forward 和 backward 中使用 - self.matmul_1 = Matmul() self.relu_1 = Relu() @@ -162,21 +160,6 @@ class NumpyModel: self.softmax_3 = Softmax() self.log_3 = Log() - # 以下变量需要在 backward 中更新 - - self.x1_grad: np.ndarray = None - self.W1_grad: np.ndarray = None - self.relu_1_grad: np.ndarray = None - - self.x2_grad: np.ndarray = None - self.W2_grad: np.ndarray = None - self.relu_2_grad: np.ndarray = None - - self.x3_grad: np.ndarray = None - self.W3_grad: np.ndarray = None - self.softmax_grad: np.ndarray = None - self.log_grad: np.ndarray = None - def forward(self, x: np.ndarray) -> np.ndarray: ''' Args: @@ -203,7 +186,7 @@ class NumpyModel: size: int y /= size - self.log_grad = self.log_3.backward(y) + self.log_grad = self.log_3.backward(-y) self.softmax_grad = self.softmax_3.backward(self.log_grad) self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index c607208..38530cd 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -18,7 +18,9 @@ def check_result(numpy_result, torch_result=None): return flag T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() direction = T / torch_result.numel() < err_p - result = direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + result = direction and ( + (torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon + ).item() print(result) return result @@ -153,13 +155,13 @@ def test_model(): check_result(numpy_model.W1_grad, torch_model.W1.grad) ] check_flag_2 = sum(check_flag_2) / 5 - print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) + print("+ {:12} {}/{}".format("backward", int(20 * check_flag_2), 20)) except Exception as err: print("[Runtime Error in backward, error: {}]".format(err)) print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False - return 10 * check_flag_1 + 20 * check_flag_2 + return int(10 * check_flag_1 + 20 * check_flag_2) if __name__ == "__main__": -- Gitee From b1dcf339919d3c86853c11bd93999cf08ee892a9 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:33 +0800 Subject: [PATCH 15/73] fix: merge fixes from upstream --- .../submission/18307130003/numpy_fnn.py | 16 ++++++++++++ .../submission/18307130003/numpy_mnist.py | 24 +++++++++++++---- .../submission/18307130003/tester_demo.py | 26 ++++++++++++------- .../submission/18307130003/torch_mnist.py | 24 +++++++++++------ 4 files changed, 67 insertions(+), 23 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index ac9ee2f..46823b2 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -140,6 +140,22 @@ class Softmax(NumpyOp): return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) +class NumpyLoss: + ''' + Loss function. + ''' + + def __init__(self): + self.target: np.ndarray = None + + def get_loss(self, pred: np.ndarray, target: np.ndarray) -> float: + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self) -> np.ndarray: + return -self.target / self.target.shape[0] + + class NumpyModel: ''' An FNN model implemented in NumPy. diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index c92e1a7..630e38f 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,15 +1,28 @@ +from typing import List import numpy as np -from numpy_fnn import NumpyModel -from utils import download_mnist, batch, mini_batch, get_torch_initialization, plot_curve, one_hot +from numpy_fnn import NumpyModel, NumpyLoss +from utils import ( + download_mnist, + batch, + mini_batch, + get_torch_initialization, + plot_curve, + one_hot, +) def numpy_run(): + ''' + Train the FNN network on MNIST. + ''' + train_dataset, test_dataset = download_mnist() model = NumpyModel() + numpy_loss = NumpyLoss() model.W1, model.W2, model.W3 = get_torch_initialization() - train_loss = [] + train_loss: List[float] = [] epoch_number = 3 learning_rate = 0.1 @@ -19,8 +32,9 @@ def numpy_run(): y = one_hot(y) y_pred = model.forward(x.numpy()) - loss = (-y_pred * y).sum(axis=1).mean() - model.backward(y) + loss = numpy_loss.get_loss(y_pred, y) + + model.backward(numpy_loss.backward()) model.optimize(learning_rate) train_loss.append(loss.item()) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 38530cd..68874de 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -1,12 +1,17 @@ import numpy as np import torch -from torch import matmul as torch_matmul, relu as torch_relu, softmax as torch_softmax, log as torch_log - -from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel +from torch import ( + matmul as torch_matmul, + relu as torch_relu, + softmax as torch_softmax, + log as torch_log, +) + +from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel, NumpyLoss from torch_mnist import TorchModel from utils import get_torch_initialization, one_hot -err_epsilon = 1e-3 +err_epsilon = 1e-6 err_p = 0.4 @@ -42,7 +47,7 @@ def case_1(): return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), - (numpy_W_grad, torch_W.grad) + (numpy_W_grad, torch_W.grad), ]) @@ -115,6 +120,7 @@ def case_5(): def test_model(): try: + numpy_loss = NumpyLoss() numpy_model = NumpyModel() torch_model = TorchModel() torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = ( @@ -134,8 +140,7 @@ def test_model(): loss.backward() y_pred_numpy = numpy_model.forward(x2) - y2 = y.numpy() - loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() + numpy_loss.get_loss(y_pred_numpy, y.numpy()) check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) @@ -145,11 +150,12 @@ def test_model(): return 0 try: - numpy_model.backward(y2) + numpy_model.backward(numpy_loss.backward()) check_flag_2 = [ - check_result(numpy_model.log_grad, torch_model.log.grad), - check_result(numpy_model.softmax_grad, torch_model.softmax.grad), + check_result(numpy_model.log_grad, torch_model.log_input.grad), + check_result(numpy_model.softmax_grad, + torch_model.softmax_input.grad), check_result(numpy_model.W3_grad, torch_model.W3.grad), check_result(numpy_model.W2_grad, torch_model.W2.grad), check_result(numpy_model.W1_grad, torch_model.W1.grad) diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py index c1315f0..dec6c89 100644 --- a/assignment-2/submission/18307130003/torch_mnist.py +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -8,17 +8,26 @@ class TorchModel: self.W1 = torch.randn((28 * 28, 256), requires_grad=True) self.W2 = torch.randn((256, 64), requires_grad=True) self.W3 = torch.randn((64, 10), requires_grad=True) + self.softmax_input = None + self.log_input = None def forward(self, x): x = x.reshape(-1, 28 * 28) x = torch.relu(torch.matmul(x, self.W1)) x = torch.relu(torch.matmul(x, self.W2)) x = torch.matmul(x, self.W3) - self.softmax = torch.softmax(x, 1) - self.log = torch.log(self.softmax) - self.softmax.retain_grad() # for test only - self.log.retain_grad() # for test only - return self.log + + self.softmax_input = x + self.softmax_input.retain_grad() + + x = torch.softmax(x, 1) + + self.log_input = x + self.log_input.retain_grad() + + x = torch.log(x) + + return x def optimize(self, learning_rate): with torch.no_grad(): @@ -35,9 +44,8 @@ def torch_run(): train_dataset, test_dataset = download_mnist() model = TorchModel() - model.W1.data, model.W2.data, model.W3.data = ( - get_torch_initialization(numpy=False) - ) + model.W1.data, model.W2.data, model.W3.data = get_torch_initialization( + numpy=False) train_loss = [] -- Gitee From bd7be588c6231c734af4227b6a09dfc9f5b6f943 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:36 +0800 Subject: [PATCH 16/73] fix: minor fix for previous changes --- assignment-2/submission/18307130003/numpy_fnn.py | 6 +----- assignment-2/submission/18307130003/numpy_mnist.py | 8 +++++--- 2 files changed, 6 insertions(+), 8 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 46823b2..6db4b6c 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -198,11 +198,7 @@ class NumpyModel: y: shape(N, d) ''' - for size in y.shape: - size: int - y /= size - - self.log_grad = self.log_3.backward(-y) + self.log_grad = self.log_3.backward(y) self.softmax_grad = self.softmax_3.backward(self.log_grad) self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index 630e38f..c584c4c 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,5 +1,6 @@ from typing import List import numpy as np +from torch import Tensor from numpy_fnn import NumpyModel, NumpyLoss from utils import ( download_mnist, @@ -29,9 +30,10 @@ def numpy_run(): for epoch in range(epoch_number): for x, y in mini_batch(train_dataset): - y = one_hot(y) + x: np.ndarray = x.numpy() + y: np.ndarray = one_hot(y) - y_pred = model.forward(x.numpy()) + y_pred = model.forward(x) loss = numpy_loss.get_loss(y_pred, y) model.backward(numpy_loss.backward()) @@ -40,7 +42,7 @@ def numpy_run(): train_loss.append(loss.item()) x, y = batch(test_dataset)[0] - accuracy = np.mean((model.forward(x).argmax(axis=1) == y)) + accuracy: float = np.mean((model.forward(x).argmax(axis=1) == y)) print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) plot_curve(train_loss) -- Gitee From 4133f19b1c4eec8e7e392cd47f61feaa13115c9d Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 22:47:24 +0800 Subject: [PATCH 17/73] feat: mini_batch in numpy --- .../submission/18307130003/numpy_mnist.py | 34 ++++++++++++++++--- 1 file changed, 30 insertions(+), 4 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index c584c4c..101aac0 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,17 +1,43 @@ -from typing import List +from typing import Any, List, Tuple import numpy as np -from torch import Tensor from numpy_fnn import NumpyModel, NumpyLoss from utils import ( download_mnist, batch, - mini_batch, + # mini_batch, get_torch_initialization, plot_curve, one_hot, ) +def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: + ''' + Split the data and labels from the given dataset into batches. + + Args: + dataset: the given dataset + batch_size: the size of retrieved data + + Returns: + Batches of [data, labels] pair. + ''' + + data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) + labels: np.ndarray = np.array([pair[1] for pair in dataset]) + + # Shuffle the dataset + size: int = len(dataset) + indices: np.ndarray = np.arange(size) + np.random.shuffle(indices) + + batches: List[Tuple[np.ndarray, np.ndarray]] = [] + for i in range(0, size, batch_size): + chunk: np.ndarray = indices[i:i+batch_size] + batches.append((data[chunk], labels[chunk])) + return batches + + def numpy_run(): ''' Train the FNN network on MNIST. @@ -30,7 +56,7 @@ def numpy_run(): for epoch in range(epoch_number): for x, y in mini_batch(train_dataset): - x: np.ndarray = x.numpy() + x: np.ndarray y: np.ndarray = one_hot(y) y_pred = model.forward(x) -- Gitee From 316e52ae3131570983d4d4c846308fc81930a824 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 23:02:30 +0800 Subject: [PATCH 18/73] chore: doc string minor fix --- assignment-2/submission/18307130003/numpy_fnn.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 6db4b6c..7849408 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -14,7 +14,7 @@ class NumpyOp: class Matmul(NumpyOp): ''' - Matrix multiplication unit.. + Matrix multiplication unit. ''' def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: -- Gitee From 9458972394e6dcbd455d23e729ac17ba14a37ddf Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:25:44 +0800 Subject: [PATCH 19/73] doc: backward chap. 1 --- assignment-2/submission/18307130003/README.md | 434 +----------------- 1 file changed, 22 insertions(+), 412 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 13d2047..062594f 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -1,44 +1,10 @@ - - # 实验报告 本次作业完成了选题 1 的实验内容,利用 NumPy 实现了一个 FNN 模型,并在 MNIST 数据集上进行了训练。 ## 目录 -- [实验报告](#实验报告) - - [目录](#目录) - - [FNN 算子的反向传播](#fnn-算子的反向传播) - - [1. Matmul](#1-matmul) - - [1.1 公式推导](#11-公式推导) - - [1.2 代码实现](#12-代码实现) - - [2. Relu](#2-relu) - - [2.1 公式推导](#21-公式推导) - - [2.2 代码实现](#22-代码实现) - - [3. Log](#3-log) - - [3.1 公式推导](#31-公式推导) - - [3.2 代码实现](#32-代码实现) - - [4. Softmax](#4-softmax) - - [4.1 公式推导](#41-公式推导) - - [4.2 代码实现](#42-代码实现) - - [函数 `mini_batch` 实现](#函数-mini_batch-实现) - - [实验过程与结果](#实验过程与结果) - - [1. 实验 1](#1-实验-1) - - [1.1 参数](#11-参数) - - [1.2 预测准确率](#12-预测准确率) - - [1.3 损失函数值](#13-损失函数值) - - [2. 实验 2](#2-实验-2) - - [2.1 参数](#21-参数) - - [2.2 预测准确率](#22-预测准确率) - - [2.3 损失函数值](#23-损失函数值) - - [3. 实验 3](#3-实验-3) - - [3.1 参数](#31-参数) - - [3.2 预测准确率](#32-预测准确率) - - [3.3 损失函数值](#33-损失函数值) - - [4. 实验 4](#4-实验-4) - - [4.1 参数](#41-参数) - - [4.2 预测准确率](#42-预测准确率) - - [4.3 损失函数值](#43-损失函数值) +[TOC] ## FNN 算子的反向传播 @@ -48,86 +14,62 @@ 输入一个 $n\times d$ 的矩阵 $X$ 和一个 $d\times d'$ 的矩阵 $W$,算子 `Matmul` 的正向传播公式为: - - -Equation 1.1 +$$ 输出一个 $n\times d'$ 的矩阵 $Y$。 对于梯度的反向传播,有 - - -Equation 1.2 +$$ 我们利用向量化(vectorization)进行对矩阵求导的求解: - - -Equation 1.3 - -这里 $\mathit{vec}(X_{m\times n})$ 表示向量 - - - -Equation 1.3.1 +$$ -$\otimes$ 表示 Kronecker 积,下标表示矩阵或向量的维度。 +这里 $\otimes$ 表示 Kronecker 积,下标表示矩阵或向量的维度。 因此有 - - -Equation 1.4 +$$ 类似 $(1.3)$ 的推导,同理可得 - - -Equation 1.5 +$$ #### 1.2 代码实现 @@ -174,65 +116,6 @@ class Matmul(NumpyOp): #### 2.1 公式推导 -输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Relu` 的正向传播公式为: - - - -Equation 2.1 - -输出一个 $n\times d$ 的矩阵 $Y$。 - -对于梯度的反向传播,有 - - - -Equation 2.2 - -这里 $\odot$ 表示 Hadamard 积,即逐元素(element-wise)乘积。 - -其中,对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$,由 $(2.1)$ 有 - - - -Equation 2.3 - -因此,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$,令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$,由 $(2.2)$ 有 - - - -Equation 2.4 - #### 2.2 代码实现 ```python {.line-numbers} @@ -265,56 +148,16 @@ class Relu(NumpyOp): ''' x: np.ndarray = self.memory['x'] - return np.where(x > 0, grad_y, 0) + grad_y[x < 0] = 0 + return grad_y ``` ### 3. Log #### 3.1 公式推导 -输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Log` 的正向传播公式为: - - - -Equation 3.1 - -输出一个 $n\times d$ 的矩阵 $Y$。 - -对于梯度的反向传播,有 - - - -Equation 3.2 - -其中,对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$,由 $(3.1)$ 有 - - - -Equation 3.3 - -因此,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$,令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$,由 $(3.2)$ 有 - - - -Equation 3.4 - #### 3.2 代码实现 -为了防止 $X_{ij} = 0$ 时出现 $\log{X_{ij}} = -\infty$ 导致溢出,这里我们给 $X_{ij}$ 附加了一个 $\epsilon = 10^{-12}$ 的修正。 - ```python {.line-numbers} # numpy_fnn.py @@ -352,70 +195,6 @@ class Log(NumpyOp): #### 4.1 公式推导 -输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Softmax` 的正向传播公式为: - - - -Equation 4.1 - -输出一个 $n\times d$ 的矩阵 $Y$。 - -对于梯度的反向传播,有 - - - -Equation 4.2 - -其中,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$ 有 - - - -Equation 4.3 - #### 4.2 代码实现 ```python {.line-numbers} @@ -451,172 +230,3 @@ class Softmax(NumpyOp): y: np.ndarray = self.memory['y'] return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) ``` - -## 函数 `mini_batch` 实现 - -我们使用 NumPy 重写了函数 `mini_batch`,用于之后的训练。 - -```python {.line-numbers} -# numpy_mnist.py - -def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: - ''' - Split the data and labels from the given dataset into batches. - - Args: - dataset: the given dataset - batch_size: the size of retrieved data - - Returns: - Batches of [data, labels] pair. - ''' - - data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) - labels: np.ndarray = np.array([pair[1] for pair in dataset]) - - # Shuffle the dataset - size: int = len(dataset) - indices: np.ndarray = np.arange(size) - np.random.shuffle(indices) - - batches: List[Tuple[np.ndarray, np.ndarray]] = [] - for i in range(0, size, batch_size): - chunk: np.ndarray = indices[i:i+batch_size] - batches.append((data[chunk], labels[chunk])) - return batches -``` - -## 实验过程与结果 - -执行以下命令开始训练。 - -```bash -python ./numpy_mnist.py -``` - -### 1. 实验 1 - -#### 1.1 参数 - -```python {.line-numbers} -epoch_number = 3 -batch_size = 128 -learning_rate = 0.1 -``` - -#### 1.2 预测准确率 - -```text -[0] Accuracy: 0.9485 -[1] Accuracy: 0.9647 -[2] Accuracy: 0.9715 -``` - -#### 1.3 损失函数值 - -![Loss value 1](./img/loss_value_1.png) - -### 2. 实验 2 - -这次,我们调大训练轮数(`epoch_number`),观察预测准确率的变化。 - -#### 2.1 参数 - -```python {.line-numbers} -epoch_number = 10 -batch_size = 128 -learning_rate = 0.1 -``` - -#### 2.2 预测准确率 - -```text -[0] Accuracy: 0.9496 -[1] Accuracy: 0.9600 -[2] Accuracy: 0.9675 -[3] Accuracy: 0.9761 -[4] Accuracy: 0.9755 -[5] Accuracy: 0.9775 -[6] Accuracy: 0.9791 -[7] Accuracy: 0.9795 -[8] Accuracy: 0.9781 -[9] Accuracy: 0.9810 -``` - -可见,训练轮数越多,预测准确率越高,但到达一定准确率后开始波动,不再明显上升。 - -#### 2.3 损失函数值 - -![Loss value 2](./img/loss_value_2.png) - -可见,训练轮数越多,损失函数值越低,波动越小。 - -### 3. 实验 3 - -这次,我们调大批处理时每批数据大小(`batch_size`),观察预测准确率的变化。 - -#### 3.1 参数 - -```python {.line-numbers} -epoch_number = 10 -batch_size = 256 -learning_rate = 0.1 -``` - -#### 3.2 预测准确率 - -```text -[0] Accuracy: 0.9253 -[1] Accuracy: 0.9477 -[2] Accuracy: 0.9522 -[3] Accuracy: 0.9651 -[4] Accuracy: 0.9680 -[5] Accuracy: 0.9731 -[6] Accuracy: 0.9755 -[7] Accuracy: 0.9766 -[8] Accuracy: 0.9766 -[9] Accuracy: 0.9790 -``` - -可见,每批数据的大小越大,训练速度越慢,但最终达到的准确率没有明显变化。 - -#### 3.3 损失函数值 - -![Loss value 3](./img/loss_value_3.png) - -可见,每批数据的大小越大,损失函数值整体的波动越小。 - -### 4. 实验 4 - -这次,我们提高学习率(`learning_rate`),观察预测准确率的变化。 - -#### 4.1 参数 - -```python {.line-numbers} -epoch_number = 10 -batch_size = 256 -learning_rate = 0.5 -``` - -#### 4.2 预测准确率 - -```text -[0] Accuracy: 0.9505 -[1] Accuracy: 0.9675 -[2] Accuracy: 0.9706 -[3] Accuracy: 0.9471 -[4] Accuracy: 0.9737 -[5] Accuracy: 0.8980 -[6] Accuracy: 0.9757 -[7] Accuracy: 0.9573 -[8] Accuracy: 0.9770 -[9] Accuracy: 0.9792 -``` - -可见,学习率越高,训练速度越快,但训练时的波动也可能较大。 - -#### 4.3 损失函数值 - -![Loss value 4](./img/loss_value_4.png) - -可见,学习率越高,损失函数值下降越快,但整体的波动也可能较大。 -- Gitee From 1ec2a80d87ab131f3bae324631f9983c18babe4a Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:28:08 +0800 Subject: [PATCH 20/73] doc: create TOC --- assignment-2/submission/18307130003/README.md | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 062594f..a9ac9b0 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -4,7 +4,21 @@ ## 目录 -[TOC] +- [实验报告](#实验报告) + - [目录](#目录) + - [FNN 算子的反向传播](#fnn-算子的反向传播) + - [1. Matmul](#1-matmul) + - [1.1 公式推导](#11-公式推导) + - [1.2 代码实现](#12-代码实现) + - [2. Relu](#2-relu) + - [2.1 公式推导](#21-公式推导) + - [2.2 代码实现](#22-代码实现) + - [3. Log](#3-log) + - [3.1 公式推导](#31-公式推导) + - [3.2 代码实现](#32-代码实现) + - [4. Softmax](#4-softmax) + - [4.1 公式推导](#41-公式推导) + - [4.2 代码实现](#42-代码实现) ## FNN 算子的反向传播 -- Gitee From 7bca1f67ff47bedac2971c91c2ceaea23bd1b9ed Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:42:00 +0800 Subject: [PATCH 21/73] doc: minor fix latex layout --- assignment-2/submission/18307130003/README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index a9ac9b0..8216661 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -48,22 +48,22 @@ $$ $$ \begin{split} \mathit{vec}(\frac{\partial z}{\partial X}_{n\times d}) -&= {(\frac{\partial Y}{\partial X})^T}_{nd\times nd'} +&= {(\frac{\partial Y}{\partial X})^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac {\partial ({\mathit{vec}(X\times W)}_{nd'})} {\partial ({\mathit{vec}(X)}_{nd})} - })^T}_{nd\times nd'} + })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac {\partial ( {\mathit{vec}(X)}_{nd} - \times {(I_n\otimes W)}_{nd\times nd'} + \times {(I_n\otimes W)}_{nd\times {nd'}} )} {\partial ({\mathit{vec}(X)}_{nd})} - })^T}_{nd\times nd'} + })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ -&= {(I_n\otimes W)}_{nd\times nd'} +&= {(I_n\otimes W)}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= \mathit{vec}({(\frac{\partial z}{\partial Y}\times W^T)}_{n\times d}) \end{split} \tag{1.3} -- Gitee From 39f1b63f0dc78ca07553d93bf59c666487c070d2 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:58:22 +0800 Subject: [PATCH 22/73] doc: add some details for chap. 1 --- assignment-2/submission/18307130003/README.md | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 8216661..488bde9 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -69,7 +69,18 @@ $$ \end{split} \tag{1.3} $$ -这里 $\otimes$ 表示 Kronecker 积,下标表示矩阵或向量的维度。 +这里 $\mathit{vec}(X_{m\times n})$ 表示向量 + +$$ +\begin{split} +[&x_{11}, x_{12},\ &..., x_{1n}, \\ + &x_{21}, x_{22},\ &..., x_{2n}, \\ + &&... \\ + &x_{m1}, x_{m2},\ &..., x_{mn}] +\end{split} +$$ + +$\otimes$ 表示 Kronecker 积,下标表示矩阵或向量的维度。 因此有 -- Gitee From 68f57f939570e16f7a4b06d410ae053ebdcd5669 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 14:13:49 +0800 Subject: [PATCH 23/73] doc: backward chap. 2 --- assignment-2/submission/18307130003/README.md | 60 +++++++++++++++++-- .../submission/18307130003/numpy_fnn.py | 3 +- 2 files changed, 56 insertions(+), 7 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 488bde9..cbb037b 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -51,8 +51,8 @@ $$ &= {(\frac{\partial Y}{\partial X})^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac - {\partial ({\mathit{vec}(X\times W)}_{nd'})} - {\partial ({\mathit{vec}(X)}_{nd})} + {\partial {\mathit{vec}(X\times W)}_{nd'}} + {\partial {\mathit{vec}(X)}_{nd}} })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac @@ -60,7 +60,7 @@ $$ {\mathit{vec}(X)}_{nd} \times {(I_n\otimes W)}_{nd\times {nd'}} )} - {\partial ({\mathit{vec}(X)}_{nd})} + {\partial {\mathit{vec}(X)}_{nd}} })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {(I_n\otimes W)}_{nd\times {nd'}} @@ -141,6 +141,57 @@ class Matmul(NumpyOp): #### 2.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Relu` 的正向传播公式为: + +$$ +Y_{ij} = \left\{ + \begin{aligned} + &X_{ij}\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播,有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} \\ +&= \frac{\partial z}{\partial Y}_{n\times d} + \odot \frac{\partial Y}{\partial X}_{n\times d} +\end{split} \tag{2.2} +$$ + +这里 $\odot$ 表示 Hadamard 积,即逐元素(element-wise)乘积。 + +其中,对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$,由 $(2.1)$ 有 + +$$ +{Y'}_{ij} = \left\{ + \begin{aligned} + &1\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.3} +$$ + +因此,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$,令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$,由 $(2.2)$ 有 + +$$ +{Z'}_{ij} = \left\{ + \begin{aligned} + &{({Z_Y}')}_{ij}\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.4} +$$ + #### 2.2 代码实现 ```python {.line-numbers} @@ -173,8 +224,7 @@ class Relu(NumpyOp): ''' x: np.ndarray = self.memory['x'] - grad_y[x < 0] = 0 - return grad_y + return np.where(x > 0, grad_y, 0) ``` ### 3. Log diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 7849408..4331007 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -75,8 +75,7 @@ class Relu(NumpyOp): ''' x: np.ndarray = self.memory['x'] - grad_y[x < 0] = 0 - return grad_y + return np.where(x > 0, grad_y, 0) class Log(NumpyOp): -- Gitee From 8595d0fd75b48cdc10256f88541a04d2321cb3bd Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 14:28:13 +0800 Subject: [PATCH 24/73] doc: backward chap. 3 --- assignment-2/submission/18307130003/README.md | 33 +++++++++++++++++++ 1 file changed, 33 insertions(+) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index cbb037b..8ba1cac 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -231,8 +231,41 @@ class Relu(NumpyOp): #### 3.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Log` 的正向传播公式为: + +$$ +Y_{ij} = \log{X_{ij}} \tag{3.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播,有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} \\ +&= \frac{\partial z}{\partial Y}_{n\times d} + \odot \frac{\partial Y}{\partial X}_{n\times d} +\end{split} \tag{3.2} +$$ + +其中,对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$,由 $(3.1)$ 有 + +$$ +{Y'}_{ij} = \frac{1}{X_{ij}} \tag{3.3} +$$ + +因此,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$,令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$,由 $(3.2)$ 有 + +$$ +{Z'}_{ij} = \frac{{({Z_Y}')}_{ij}}{X_{ij}} \tag{3.4} +$$ + #### 3.2 代码实现 +为了防止 $X_{ij} = 0$ 时出现 $\log{X_{ij}} = -\infty$ 导致溢出,这里我们给 $X_{ij}$ 附加了一个 $\epsilon = 10^{-12}$ 的修正。 + ```python {.line-numbers} # numpy_fnn.py -- Gitee From 06d9c5a56d0b01fb0e2bbca63a56b25485962034 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 17:16:16 +0800 Subject: [PATCH 25/73] doc: backward chap. 4 --- assignment-2/submission/18307130003/README.md | 58 +++++++++++++++++++ 1 file changed, 58 insertions(+) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 8ba1cac..a83d87d 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -303,6 +303,64 @@ class Log(NumpyOp): #### 4.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Softmax` 的正向传播公式为: + +$$ +Y_{ij} = \frac{e^{X_{ij}}}{\sum\limits_{k=1}^d e^{X_{ik}}} \tag{4.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播,有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} +\end{split} \tag{4.2} +$$ + +其中,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$ 有 + +$$ +\begin{split} +{Z'}_{ij} +&= \frac{\partial z}{\partial X_{ij}} \\ +&= {(\frac{\partial z}{\partial Y_i})}_d + \cdot {(\frac{\partial Y_i}{\partial X_{ij}})}_d \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{\partial Y_{ij}}{\partial X_{ij}} + + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{\partial Y_{ik}}{\partial X_{ij}} \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{\partial}{\partial X_{ij}}( + \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + ) + + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{\partial}{\partial X_{ij}}( + \frac{e^{X_{ik}}}{\sum\limits_{t=1}^d e^{X_{it}}} + ) \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + \cdot (1 - \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}}) - + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + \cdot \frac{e^{X_{ik}}}{\sum\limits_{t=1}^d e^{X_{it}}} \\ +&= \frac{\partial z}{\partial Y_{ij}}\cdot Y_{ij}\cdot (1 - Y_{ij}) - + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}}\cdot Y_{ij}\cdot Y_{ik} \\ +&= Y_{ij}\cdot ( + \frac{\partial z}{\partial Y_{ij}} - + \sum\limits_{k=1}^d + \frac{\partial z}{\partial Y_{ik}}\cdot Y_{ik} + ) +\end{split} +\tag{4.3} +$$ + #### 4.2 代码实现 ```python {.line-numbers} -- Gitee From 1cfb2b14f9d44b86ee35be840b86131f7bd34e1f Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 18:12:19 +0800 Subject: [PATCH 26/73] doc: report done --- assignment-2/submission/18307130003/README.md | 187 ++++++++++++++++++ .../submission/18307130003/numpy_mnist.py | 7 +- 2 files changed, 191 insertions(+), 3 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index a83d87d..61860fc 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -19,6 +19,24 @@ - [4. Softmax](#4-softmax) - [4.1 公式推导](#41-公式推导) - [4.2 代码实现](#42-代码实现) + - [函数 `mini_batch` 实现](#函数-mini_batch-实现) + - [实验过程与结果](#实验过程与结果) + - [1. 实验 1](#1-实验-1) + - [1.1 参数](#11-参数) + - [1.2 预测准确率](#12-预测准确率) + - [1.3 损失函数值](#13-损失函数值) + - [2. 实验 2](#2-实验-2) + - [2.1 参数](#21-参数) + - [2.2 预测准确率](#22-预测准确率) + - [2.3 损失函数值](#23-损失函数值) + - [3. 实验 3](#3-实验-3) + - [3.1 参数](#31-参数) + - [3.2 预测准确率](#32-预测准确率) + - [3.3 损失函数值](#33-损失函数值) + - [4. 实验 4](#4-实验-4) + - [4.1 参数](#41-参数) + - [4.2 预测准确率](#42-预测准确率) + - [4.3 损失函数值](#43-损失函数值) ## FNN 算子的反向传播 @@ -396,3 +414,172 @@ class Softmax(NumpyOp): y: np.ndarray = self.memory['y'] return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) ``` + +## 函数 `mini_batch` 实现 + +我们使用 NumPy 重写了函数 `mini_batch`,用于之后的训练。 + +```python {.line-numbers} +# numpy_mnist.py + +def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: + ''' + Split the data and labels from the given dataset into batches. + + Args: + dataset: the given dataset + batch_size: the size of retrieved data + + Returns: + Batches of [data, labels] pair. + ''' + + data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) + labels: np.ndarray = np.array([pair[1] for pair in dataset]) + + # Shuffle the dataset + size: int = len(dataset) + indices: np.ndarray = np.arange(size) + np.random.shuffle(indices) + + batches: List[Tuple[np.ndarray, np.ndarray]] = [] + for i in range(0, size, batch_size): + chunk: np.ndarray = indices[i:i+batch_size] + batches.append((data[chunk], labels[chunk])) + return batches +``` + +## 实验过程与结果 + +执行以下命令开始训练。 + +```bash +python ./numpy_mnist.py +``` + +### 1. 实验 1 + +#### 1.1 参数 + +```python {.line-numbers} +epoch_number = 3 +batch_size = 128 +learning_rate = 0.1 +``` + +#### 1.2 预测准确率 + +```text +[0] Accuracy: 0.9485 +[1] Accuracy: 0.9647 +[2] Accuracy: 0.9715 +``` + +#### 1.3 损失函数值 + +![Loss value 1](./img/loss_value_1.png) + +### 2. 实验 2 + +这次,我们调大训练轮数(`epoch_number`),观察预测准确率的变化。 + +#### 2.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 128 +learning_rate = 0.1 +``` + +#### 2.2 预测准确率 + +```text +[0] Accuracy: 0.9496 +[1] Accuracy: 0.9600 +[2] Accuracy: 0.9675 +[3] Accuracy: 0.9761 +[4] Accuracy: 0.9755 +[5] Accuracy: 0.9775 +[6] Accuracy: 0.9791 +[7] Accuracy: 0.9795 +[8] Accuracy: 0.9781 +[9] Accuracy: 0.9810 +``` + +可见,训练轮数越多,预测准确率越高,但到达一定准确率后开始波动,不再明显上升。 + +#### 2.3 损失函数值 + +![Loss value 2](./img/loss_value_2.png) + +可见,训练轮数越多,损失函数值越低,波动越小。 + +### 3. 实验 3 + +这次,我们调大批处理时每批数据大小(`batch_size`),观察预测准确率的变化。 + +#### 3.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 256 +learning_rate = 0.1 +``` + +#### 3.2 预测准确率 + +```text +[0] Accuracy: 0.9253 +[1] Accuracy: 0.9477 +[2] Accuracy: 0.9522 +[3] Accuracy: 0.9651 +[4] Accuracy: 0.9680 +[5] Accuracy: 0.9731 +[6] Accuracy: 0.9755 +[7] Accuracy: 0.9766 +[8] Accuracy: 0.9766 +[9] Accuracy: 0.9790 +``` + +可见,每批数据的大小越大,训练速度越慢,但最终达到的准确率没有明显变化。 + +#### 3.3 损失函数值 + +![Loss value 3](./img/loss_value_3.png) + +可见,每批数据的大小越大,损失函数值整体的波动越小。 + +### 4. 实验 4 + +这次,我们提高学习率(`learnin_rate`),观察预测准确率的变化。 + +#### 4.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 256 +learning_rate = 0.5 +``` + +#### 4.2 预测准确率 + +```text +[0] Accuracy: 0.9505 +[1] Accuracy: 0.9675 +[2] Accuracy: 0.9706 +[3] Accuracy: 0.9471 +[4] Accuracy: 0.9737 +[5] Accuracy: 0.8980 +[6] Accuracy: 0.9757 +[7] Accuracy: 0.9573 +[8] Accuracy: 0.9770 +[9] Accuracy: 0.9792 +``` + +可见,学习率越高,训练速度越快,但训练时的波动也可能较大。 + +#### 4.3 损失函数值 + +![Loss value 4](./img/loss_value_4.png) + +可见,学习率越高,损失函数值下降越快,但整体的波动也可能较大。 diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index 101aac0..f992979 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -51,11 +51,12 @@ def numpy_run(): train_loss: List[float] = [] - epoch_number = 3 - learning_rate = 0.1 + epoch_number = 10 + batch_size = 256 + learning_rate = 0.5 for epoch in range(epoch_number): - for x, y in mini_batch(train_dataset): + for x, y in mini_batch(train_dataset, batch_size=batch_size): x: np.ndarray y: np.ndarray = one_hot(y) -- Gitee From b495be6939825c3be9a10e4aee3117e014e8d7bc Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 19:27:04 +0800 Subject: [PATCH 27/73] doc: fix tex layout for gitee --- assignment-2/submission/18307130003/README.md | 115 ++++++++++++------ 1 file changed, 76 insertions(+), 39 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 61860fc..6361105 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -1,3 +1,5 @@ + + # 实验报告 本次作业完成了选题 1 的实验内容,利用 NumPy 实现了一个 FNN 模型,并在 MNIST 数据集上进行了训练。 @@ -46,24 +48,28 @@ 输入一个 $n\times d$ 的矩阵 $X$ 和一个 $d\times d'$ 的矩阵 $W$,算子 `Matmul` 的正向传播公式为: -$$ + + +Equation 1.1 输出一个 $n\times d'$ 的矩阵 $Y$。 对于梯度的反向传播,有 -$$ + + +Equation 1.2 我们利用向量化(vectorization)进行对矩阵求导的求解: -$$ + + +Equation 1.3 这里 $\mathit{vec}(X_{m\times n})$ 表示向量 -$$ + + +Equation 1.3.1 $\otimes$ 表示 Kronecker 积,下标表示矩阵或向量的维度。 因此有 -$$ + + +Equation 1.4 类似 $(1.3)$ 的推导,同理可得 -$$ + + +Equation 1.5 #### 1.2 代码实现 @@ -161,7 +176,7 @@ class Matmul(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Relu` 的正向传播公式为: -$$ + + +Equation 2.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播,有 -$$ + + +Equation 2.2 这里 $\odot$ 表示 Hadamard 积,即逐元素(element-wise)乘积。 -其中,对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$,由 $(2.1)$ 有 +其中,对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$,由 $(2.1)$ 有 -$$ + -因此,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$,令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$,由 $(2.2)$ 有 +Equation 2.3 -$$ +因此,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$,令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$,由 $(2.2)$ 有 + + + +Equation 2.4 #### 2.2 代码实现 @@ -251,34 +274,42 @@ class Relu(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Log` 的正向传播公式为: -$$ + + +Equation 3.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播,有 -$$ + -其中,对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$,由 $(3.1)$ 有 +Equation 3.2 -$$ +其中,对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$,由 $(3.1)$ 有 + + + +Equation 3.3 -因此,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$,令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$,由 $(3.2)$ 有 +因此,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$,令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$,由 $(3.2)$ 有 -$$ + + +Equation 3.4 #### 3.2 代码实现 @@ -323,24 +354,28 @@ class Log(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$,对于 $X$ 中的每个元素 $X_{ij}$,算子 `Softmax` 的正向传播公式为: -$$ + + +Equation 4.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播,有 -$$ + -其中,对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$ 有 +Equation 4.2 -$$ +其中,对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$ 有 + + + +Equation 4.3 #### 4.2 代码实现 -- Gitee From b67730332426aa0e245100fff1d9096452f7f176 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 19:29:11 +0800 Subject: [PATCH 28/73] doc: fix typo --- assignment-2/submission/18307130003/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 6361105..13d2047 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -588,7 +588,7 @@ learning_rate = 0.1 ### 4. 实验 4 -这次,我们提高学习率(`learnin_rate`),观察预测准确率的变化。 +这次,我们提高学习率(`learning_rate`),观察预测准确率的变化。 #### 4.1 参数 -- Gitee From e30bf86b02c69c6bf081207779f55b1b35b0a393 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 3 Jun 2021 18:19:02 +0800 Subject: [PATCH 29/73] chore: initialize ass. 3 --- assignment-3/submission/18307130003/source.py | 474 +----------------- 1 file changed, 19 insertions(+), 455 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 1f75260..7ce55d3 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,473 +1,37 @@ -from abc import ABC, abstractmethod -import math import numpy as np -from utils import ( - UniformParameters, - assert_, - distance, - multinormal_pdf, - normal_pdf, -) -class Model(ABC): - ''' - The abstract class (ABC) of a model. - ''' - - @abstractmethod - def __init__(self, n_clusters: int, n_epochs: int) -> None: - ''' - Args: - `n_clusters`: the number of clusters to partition into - `n_epochs`: the number of epochs to run in total - ''' - - # Dataset properties - self.train_data: np.ndarray = None - self.data_size: int = 0 - self.dimension: int = 0 - - # Model parameters - self.k: int = n_clusters - self.n_epochs: int = n_epochs - - # Others - self.rng: np.random.Generator = np.random.default_rng() - self.FLOAT_MAX: float = np.finfo(float).max - self.EPS: float = np.finfo(float).eps - - @abstractmethod - def fit(self, train_data: np.ndarray) -> float: - ''' - Train the model using training data. - - Args: - `train_data`: shape(N, d) - - Return: - The training loss. - ''' +class KMeans: + def __init__(self, n_clusters): pass - @abstractmethod - def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the labels of testing data using the pre-trained model. - - Args: - `test_data`: shape(N, d) - - Return: - The predicted labels of testing data, shape(N). - ''' - + def fit(self, train_data): pass + def predict(self, test_data): + pass -class KMeans(Model): - ''' - k-means clustering algorithm, which aims to partition n observations into k - clusters in which each observation belongs to the cluster with the nearest - mean, serving as a prototype of the cluster. - ''' - - def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: - - super().__init__(n_clusters, n_epochs) - - # Model parameters - self.centroids: np.ndarray = None - - def label(self, point: np.ndarray, centroids: np.ndarray) -> int: - ''' - Args: - `point`: shape(d) - `centroids`: shape(k, d) - - Return: - The index of the closest centroid to the point. - ''' - - return np.argmin([distance(point, c) for c in centroids]) - - def fit(self, train_data: np.ndarray) -> float: - - self.data_size: int = train_data.shape[0] - self.dimension: int = ( - train_data.shape[1] if len(train_data.shape) > 1 - else 1 - ) - self.train_data = ( - train_data if self.dimension > 1 - else train_data.reshape(self.data_size,) - ) - min_loss = self.FLOAT_MAX - - # Run n_epochs times to find the best model. - for i in range(self.n_epochs): - # Select k initial centroids randomly from training data. - centroids: np.ndarray = train_data[ - np.random.choice(self.data_size, size=self.k, replace=False) - ] - labels: np.ndarray = np.zeros(self.data_size, dtype=int) - - while True: - # Assign labels to points based on their closest centroids. - new_labels = np.array([ - self.label(point, centroids) for point in train_data - ]) - - # Check for convergence. - if np.array_equal(new_labels, labels): - break - labels = new_labels - - # Find new centroids from the means of points in each cluster. - centroids = np.array([ - np.mean(train_data[labels == i], axis=0) for i in range(self.k) - ]) - - loss: float = np.sum((train_data - centroids[labels]) ** 2) - if loss < min_loss: - min_loss = loss - self.centroids = centroids - - print('Training progress: {}/{}, \tloss: {}'.format( - i + 1, self.n_epochs, loss, - ), end='\r') - - print() - return min_loss - - def predict(self, test_data: np.ndarray) -> np.ndarray: - - return np.array([ - self.label(point, self.centroids) for point in test_data - ]) - - -class GaussianMixture(Model): - ''' - Gaussian Mixture Model (GMM) is a probabilistic model that assumes there - are a certain number of Gaussian distributions, and each of these - distributions represent a cluster. Hence, a GMM tends to group the data - points belonging to a single distribution together. - ''' - - def __init__(self, n_clusters: int, n_epochs: int = 5) -> None: - - super().__init__(n_clusters, n_epochs) - - # Dataset properties - self.train_data: np.ndarray = None - self.data_size: int = 0 - self.dimension: int = 0 - - # Model parameters - - # means: shape(k, d) - self.means: np.ndarray = None - # covs: shape(k, d, d) - self.covs: np.ndarray = None - # scales: shape(k) - self.scales: np.ndarray = None - # weights: shape(k) - self.weights: np.ndarray = None - # likelihoods: shape(N, k) - self.likelihoods: np.ndarray = None - - self.best_means: np.ndarray = None - self.best_covs: np.ndarray = None - self.best_scales: np.ndarray = None - self.best_weights: np.ndarray = None - self.best_likelihoods: np.ndarray = None - - def _init_params(self) -> None: - ''' - Randomly initialize the starting parameters. - ''' - - # Select k initial centroids randomly from training data. - self.means = self.train_data[ - np.random.choice(self.data_size, size=self.k, replace=False) - ] - - if self.dimension > 1: - # Initialize the coefficient of variation of each Gaussian - # distribution to be an identity matrix. - self.covs = np.array([ - np.identity(self.dimension) for _i in range(self.k) - ]) - else: - # Initialize the standard deviation of each Gaussian distribution - # to be 1. - self.scales = np.ones(self.k) - - # Initialize the likelihood that an observation belongs to a cluster - # to be 1/k for all clusters. - self.weights = np.ones(self.k) / self.k - - def _e_step(self, dataset: np.ndarray = None, test_mode: bool = False) -> None: - ''' - In the E(xpectation) step, we calculate the likelihood of each - observation x_i belonging to each cluster using the current estimated - parameters. - - Args: - `dataset`: shape(N, d) - `test_mode`: whether test data is being used - ''' - - if dataset is None: - dataset = self.train_data - data_size: int = dataset.shape[0] - - if test_mode: - self.means = self.best_means - self.covs = self.best_covs - self.scales = self.best_scales - self.weights = self.best_weights - self.likelihoods = self.best_likelihoods - - # Calculate the posterior probability that an observation belongs to - # each Gaussian distribution, using Bayes' Theorem. - self.likelihoods = np.zeros((data_size, self.k)) - for i, x_i in enumerate(dataset): - # Calculate the likelihood of each observation x_i. - if self.dimension > 1: - f_i: np.ndarray = np.array([ - self.weights[k] * multinormal_pdf( - x_i, self.means[k], self.covs[k] + self.EPS - ) for k in range(self.k) - ]) - else: - f_i: np.ndarray = np.array([ - self.weights[k] * normal_pdf( - x_i, self.means[k], self.scales[k] + self.EPS - ) for k in range(self.k) - ]) - f_i_sum: float = np.sum(f_i) + self.EPS - self.likelihoods[i] = f_i / f_i_sum - - def _m_step(self) -> None: - ''' - In the M(aximization) step, we re-estimate our learning parameters for - each cluster. - ''' - - # shape(n, k).sum(axis=0) = shape(k) - cluster_likelihoods: np.ndarray = np.sum( - self.likelihoods, axis=0 - ) + self.EPS - assert_( - 'cluster_likelihoods.shape', - cluster_likelihoods.shape, - (self.k,), - ) - - # shape(k) / scalar = shape(k) - self.weights = cluster_likelihoods / self.data_size - assert_('weights.shape', self.weights.shape, (self.k,)) - - if self.dimension > 1: - # shape(k, n) * shape(n, d) = shape(k, d) - self.means = np.matmul( - self.likelihoods.T, self.train_data - ) / cluster_likelihoods[:, None] - assert_('means.shape', self.means.shape, (self.k, self.dimension)) - - # shape(k, d, d) - self.covs = np.array([ - # shape(d, d) / scalar = shape(d, d) - np.sum([ - # scalar * shape(d, 1) * shape(1, d) = shape(d, d) - self.likelihoods[i, k] * np.matmul( - x_m.reshape((self.dimension, 1)), - x_m.reshape((1, self.dimension)), - ) - # shape(n, d) - shape(d) = shape(n, d) - for i, x_m in enumerate(self.train_data - self.means[k]) - ], axis=0) / cluster_likelihoods[k] - for k in range(self.k) - ]) - assert_( - 'covs.shape', - self.covs.shape, - (self.k, self.dimension, self.dimension), - ) - else: - # shape(k, n) * shape(n) = shape(k) - # shape(k) / shape(k) = shape(k) - self.means = np.dot( - self.likelihoods.T, self.train_data - ) / cluster_likelihoods - assert_('means.shape', self.means.shape, (self.k,)) - - # shape(k) - self.scales = np.array([ - np.sqrt(np.sum([ - self.likelihoods[i, k] * (x_m ** 2) - for i, x_m in enumerate(self.train_data - self.means[k]) - ], axis=0) / cluster_likelihoods[k]) - for k in range(self.k) - ]) - assert_('scales.shape', self.scales.shape, (self.k,)) - - def fit(self, train_data: np.ndarray) -> float: - - self.data_size: int = train_data.shape[0] - self.dimension: int = ( - train_data.shape[1] if len(train_data.shape) > 1 - else 1 - ) - self.train_data = ( - train_data if self.dimension > 1 - else train_data.reshape(self.data_size,) - ) - min_loss = 0.0 - - # Run n_epochs times to find the best model. - for i in range(self.n_epochs): - self._init_params() - labels: np.ndarray = np.zeros(self.data_size, dtype=int) - - while True: - self._e_step() - self._m_step() - - # Assign labels to points based on the most possible cluster - # according to the likelihood matrix. - new_labels = np.argmax(self.likelihoods, axis=1) - - # Check for convergence. - if np.array_equal(new_labels, labels): - break - labels = new_labels - - loss: float = -np.mean(np.max(self.likelihoods, axis=1)) - if loss < min_loss: - min_loss = loss - self.best_means = self.means - self.best_covs = self.covs - self.best_scales = self.scales - self.best_weights = self.weights - self.best_likelihoods = self.likelihoods - - print('Training progress: {}/{}, \tloss: {}'.format( - i + 1, self.n_epochs, loss, - ), end='\r') - - print() - return min_loss - - def predict(self, test_data: np.ndarray) -> np.ndarray: - - self._e_step(dataset=test_data, test_mode=True) - return np.argmax(self.likelihoods, axis=1) - - -class ClusteringAlgorithm(Model): - ''' - Based on k-means clustering algorithm, using Gap Statistic to estimate the - number of clusters in the dataset automatically. - ''' - - def __init__( - self, max_n_clusters: int, n_epochs: int = 10, n_ref: int = 5 - ) -> None: - ''' - Args: - `max_n_clusters`: the maximum number of clusters to test - `n_epochs`: the number of epochs to run in total - `n_ref`: the number of reference datasets in Gap Statistic - ''' - - # Not setting the number of clusters at the beginning. - super().__init__(0, n_epochs) - - # Model parameters - self.max_k = max_n_clusters - self.n_ref = n_ref - self.gaps: np.ndarray = None - self.BREAK_THRESHOLD = 3 - - self.best_model = None - - def generate_uniform(self, param: UniformParameters) -> np.ndarray: - ''' - Generate a dataset from a uniform distribution with given parameters. - - Args: - `param`: parameters used to generate a dataset - - Return: - shape(N, d) - ''' - - size, (low, high) = param - dimension: int - if np.isscalar(low): - assert_('np.isscalar(high)', np.isscalar(high), True) - dimension = 1 - return self.rng.uniform(low, high, size) - else: - assert_('low.shape[0]', low.shape[0], high.shape[0]) - dimension = low.shape[0] - return self.rng.uniform(low, high, (size, dimension)) - - def fit(self, train_data: np.ndarray) -> float: - gaps, max_gap, prev_gap = [0.0], 0.0, 0.0 - min_loss = self.FLOAT_MAX - # Break the loop if the gap statistics is not likely to ascend anymore. - break_counter = 0 +class GaussianMixture: - for k in range(1, self.max_k + 1): - model = KMeans(k, self.n_epochs) - loss = model.fit(train_data) + def __init__(self, n_clusters): + pass - low: np.ndarray = np.amin(train_data, axis=0) - high: np.ndarray = np.amax(train_data, axis=0) + def fit(self, train_data): + pass - # Generate n_ref reference datasets, cluster each one using the - # current model, and calculate the gap statistic. - log_random_loss: float = np.mean([ - # Since the dataset is generated from a uniform distribution, - # there's no need to run the k-means clustering algorithm for - # multiple times. - math.log(KMeans(k, 1).fit(self.generate_uniform( - UniformParameters( - size=model.data_size, - intervals=(low, high), - ) - ))) for _i in range(self.n_ref) - ]) - gap = log_random_loss - math.log(loss) - gaps.append(gap) - print('Tried k: {}/{}, \tgap statistics: {}'.format( - k, self.max_k, gap - )) + def predict(self, test_data): + pass - if gap > max_gap: - max_gap = gap - min_loss = loss - self.best_model = model - if gap > prev_gap: - break_counter = 0 - else: - break_counter += 1 - if break_counter >= self.BREAK_THRESHOLD: - print('Gap statistics is not ascending, loop terminated.') - break - prev_gap = gap +class ClusteringAlgorithm: - self.gaps = np.array(gaps) - print('Estimated k: {}'.format(self.best_model.k)) - return min_loss + def __init__(self): + pass - def predict(self, test_data: np.ndarray) -> np.ndarray: + def fit(self, train_data): + pass - return self.best_model.predict(test_data) + def predict(self, test_data): + pass -- Gitee From 36ba7c37315d1269adde27bfdf6ae58cdd20a247 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 4 Jun 2021 00:11:59 +0800 Subject: [PATCH 30/73] feat: implement k-means clustering algorithm --- assignment-3/submission/18307130003/source.py | 93 +++++++++++++++++-- 1 file changed, 87 insertions(+), 6 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 7ce55d3..29d9802 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,16 +1,97 @@ +from typing import Tuple import numpy as np +def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: + ''' + Args: + `point_1`: shape(d) + `point_2`: shape(d) + + Return: + The Euclidean distance between two points. + ''' + + return np.linalg.norm(point_1 - point_2) + + class KMeans: + ''' + k-means clustering algorithm, which aims to partition n observations into k + clusters in which each observation belongs to the cluster with the nearest + mean, serving as a prototype of the cluster. + ''' - def __init__(self, n_clusters): - pass + def __init__(self, n_clusters: int) -> None: + ''' + Args: + `n_clusters`: the number of clusters to partition into + ''' - def fit(self, train_data): - pass + self.k: int = n_clusters + self.eps: float = np.finfo(float).eps - def predict(self, test_data): - pass + def label(self, point: np.ndarray, centroids: np.ndarray) -> int: + ''' + Args: + `point`: shape(d) + `centroids`: shape(k, d) + + Return: + The index of the closest centroid to the point. + ''' + + return np.argmin([distance(point, c) for c in centroids]) + + def fit(self, train_data: np.ndarray) -> None: + ''' + Train the model using training data. + + Args: + `train_data`: shape(N, d) + ''' + + shape: Tuple[int, int] = train_data.shape + data_size: int = shape[0] + + # Select k initial centroids randomly from training data. + self.centroids: np.ndarray = train_data[ + np.random.choice(data_size, size=self.k, replace=False) + ] + + labels: np.ndarray = np.zeros(data_size, dtype=int) + + while True: + # Assign labels to points based on their closest centroids. + labels = np.array([ + self.label(point, self.centroids) for point in train_data + ]) + + # Find new centroids from the means of points in each cluster. + new_centroids = np.array([ + np.mean(train_data[labels == i], axis=0) for i in range(self.k) + ]) + + # Check for convergence + if distance(new_centroids, self.centroids) < self.eps: + break + + self.centroids = new_centroids + + def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the labels of testing data using the pre-trained model. + + Args: + `test_data`: shape(N, d) + + Return: + The predicted labels of testing data, shape(N). + ''' + + return np.array([ + self.label(point, self.centroids) for point in test_data + ]) class GaussianMixture: -- Gitee From 702efc9c2c735e487efd34be2e154a7b51f20ba7 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sat, 5 Jun 2021 22:57:56 +0800 Subject: [PATCH 31/73] fix: train the model multiple times for better result refactor: create abstract class Model for models --- assignment-3/submission/18307130003/source.py | 114 +++++++++++------- 1 file changed, 72 insertions(+), 42 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 29d9802..0e5ff47 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,3 +1,4 @@ +from abc import ABC, abstractmethod from typing import Tuple import numpy as np @@ -15,21 +16,57 @@ def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: return np.linalg.norm(point_1 - point_2) -class KMeans: +class Model(ABC): + ''' + The abstract class (ABC) of a model. + ''' + + @abstractmethod + def __init__(self) -> None: + pass + + @abstractmethod + def fit(self, train_data: np.ndarray) -> None: + ''' + Train the model using training data. + + Args: + `train_data`: shape(N, d) + ''' + + pass + + @abstractmethod + def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the labels of testing data using the pre-trained model. + + Args: + `test_data`: shape(N, d) + + Return: + The predicted labels of testing data, shape(N). + ''' + + pass + + +class KMeans(Model): ''' k-means clustering algorithm, which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. ''' - def __init__(self, n_clusters: int) -> None: + def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: ''' Args: `n_clusters`: the number of clusters to partition into + `n_epochs`: the number of epochs to run in total ''' self.k: int = n_clusters - self.eps: float = np.finfo(float).eps + self.n_epochs: int = n_epochs def label(self, point: np.ndarray, centroids: np.ndarray) -> int: ''' @@ -44,50 +81,43 @@ class KMeans: return np.argmin([distance(point, c) for c in centroids]) def fit(self, train_data: np.ndarray) -> None: - ''' - Train the model using training data. - - Args: - `train_data`: shape(N, d) - ''' shape: Tuple[int, int] = train_data.shape data_size: int = shape[0] - - # Select k initial centroids randomly from training data. - self.centroids: np.ndarray = train_data[ - np.random.choice(data_size, size=self.k, replace=False) - ] - - labels: np.ndarray = np.zeros(data_size, dtype=int) - - while True: - # Assign labels to points based on their closest centroids. - labels = np.array([ - self.label(point, self.centroids) for point in train_data - ]) - - # Find new centroids from the means of points in each cluster. - new_centroids = np.array([ - np.mean(train_data[labels == i], axis=0) for i in range(self.k) - ]) - - # Check for convergence - if distance(new_centroids, self.centroids) < self.eps: - break - - self.centroids = new_centroids + min_loss: float = np.finfo(float).max + + # Run n_epochs times to find the best model + for i in range(self.n_epochs): + # Select k initial centroids randomly from training data. + centroids: np.ndarray = train_data[ + np.random.choice(data_size, size=self.k, replace=False) + ] + labels: np.ndarray = np.zeros(data_size, dtype=int) + + while True: + # Assign labels to points based on their closest centroids. + new_labels = np.array([ + self.label(point, centroids) for point in train_data + ]) + + # Check for convergence + if np.array_equal(new_labels, labels): + break + labels = new_labels + + # Find new centroids from the means of points in each cluster. + centroids = np.array([ + np.mean(train_data[labels == i], axis=0) for i in range(self.k) + ]) + + loss: float = np.mean((train_data - centroids[labels]) ** 2) + if loss < min_loss: + min_loss = loss + self.centroids = centroids + + print(f'Progress: {i + 1} / {self.n_epochs}', end='\r') def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the labels of testing data using the pre-trained model. - - Args: - `test_data`: shape(N, d) - - Return: - The predicted labels of testing data, shape(N). - ''' return np.array([ self.label(point, self.centroids) for point in test_data -- Gitee From 165809d0a4970bed1dbf96fc6cf7e76f070a751c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sat, 5 Jun 2021 22:59:40 +0800 Subject: [PATCH 32/73] feat: implement a tester docs: create 2 figures for k-means clustering algorithm --- .../18307130003/img/k-means_test_1.png | Bin 0 -> 72911 bytes 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- Model, - KMeans, - GaussianMixture as GMM, -) -from utils import assert_, NormalParameters +from source import Model, KMeans + + +class Parameters(NamedTuple): + ''' + Attributes: + `mean`: the mean of dataset + `cov`: the coefficient of variation (COV) of dataset + `size`: the number of points in the dataset + ''' + + mean: Tuple[int, int] + cov: List[List[float]] + size: int class TestSuite: @@ -17,11 +23,11 @@ class TestSuite: ''' def __init__(self) -> None: - self.rng: np.random.Generator = np.random.default_rng() + pass - def generate_normal(self, param: NormalParameters) -> np.ndarray: + def generate(self, param: Parameters) -> np.ndarray: ''' - Generate a dataset from a Gaussian distribution with given parameters. + Generate a dataset with given parameters. Args: `param`: parameters used to generate a dataset @@ -30,11 +36,8 @@ class TestSuite: shape(N, d) ''' - size, mean, cov, scale = param - if len(mean) > 1: - return self.rng.multivariate_normal(mean, cov, size) - else: - return self.rng.normal(mean[0], scale, size) + mean, cov, size = param + return np.random.multivariate_normal(mean, cov, size) def combine(self, *datasets: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: ''' @@ -59,7 +62,7 @@ class TestSuite: labels = labels[indices] return dataset, labels - def generate_data(self, *params: NormalParameters) -> Tuple[np.ndarray, int]: + def generate_data(self, *params: Parameters) -> Tuple[np.ndarray, int]: ''' Generate a dataset for tests. @@ -72,164 +75,95 @@ class TestSuite: ''' dataset, _labels = self.combine(*tuple( - self.generate_normal(p) for p in params + self.generate(p) for p in params )) n_clusters: int = len(params) return dataset, n_clusters - def train( - self, train_data: np.ndarray, model: Model - ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + def evaluate( + self, dataset: np.ndarray, model_class: Type[Model], n_clusters: int + ) -> Tuple[np.ndarray, np.ndarray]: ''' - Train a model with training data. + Evaluate a model with a given dataset. Args: - `train_data`: shape(N, d) - `model`: the model that we need to train + `dataset`: shape(N, d) + `model_class`: the model class that we need to evaluate `n_clusters`: the number of clusters to partition into Return: - `train_labels`: the predicted labels of training data, shape(N) - `centroids`: the centroids calculated from training data, shape(k, d) - `gaps`: the gap statistics of each k, shape(k + 1) + `labels`: The predicted labels of testing data, shape(N) + `centroids`: (Optional) \ + The centroids calculated from training data, shape(k, d) ''' - model.fit(train_data) - train_labels = model.predict(train_data) - centroids: np.ndarray = None - gaps: np.ndarray = None - - if isinstance(model, KMeans): - centroids = model.centroids - elif isinstance(model, GMM): - centroids = model.means - elif isinstance(model, AutoKMeans): - centroids = model.best_model.centroids - gaps = model.gaps - return train_labels, centroids, gaps - - def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: - ''' - Evaluate a model with testing data. + model = model_class(n_clusters) + model.fit(dataset) + labels = model.predict(dataset) + centroids = model.centroids if isinstance(model, KMeans) else None + return labels, centroids - Args: - `test_data`: shape(N, d) - `model`: the model that we need to evaluate + def k_means_data_1(self) -> Tuple[np.ndarray, int]: + ''' + Test data 1 for k-means clustering algorithm. Return: - `test_labels`: The predicted labels of testing data, shape(N) + `dataset`: shape(N, d) + `n_clusters`: the number of clusters to partition into ''' - test_labels = model.predict(test_data) - return test_labels - - def test_data_1(self) -> Tuple[np.ndarray, int]: - return self.generate_data( - NormalParameters( - size=800, + Parameters( mean=(1, 2), cov=[[73, 0], [0, 22]], + size=800, ), - NormalParameters( - size=200, + Parameters( mean=(16, -5), cov=[[21.2, 0], [0, 32.1]], + size=200, ), - NormalParameters( - size=1000, + Parameters( mean=(10, 22), cov=[[10, 5], [5, 10]], + size=1000, ), ) - def test_data_2(self) -> Tuple[np.ndarray, int]: + def k_means_data_2(self) -> Tuple[np.ndarray, int]: + ''' + Test data 2 for k-means clustering algorithm. + + Return: + `dataset`: shape(N, d) + `n_clusters`: the number of clusters to partition into + ''' return self.generate_data( - NormalParameters( - size=800, + Parameters( mean=(1, 0), cov=[[73, 0], [0, 22]], + size=800, ), - NormalParameters( - size=400, + Parameters( mean=(20, 15), cov=[[21.2, 0], [0, 32.1]], + size=400, ), - NormalParameters( - size=1000, + Parameters( mean=(10, -22), cov=[[10, 5], [5, 10]], + size=1000, ), - NormalParameters( - size=500, + Parameters( mean=(-12, -6), cov=[[7, 3], [3, 16]], + size=500, ), - NormalParameters( - size=600, + Parameters( mean=(-15, 17), cov=[[15, 0], [0, 12]], - ), - ) - - def test_data_3(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(-6, 3, 5), - cov=[[73, 0, 0], [0, 50, 0], [0, 0, 22]], - ), - NormalParameters( - size=500, - mean=(12, 0, -10), - cov=[[20, 5, 0], [5, 20, 0], [0, 0, 20]], - ), - NormalParameters( - size=800, - mean=(10, -20, 0), - cov=[[10, 1, 3], [1, 10, 0], [3, 0, 10]], - ), - ) - - def test_data_4(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=100, - mean=(-20,), - scale=2, - ), - NormalParameters( - size=150, - mean=(0,), - scale=1, - ), - NormalParameters( - size=100, - mean=(15,), - scale=2, - ), - ) - - def test_data_5(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(0, -5), - cov=[[73, 0], [0, 2]], - ), - NormalParameters( - size=500, - mean=(-3, 0), - cov=[[100, 0], [0, 2]], - ), - NormalParameters( - size=500, - mean=(2, 5), - cov=[[70, 1], [1, 3]], + size=600, ), ) @@ -241,55 +175,22 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - ('k-means_1', self.test_data_1, KMeans, 0), - ('k-means_2', self.test_data_2, KMeans, 0), - ('k-means_3', self.test_data_3, KMeans, 0), - ('k-means_4', self.test_data_4, KMeans, 0), - ('k-means_5', self.test_data_5, KMeans, 0), - ('gmm_1', self.test_data_1, GMM, 0), - ('gmm_2', self.test_data_2, GMM, 0), - ('gmm_3', self.test_data_3, GMM, 0), - ('gmm_4', self.test_data_4, GMM, 0), - ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), - ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), - ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), - ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), - ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), + ('k-means_test_1', self.k_means_data_1, KMeans, 0), + ('k-means_test_2', self.k_means_data_2, KMeans, 0), ] for testcase in testcases: - name, get_dataset, model_class, n_clusters = testcase - - # Obtain training data and testing data - dataset, real_n_clusters = get_dataset() - train_size: int = math.floor(dataset.shape[0] * 0.8) - train_data: np.ndarray = dataset[:train_size] - test_data: np.ndarray = dataset[train_size:] - - # Train the model with training data - model = model_class(n_clusters or real_n_clusters) - train_labels, centroids, gaps = self.train(train_data, model) - - # Evaluate the model with testing data - test_labels = self.evaluate(test_data, model) - - # Visualize the datasets with labels - visualize(name + '_train', train_data, train_labels, centroids) - visualize(name + '_test', test_data, test_labels, centroids) - - # Visualize the gap statistics for - if gaps is not None: - visualize_gaps(name + '_gaps', gaps) - - print(f'{name}: Done.') + test_name, get_dataset, model_class, n_clusters = testcase + dataset, dataset_n_clusters = get_dataset() + labels, centroids = self.evaluate( + dataset, model_class, n_clusters or dataset_n_clusters + ) + visualize(test_name, dataset, labels, centroids) + print(f'\n{test_name}: Done.') def visualize( - name: str, - dataset: np.ndarray, - labels: np.ndarray, - centroids: np.ndarray = None, + name: str, dataset: np.ndarray, labels: np.ndarray, centroids: np.ndarray = None ) -> None: ''' Visualize a dataset with labels. @@ -301,44 +202,12 @@ def visualize( `centroids`: shape(k, d) ''' - assert_('dataset.shape[0]', dataset.shape[0], labels.shape[0]) - - # Plot the data points and the centroids. - if len(dataset.shape) > 1: - plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) - if centroids is not None: - plt.scatter( - centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5, - ) - else: - plt.scatter(dataset, np.zeros(dataset.shape[0]), c=labels, s=30) - if centroids is not None: - plt.yticks([]) - plt.scatter( - centroids, np.zeros(centroids.shape[0]), - c='black', s=100, alpha=0.5, - ) - - # Save the figure to a local file. - plt.savefig(f'img/{name}') - plt.clf() - - -def visualize_gaps(name: str, gaps: np.ndarray) -> None: - ''' - Visualize the gap statistics. - - Args: - `name`: the output filename when saving the figure - `gaps`: the gap statistics of each k, shape(k + 1) - ''' - - # Plot the gap statistics. - indices = np.arange(1, gaps.shape[0], dtype=int) - plt.xticks(indices) - plt.plot(indices, gaps[indices], '-bo') - - # Save the figure to a local file. + assert dataset.shape[0] == labels.shape[0] + plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30, cmap='viridis') + if centroids is not None: + plt.scatter( + centroids[:, 0], centroids[:, 1], c='black', s=150, alpha=0.5 + ) plt.savefig(f'img/{name}') plt.clf() -- Gitee From c0f2228062b61604e67d94466f6413bb35a03f3c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 6 Jun 2021 00:44:14 +0800 Subject: [PATCH 33/73] fix: separate training data and testing data fix: minor changes docs: change figures used --- .../18307130003/img/k-means_test_1.png | Bin 72911 -> 0 bytes .../18307130003/img/k-means_test_2.png | Bin 81425 -> 0 bytes assignment-3/submission/18307130003/source.py | 2 +- assignment-3/submission/18307130003/tester.py | 87 +++++++++++++----- 4 files changed, 66 insertions(+), 23 deletions(-) delete mode 100644 assignment-3/submission/18307130003/img/k-means_test_1.png delete mode 100644 assignment-3/submission/18307130003/img/k-means_test_2.png diff --git a/assignment-3/submission/18307130003/img/k-means_test_1.png b/assignment-3/submission/18307130003/img/k-means_test_1.png deleted file mode 100644 index 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--git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index f27bc81..93d1c74 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -1,6 +1,7 @@ from typing import Callable, List, NamedTuple, Tuple, Type import numpy as np import matplotlib.pyplot as plt +from math import floor from source import Model, KMeans @@ -80,28 +81,40 @@ class TestSuite: n_clusters: int = len(params) return dataset, n_clusters - def evaluate( - self, dataset: np.ndarray, model_class: Type[Model], n_clusters: int - ) -> Tuple[np.ndarray, np.ndarray]: + def train(self, train_data: np.ndarray, model: Model) -> Tuple[np.ndarray, np.ndarray]: ''' - Evaluate a model with a given dataset. + Train a model with training data. Args: - `dataset`: shape(N, d) - `model_class`: the model class that we need to evaluate + `train_data`: shape(N, d) + `model`: the model that we need to train `n_clusters`: the number of clusters to partition into Return: - `labels`: The predicted labels of testing data, shape(N) + `train_labels`: The predicted labels of training data, shape(N) `centroids`: (Optional) \ The centroids calculated from training data, shape(k, d) ''' - model = model_class(n_clusters) - model.fit(dataset) - labels = model.predict(dataset) + model.fit(train_data) + train_labels = model.predict(train_data) centroids = model.centroids if isinstance(model, KMeans) else None - return labels, centroids + return train_labels, centroids + + def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: + ''' + Evaluate a model with testing data. + + Args: + `test_data`: shape(N, d) + `model`: the model that we need to evaluate + + Return: + `test_labels`: The predicted labels of testing data, shape(N) + ''' + + test_labels = model.predict(test_data) + return test_labels def k_means_data_1(self) -> Tuple[np.ndarray, int]: ''' @@ -175,22 +188,48 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - ('k-means_test_1', self.k_means_data_1, KMeans, 0), - ('k-means_test_2', self.k_means_data_2, KMeans, 0), + ('k-means_1', self.k_means_data_1, KMeans, 0), + ('k-means_2', self.k_means_data_2, KMeans, 0), ] for testcase in testcases: - test_name, get_dataset, model_class, n_clusters = testcase - dataset, dataset_n_clusters = get_dataset() - labels, centroids = self.evaluate( - dataset, model_class, n_clusters or dataset_n_clusters + name, get_dataset, model_class, n_clusters = testcase + + # Obtain training data and testing data + dataset, real_n_clusters = get_dataset() + train_size: int = floor(dataset.shape[0] * 0.8) + train_data: np.ndarray = dataset[:train_size] + test_data: np.ndarray = dataset[train_size:] + + # Train the model with training data + model = model_class(n_clusters or real_n_clusters) + train_predicted_labels, centroids = self.train(train_data, model) + + # Evaluate the model with testing data + test_predicted_labels = self.evaluate(test_data, model) + + # Visualize the datasets with labels + visualize( + name + '_train', + train_data, + train_predicted_labels, + centroids, + ) + visualize( + name + '_test', + test_data, + test_predicted_labels, + centroids, ) - visualize(test_name, dataset, labels, centroids) - print(f'\n{test_name}: Done.') + + print(f'\n{name}: Done.') def visualize( - name: str, dataset: np.ndarray, labels: np.ndarray, centroids: np.ndarray = None + name: str, + dataset: np.ndarray, + labels: np.ndarray, + centroids: np.ndarray = None, ) -> None: ''' Visualize a dataset with labels. @@ -203,11 +242,15 @@ def visualize( ''' assert dataset.shape[0] == labels.shape[0] - plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30, cmap='viridis') + + # Plot the data points and the centroids + plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) if centroids is not None: plt.scatter( - centroids[:, 0], centroids[:, 1], c='black', s=150, alpha=0.5 + centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5 ) + + # Save the figure to a local file plt.savefig(f'img/{name}') plt.clf() -- Gitee From 58b82293d0e98a6d280042651a1eff1c69cadd7c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 6 Jun 2021 00:49:08 +0800 Subject: [PATCH 34/73] style: shorten variable names --- assignment-3/submission/18307130003/tester.py | 18 ++++-------------- 1 file changed, 4 insertions(+), 14 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 93d1c74..e61ce8e 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -203,24 +203,14 @@ class TestSuite: # Train the model with training data model = model_class(n_clusters or real_n_clusters) - train_predicted_labels, centroids = self.train(train_data, model) + train_labels, centroids = self.train(train_data, model) # Evaluate the model with testing data - test_predicted_labels = self.evaluate(test_data, model) + test_labels = self.evaluate(test_data, model) # Visualize the datasets with labels - visualize( - name + '_train', - train_data, - train_predicted_labels, - centroids, - ) - visualize( - name + '_test', - test_data, - test_predicted_labels, - centroids, - ) + visualize(name + '_train', train_data, train_labels, centroids) + visualize(name + '_test', test_data, test_labels, centroids) print(f'\n{name}: Done.') -- Gitee From 600d19ea06cd5d88ae188bcd10f2e378ad1839bb Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 6 Jun 2021 02:36:40 +0800 Subject: [PATCH 35/73] feat: support more dimensions for k-means test: add more tests for k-means docs: add figures for k-means_3, k-means_4 --- .../18307130003/img/k-means_4_test.png | Bin 7800 -> 11367 bytes 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a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index e61ce8e..7208fd7 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -1,4 +1,4 @@ -from typing import Callable, List, NamedTuple, Tuple, Type +from typing import Callable, List, NamedTuple, Tuple, Type, Union import numpy as np import matplotlib.pyplot as plt from math import floor @@ -8,14 +8,20 @@ from source import Model, KMeans class Parameters(NamedTuple): ''' Attributes: - `mean`: the mean of dataset - `cov`: the coefficient of variation (COV) of dataset - `size`: the number of points in the dataset + `dimension`: the dimension of data points + `mean`: the mean of the distribution + `cov`: (for dimension > 1) \ + the coefficient of variation of the distribution + `scale`: (for dimension == 1) \ + the standard deviation of the distribution + `size`: the number of data points in the dataset ''' - mean: Tuple[int, int] - cov: List[List[float]] - size: int + dimension: int + mean: Union[Tuple[float, ...], float] + cov: List[List[float]] = [[0]] + scale: float = 0 + size: int = 1000 class TestSuite: @@ -24,7 +30,7 @@ class TestSuite: ''' def __init__(self) -> None: - pass + self.rng: np.random.Generator = np.random.default_rng() def generate(self, param: Parameters) -> np.ndarray: ''' @@ -37,8 +43,11 @@ class TestSuite: shape(N, d) ''' - mean, cov, size = param - return np.random.multivariate_normal(mean, cov, size) + dimension, mean, cov, scale, size = param + if dimension > 1: + return self.rng.multivariate_normal(mean, cov, size) + else: + return self.rng.normal(mean, scale, size) def combine(self, *datasets: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: ''' @@ -92,8 +101,7 @@ class TestSuite: Return: `train_labels`: The predicted labels of training data, shape(N) - `centroids`: (Optional) \ - The centroids calculated from training data, shape(k, d) + `centroids`: The centroids calculated from training data, shape(k, d) ''' model.fit(train_data) @@ -119,24 +127,23 @@ class TestSuite: def k_means_data_1(self) -> Tuple[np.ndarray, int]: ''' Test data 1 for k-means clustering algorithm. - - Return: - `dataset`: shape(N, d) - `n_clusters`: the number of clusters to partition into ''' return self.generate_data( Parameters( + dimension=2, mean=(1, 2), cov=[[73, 0], [0, 22]], size=800, ), Parameters( + dimension=2, mean=(16, -5), cov=[[21.2, 0], [0, 32.1]], size=200, ), Parameters( + dimension=2, mean=(10, 22), cov=[[10, 5], [5, 10]], size=1000, @@ -146,40 +153,93 @@ class TestSuite: def k_means_data_2(self) -> Tuple[np.ndarray, int]: ''' Test data 2 for k-means clustering algorithm. - - Return: - `dataset`: shape(N, d) - `n_clusters`: the number of clusters to partition into ''' return self.generate_data( Parameters( + dimension=2, mean=(1, 0), cov=[[73, 0], [0, 22]], size=800, ), Parameters( + dimension=2, mean=(20, 15), cov=[[21.2, 0], [0, 32.1]], size=400, ), Parameters( + dimension=2, mean=(10, -22), cov=[[10, 5], [5, 10]], size=1000, ), Parameters( + dimension=2, mean=(-12, -6), cov=[[7, 3], [3, 16]], size=500, ), Parameters( + dimension=2, mean=(-15, 17), cov=[[15, 0], [0, 12]], size=600, ), ) + def k_means_data_3(self) -> Tuple[np.ndarray, int]: + ''' + Test data 3 for k-means clustering algorithm. + ''' + + return self.generate_data( + Parameters( + dimension=3, + mean=(-6, 3, 5), + cov=[[73, 0, 0], [0, 50, 0], [0, 0, 22]], + size=800, + ), + Parameters( + dimension=3, + mean=(12, 0, -10), + cov=[[20, 5, 0], [5, 20, 0], [0, 0, 20]], + size=500, + ), + Parameters( + dimension=3, + mean=(10, -20, 0), + cov=[[10, 1, 3], [1, 10, 0], [3, 0, 10]], + size=800, + ), + ) + + def k_means_data_4(self) -> Tuple[np.ndarray, int]: + ''' + Test data 4 for k-means clustering algorithm. + ''' + + return self.generate_data( + Parameters( + dimension=1, + mean=-20, + scale=6, + size=100, + ), + Parameters( + dimension=1, + mean=0, + scale=3, + size=150, + ), + Parameters( + dimension=1, + mean=15, + scale=3, + size=100, + ), + ) + def run(self) -> None: ''' Run all the tests. @@ -190,6 +250,8 @@ class TestSuite: ]] = [ ('k-means_1', self.k_means_data_1, KMeans, 0), ('k-means_2', self.k_means_data_2, KMeans, 0), + ('k-means_3', self.k_means_data_3, KMeans, 0), + ('k-means_4', self.k_means_data_4, KMeans, 0), ] for testcase in testcases: @@ -234,11 +296,20 @@ def visualize( assert dataset.shape[0] == labels.shape[0] # Plot the data points and the centroids - plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) - if centroids is not None: - plt.scatter( - centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5 - ) + if len(dataset.shape) > 1: + plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) + if centroids is not None: + plt.scatter( + centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5, + ) + else: + plt.scatter(dataset, labels, c=labels, s=30) + if centroids is not None: + plt.yticks(range(0, centroids.shape[0])) + plt.scatter( + centroids, np.arange(0, centroids.shape[0]), + c='black', s=100, alpha=0.5, + ) # Save the figure to a local file plt.savefig(f'img/{name}') -- Gitee From ea095d4cd1632325415a267f288da136582f7979 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 6 Jun 2021 02:54:32 +0800 Subject: [PATCH 36/73] refactor: extract init method to base class --- assignment-3/submission/18307130003/source.py | 32 +++++++++++-------- 1 file changed, 19 insertions(+), 13 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index f7ef1ec..a78453b 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -22,8 +22,15 @@ class Model(ABC): ''' @abstractmethod - def __init__(self) -> None: - pass + def __init__(self, n_clusters: int, n_epochs: int) -> None: + ''' + Args: + `n_clusters`: the number of clusters to partition into + `n_epochs`: the number of epochs to run in total + ''' + + self.k: int = n_clusters + self.n_epochs: int = n_epochs @abstractmethod def fit(self, train_data: np.ndarray) -> None: @@ -59,14 +66,7 @@ class KMeans(Model): ''' def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: - ''' - Args: - `n_clusters`: the number of clusters to partition into - `n_epochs`: the number of epochs to run in total - ''' - - self.k: int = n_clusters - self.n_epochs: int = n_epochs + super().__init__(n_clusters, n_epochs) def label(self, point: np.ndarray, centroids: np.ndarray) -> int: ''' @@ -124,10 +124,16 @@ class KMeans(Model): ]) -class GaussianMixture: +class GaussianMixture(Model): + ''' + Gaussian Mixture Model (GMM) is a probabilistic model that assumes there + are a certain number of Gaussian distributions, and each of these + distributions represent a cluster. Hence, a GMM tends to group the data + points belonging to a single distribution together. + ''' - def __init__(self, n_clusters): - pass + def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: + super().__init__(n_clusters, n_epochs) def fit(self, train_data): pass -- Gitee From 747f5966798b8bd95b567edd4808e6abc2ddfffc Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 6 Jun 2021 03:00:29 +0800 Subject: [PATCH 37/73] fix: minor style fix for logging --- assignment-3/submission/18307130003/source.py | 8 +++++--- assignment-3/submission/18307130003/tester.py | 2 +- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index a78453b..9741185 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -115,7 +115,9 @@ class KMeans(Model): min_loss = loss self.centroids = centroids - print(f'Training progress: {i + 1} / {self.n_epochs}', end='\r') + print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') + + print() def predict(self, test_data: np.ndarray) -> np.ndarray: @@ -135,10 +137,10 @@ class GaussianMixture(Model): def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: super().__init__(n_clusters, n_epochs) - def fit(self, train_data): + def fit(self, train_data: np.ndarray) -> None: pass - def predict(self, test_data): + def predict(self, test_data: np.ndarray) -> np.ndarray: pass diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 7208fd7..c1e909f 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -274,7 +274,7 @@ class TestSuite: visualize(name + '_train', train_data, train_labels, centroids) visualize(name + '_test', test_data, test_labels, centroids) - print(f'\n{name}: Done.') + print(f'{name}: Done.') def visualize( -- Gitee From 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b/assignment-3/submission/18307130003/tester.py @@ -303,11 +303,11 @@ def visualize( centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5, ) else: - plt.scatter(dataset, labels, c=labels, s=30) + plt.scatter(dataset, np.zeros(dataset.shape[0]), c=labels, s=30) if centroids is not None: - plt.yticks(range(0, centroids.shape[0])) + plt.yticks(None) plt.scatter( - centroids, np.arange(0, centroids.shape[0]), + centroids, np.zeros(centroids.shape[0]), c='black', s=100, alpha=0.5, ) -- Gitee From 7cf51b3de5e45cb962986be1eaa7e6a62157ec2c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 00:52:05 +0800 Subject: [PATCH 39/73] feat: implement Gaussian Mixture Model --- assignment-3/submission/18307130003/source.py | 157 +++++++++++++++--- assignment-3/submission/18307130003/utils.py | 66 +------- 2 files changed, 140 insertions(+), 83 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 9741185..d676a66 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,19 +1,7 @@ from abc import ABC, abstractmethod from typing import Tuple import numpy as np - - -def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: - ''' - Args: - `point_1`: shape(d) - `point_2`: shape(d) - - Return: - The Euclidean distance between two points. - ''' - - return np.linalg.norm(point_1 - point_2) +from utils import distance, multinormal_pdf class Model(ABC): @@ -29,9 +17,14 @@ class Model(ABC): `n_epochs`: the number of epochs to run in total ''' + # Model parameters self.k: int = n_clusters self.n_epochs: int = n_epochs + # Others + self.FLOAT_MAX: float = np.finfo(float).max + self.EPS: float = np.finfo(float).eps + @abstractmethod def fit(self, train_data: np.ndarray) -> None: ''' @@ -66,8 +59,12 @@ class KMeans(Model): ''' def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: + super().__init__(n_clusters, n_epochs) + # Model parameters + self.centroids: np.ndarray = None + def label(self, point: np.ndarray, centroids: np.ndarray) -> int: ''' Args: @@ -82,11 +79,10 @@ class KMeans(Model): def fit(self, train_data: np.ndarray) -> None: - shape: Tuple[int, int] = train_data.shape - data_size: int = shape[0] - min_loss: float = np.finfo(float).max + data_size: int = train_data.shape[0] + min_loss = self.FLOAT_MAX - # Run n_epochs times to find the best model + # Run n_epochs times to find the best model. for i in range(self.n_epochs): # Select k initial centroids randomly from training data. centroids: np.ndarray = train_data[ @@ -100,7 +96,7 @@ class KMeans(Model): self.label(point, centroids) for point in train_data ]) - # Check for convergence + # Check for convergence. if np.array_equal(new_labels, labels): break labels = new_labels @@ -134,14 +130,133 @@ class GaussianMixture(Model): points belonging to a single distribution together. ''' - def __init__(self, n_clusters: int, n_epochs: int = 10) -> None: + def __init__(self, n_clusters: int, n_epochs: int = 1) -> None: + super().__init__(n_clusters, n_epochs) + # Dataset properties + self.train_data: np.ndarray = None + self.data_size: int = 0 + self.dimension: int = 0 + + # Model parameters + + # means: shape(k, d) + self.means: np.ndarray = None + # covs: shape(k, d, d) + self.covs: np.ndarray = None + # weights: shape(k) + self.weights: np.ndarray = None + # likelihoods: shape(N, k) + self.likelihoods: np.ndarray = None + + def _init_params(self) -> None: + ''' + Randomly initialize the starting parameters. + ''' + + # Select k initial centroids randomly from training data. + self.means = self.train_data[ + np.random.choice(self.data_size, size=self.k, replace=False) + ] + + # Initialize the coefficient of variation of each Gaussian distribution + # to be a random identity matrix. + self.covs = np.array([ + np.identity(self.dimension) for _i in range(self.k) + ]) + + # Initialize the likelihood that an observation belongs to a cluster + # to be 1/k for all clusters. + self.weights = np.ones(self.k) / self.k + + def _e_step(self, dataset: np.ndarray = None) -> None: + ''' + In the E(xpectation) step, we calculate the likelihood of each + observation x_i belonging to each cluster using the current estimated + parameters. + + Args: + `dataset`: shape(N, d) + ''' + + dataset = dataset or self.train_data + data_size: int = dataset.shape[0] + + # Calculate the posterior probability that an observation belongs to + # each multivariate Gaussian distribution, using Bayes Theorem. + self.likelihoods = np.zeros((data_size, self.k)) + for i, x_i in enumerate(dataset): + # Calculate the likelihood of each observation x_i. + f_i: np.ndarray = np.array([ + self.weights[k] * multinormal_pdf( + x_i, self.means[k], self.covs[k] + ) for k in range(self.k) + ]) + f_i_sum: float = np.sum(f_i) + self.EPS + self.likelihoods[i] = f_i / f_i_sum + + def _m_step(self) -> None: + ''' + In the M(aximization) step, we re-estimate our learning parameters for + each cluster. + ''' + + # shape(n, k).sum(axis=0) = shape(k) + cluster_likelihoods: np.ndarray = np.sum( + self.likelihoods, axis=0 + ) + self.EPS + assert cluster_likelihoods.shape == (self.k,) + + # shape(k, n) * shape(n, d) = shape(k, d) + # shape(k, d) / shape(k)[:, None] = shape(k, d) + self.means = np.matmul( + self.likelihoods.T, self.train_data + ) / cluster_likelihoods[:, None] + assert self.means.shape == (self.k, self.dimension) + + # shape(k, d, d) + self.covs = np.array([ + # shape(d, d) / scalar = shape(d, d) + np.sum([ + # scalar * shape(d, 1) * shape(d) = shape(d, d) + self.likelihoods[i, k] * x_m.T * x_m + # shape(n, d) - shape(d) = shape(n, d) + for i, x_m in enumerate(self.train_data - self.means[k]) + ]) / cluster_likelihoods[k] + for k in range(self.k) + ]) + assert self.covs.shape == (self.k, self.dimension, self.dimension) + + # shape(k) / scalar = shape(k) + self.weights = cluster_likelihoods / self.data_size + assert self.weights.shape == (self.k,) + def fit(self, train_data: np.ndarray) -> None: - pass + + self.train_data = train_data + shape: Tuple[int, int] = train_data.shape + self.data_size, self.dimension = shape + + self._init_params() + labels: np.ndarray = np.zeros(self.data_size, dtype=int) + while True: + self._e_step() + self._m_step() + + # Assign labels to points based on the most possible cluster + # according to the likelihood matrix. + new_labels = np.argmax(self.likelihoods, axis=1) + + # Check for convergence. + if np.array_equal(new_labels, labels): + break + labels = new_labels def predict(self, test_data: np.ndarray) -> np.ndarray: - pass + + self._e_step(test_data) + return np.argmax(self.likelihoods, axis=1) class ClusteringAlgorithm: diff --git a/assignment-3/submission/18307130003/utils.py b/assignment-3/submission/18307130003/utils.py index 37d82a1..b1644f1 100644 --- a/assignment-3/submission/18307130003/utils.py +++ b/assignment-3/submission/18307130003/utils.py @@ -1,34 +1,7 @@ -from typing import Any, List, NamedTuple, Tuple import numpy as np import math -class NormalParameters(NamedTuple): - ''' - Attributes: - `size`: the number of data points in the dataset - `mean`: the mean of the distribution - `cov`: the coefficient of variation of the distribution (dimension > 1) - `scale`: the standard deviation of the distribution (dimension = 1) - ''' - - size: int - mean: Tuple[float, ...] - cov: List[List[float]] = None - scale: float = None - - -class UniformParameters(NamedTuple): - ''' - Attributes: - `size`: the number of data points in the dataset - `intervals`: the range of each dimension, Tuple[shape(N), shape(N)] - ''' - - size: int - intervals: Tuple[np.ndarray, np.ndarray] - - def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: ''' Args: @@ -44,13 +17,13 @@ def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: ''' - The probability density function of a multivariate Gaussian distribution - with given parameters. + The probability density function of a multivariate Gaussian + distribution with given parameters. Args: `x`: an observation, shape(d) - `mean`: the mean of the distribution, shape(d) - `cov`: the coefficient of variation of the distribution, shape(d, d) + `mean`: shape(d) + `cov`: shape(d, d) Return: f(x | mean, cov) @@ -62,34 +35,3 @@ def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: x_m: np.ndarray = x - mean exp: float = -np.dot(x_m, np.linalg.solve(cov, x_m)) / 2 return const * math.exp(exp) - - -def normal_pdf(x: float, mean: float, scale: float) -> float: - ''' - The probability density function of a Gaussian distribution with given - parameters. - - Args: - `x`: an observation - `mean`: the mean of the distribution - `scale`: the standard deviation of the distribution - - Return: - f(x | mean, scale) - ''' - - const = (2 * math.pi) ** (-1/2) / scale - exp = -((x - mean) / scale) ** 2 / 2 - return const * math.exp(exp) - - -def assert_(var_name: str, got: Any, expected: Any) -> None: - ''' - Args: - `var_name`: variable name for logging - `got`: actual value - `expected`: expected value - ''' - - message = f'Assertion failed for {var_name}: expected {expected}, got {got}' - assert got == expected, message -- Gitee From c3592d507487928d3ba352fc8123e066f5a26a9e Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 01:35:57 +0800 Subject: [PATCH 40/73] feat: custom assert method for debugging fix: failed to update cov issue in the M step of GMM --- assignment-3/submission/18307130003/source.py | 30 +++++++++++++------ assignment-3/submission/18307130003/tester.py | 3 +- assignment-3/submission/18307130003/utils.py | 13 ++++++++ 3 files changed, 36 insertions(+), 10 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index d676a66..316c813 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,7 +1,7 @@ from abc import ABC, abstractmethod from typing import Tuple import numpy as np -from utils import distance, multinormal_pdf +from utils import assert_, distance, multinormal_pdf class Model(ABC): @@ -180,7 +180,8 @@ class GaussianMixture(Model): `dataset`: shape(N, d) ''' - dataset = dataset or self.train_data + if dataset is None: + dataset = self.train_data data_size: int = dataset.shape[0] # Calculate the posterior probability that an observation belongs to @@ -206,31 +207,42 @@ class GaussianMixture(Model): cluster_likelihoods: np.ndarray = np.sum( self.likelihoods, axis=0 ) + self.EPS - assert cluster_likelihoods.shape == (self.k,) + assert_( + 'cluster_likelihoods.shape', + cluster_likelihoods.shape, + (self.k,), + ) # shape(k, n) * shape(n, d) = shape(k, d) # shape(k, d) / shape(k)[:, None] = shape(k, d) self.means = np.matmul( self.likelihoods.T, self.train_data ) / cluster_likelihoods[:, None] - assert self.means.shape == (self.k, self.dimension) + assert_('means.shape', self.means.shape, (self.k, self.dimension)) # shape(k, d, d) self.covs = np.array([ # shape(d, d) / scalar = shape(d, d) np.sum([ - # scalar * shape(d, 1) * shape(d) = shape(d, d) - self.likelihoods[i, k] * x_m.T * x_m + # scalar * shape(d, 1) * shape(1, d) = shape(d, d) + self.likelihoods[i, k] * np.matmul( + x_m.reshape((self.dimension, 1)), + x_m.reshape((1, self.dimension)), + ) # shape(n, d) - shape(d) = shape(n, d) for i, x_m in enumerate(self.train_data - self.means[k]) - ]) / cluster_likelihoods[k] + ], axis=0) / cluster_likelihoods[k] for k in range(self.k) ]) - assert self.covs.shape == (self.k, self.dimension, self.dimension) + assert_( + 'covs.shape', + self.covs.shape, + (self.k, self.dimension, self.dimension), + ) # shape(k) / scalar = shape(k) self.weights = cluster_likelihoods / self.data_size - assert self.weights.shape == (self.k,) + assert_('weights.shape', self.weights.shape, (self.k,)) def fit(self, train_data: np.ndarray) -> None: diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index c358db4..006b5dc 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -3,6 +3,7 @@ import numpy as np import matplotlib.pyplot as plt from math import floor from source import Model, KMeans +from utils import assert_ class Parameters(NamedTuple): @@ -293,7 +294,7 @@ def visualize( `centroids`: shape(k, d) ''' - assert dataset.shape[0] == labels.shape[0] + assert_('dataset.shape[0]', dataset.shape[0], labels.shape[0]) # Plot the data points and the centroids if len(dataset.shape) > 1: diff --git a/assignment-3/submission/18307130003/utils.py b/assignment-3/submission/18307130003/utils.py index b1644f1..1c1d8fd 100644 --- a/assignment-3/submission/18307130003/utils.py +++ b/assignment-3/submission/18307130003/utils.py @@ -1,3 +1,4 @@ +from typing import Any import numpy as np import math @@ -35,3 +36,15 @@ def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: x_m: np.ndarray = x - mean exp: float = -np.dot(x_m, np.linalg.solve(cov, x_m)) / 2 return const * math.exp(exp) + + +def assert_(var_name: str, got: Any, expected: Any) -> None: + ''' + Args: + `var_name`: variable name for logging + `got`: actual value + `expected`: expected value + ''' + + message = f'Assertion failed for {var_name}: expected {expected}, got {got}' + assert got == expected, message -- Gitee From fde1a28c6b2ff99b6f744d0b74aca7e139a43a1b Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 02:22:15 +0800 Subject: [PATCH 41/73] test: add tests for GMM --- assignment-3/submission/18307130003/tester.py | 64 ++++++++++++------- 1 file changed, 42 insertions(+), 22 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 006b5dc..d85a264 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -2,7 +2,7 @@ from typing import Callable, List, NamedTuple, Tuple, Type, Union import numpy as np import matplotlib.pyplot as plt from math import floor -from source import Model, KMeans +from source import Model, KMeans, GaussianMixture as GMM from utils import assert_ @@ -107,7 +107,10 @@ class TestSuite: model.fit(train_data) train_labels = model.predict(train_data) - centroids = model.centroids if isinstance(model, KMeans) else None + if isinstance(model, KMeans): + centroids = model.centroids + elif isinstance(model, GMM): + centroids = model.means return train_labels, centroids def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: @@ -125,10 +128,7 @@ class TestSuite: test_labels = model.predict(test_data) return test_labels - def k_means_data_1(self) -> Tuple[np.ndarray, int]: - ''' - Test data 1 for k-means clustering algorithm. - ''' + def test_data_1(self) -> Tuple[np.ndarray, int]: return self.generate_data( Parameters( @@ -151,10 +151,7 @@ class TestSuite: ), ) - def k_means_data_2(self) -> Tuple[np.ndarray, int]: - ''' - Test data 2 for k-means clustering algorithm. - ''' + def test_data_2(self) -> Tuple[np.ndarray, int]: return self.generate_data( Parameters( @@ -189,10 +186,7 @@ class TestSuite: ), ) - def k_means_data_3(self) -> Tuple[np.ndarray, int]: - ''' - Test data 3 for k-means clustering algorithm. - ''' + def test_data_3(self) -> Tuple[np.ndarray, int]: return self.generate_data( Parameters( @@ -215,10 +209,7 @@ class TestSuite: ), ) - def k_means_data_4(self) -> Tuple[np.ndarray, int]: - ''' - Test data 4 for k-means clustering algorithm. - ''' + def test_data_4(self) -> Tuple[np.ndarray, int]: return self.generate_data( Parameters( @@ -240,6 +231,29 @@ class TestSuite: size=100, ), ) + + def test_data_5(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + Parameters( + dimension=2, + mean=(0, -5), + cov=[[73, 0], [0, 2]], + size=800, + ), + Parameters( + dimension=2, + mean=(-3, 0), + cov=[[100, 0], [0, 2]], + size=500, + ), + Parameters( + dimension=2, + mean=(2, 5), + cov=[[70, 1], [1, 3]], + size=500, + ), + ) def run(self) -> None: ''' @@ -249,10 +263,16 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - ('k-means_1', self.k_means_data_1, KMeans, 0), - ('k-means_2', self.k_means_data_2, KMeans, 0), - ('k-means_3', self.k_means_data_3, KMeans, 0), - ('k-means_4', self.k_means_data_4, KMeans, 0), + # ('k-means_1', self.test_data_1, KMeans, 0), + # ('k-means_2', self.test_data_2, KMeans, 0), + # ('k-means_3', self.test_data_3, KMeans, 0), + # ('k-means_4', self.test_data_4, KMeans, 0), + ('k-means_5', self.test_data_5, KMeans, 0), + # ('gmm_1', self.test_data_1, GMM, 0), + # ('gmm_2', self.test_data_2, GMM, 0), + # ('gmm_3', self.test_data_3, GMM, 0), + # ('gmm_4', self.test_data_4, GMM, 0), + ('gmm_5', self.test_data_5, GMM, 0), ] for testcase in testcases: -- Gitee From a4d16de8b77e09f1a5783be1f8c79aa4225f8054 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 02:22:54 +0800 Subject: [PATCH 42/73] fix: train GMM multiple times for better result --- assignment-3/submission/18307130003/source.py | 65 ++++++++++++++----- 1 file changed, 48 insertions(+), 17 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 316c813..ee57f01 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -130,7 +130,7 @@ class GaussianMixture(Model): points belonging to a single distribution together. ''' - def __init__(self, n_clusters: int, n_epochs: int = 1) -> None: + def __init__(self, n_clusters: int, n_epochs: int = 5) -> None: super().__init__(n_clusters, n_epochs) @@ -150,6 +150,11 @@ class GaussianMixture(Model): # likelihoods: shape(N, k) self.likelihoods: np.ndarray = None + self.best_means: np.ndarray = None + self.best_covs: np.ndarray = None + self.best_weights: np.ndarray = None + self.best_likelihoods: np.ndarray = None + def _init_params(self) -> None: ''' Randomly initialize the starting parameters. @@ -170,7 +175,7 @@ class GaussianMixture(Model): # to be 1/k for all clusters. self.weights = np.ones(self.k) / self.k - def _e_step(self, dataset: np.ndarray = None) -> None: + def _e_step(self, dataset: np.ndarray = None, test_mode: bool = False) -> None: ''' In the E(xpectation) step, we calculate the likelihood of each observation x_i belonging to each cluster using the current estimated @@ -178,12 +183,19 @@ class GaussianMixture(Model): Args: `dataset`: shape(N, d) + `test_mode`: whether test data is being used ''' if dataset is None: dataset = self.train_data data_size: int = dataset.shape[0] + if test_mode: + self.means = self.best_means + self.covs = self.best_covs + self.weights = self.best_weights + self.likelihoods = self.best_likelihoods + # Calculate the posterior probability that an observation belongs to # each multivariate Gaussian distribution, using Bayes Theorem. self.likelihoods = np.zeros((data_size, self.k)) @@ -247,27 +259,46 @@ class GaussianMixture(Model): def fit(self, train_data: np.ndarray) -> None: self.train_data = train_data - shape: Tuple[int, int] = train_data.shape - self.data_size, self.dimension = shape + self.data_size: int = train_data.shape[0] + self.dimension: int = ( + train_data.shape[1] + if len(train_data.shape) > 1 else 1 + ) + min_loss = 0 + + # Run n_epochs times to find the best model. + for i in range(self.n_epochs): + self._init_params() + labels: np.ndarray = np.zeros(self.data_size, dtype=int) + + while True: + self._e_step() + self._m_step() + + # Assign labels to points based on the most possible cluster + # according to the likelihood matrix. + new_labels = np.argmax(self.likelihoods, axis=1) - self._init_params() - labels: np.ndarray = np.zeros(self.data_size, dtype=int) - while True: - self._e_step() - self._m_step() + # Check for convergence. + if np.array_equal(new_labels, labels): + break + labels = new_labels - # Assign labels to points based on the most possible cluster - # according to the likelihood matrix. - new_labels = np.argmax(self.likelihoods, axis=1) + loss: float = -np.mean(np.max(self.likelihoods, axis=1)) + if loss < min_loss: + min_loss = loss + self.best_means = self.means + self.best_covs = self.covs + self.best_weights = self.weights + self.best_likelihoods = self.likelihoods + + print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') - # Check for convergence. - if np.array_equal(new_labels, labels): - break - labels = new_labels + print() def predict(self, test_data: np.ndarray) -> np.ndarray: - self._e_step(test_data) + self._e_step(dataset=test_data, test_mode=True) return np.argmax(self.likelihoods, axis=1) -- Gitee From 33d613389de6d17f46c06fa153be80594a645e82 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 02:26:51 +0800 Subject: [PATCH 43/73] fix: minor fix for tester --- assignment-3/submission/18307130003/tester.py | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index d85a264..cfa3437 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -263,14 +263,14 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - # ('k-means_1', self.test_data_1, KMeans, 0), - # ('k-means_2', self.test_data_2, KMeans, 0), - # ('k-means_3', self.test_data_3, KMeans, 0), - # ('k-means_4', self.test_data_4, KMeans, 0), + ('k-means_1', self.test_data_1, KMeans, 0), + ('k-means_2', self.test_data_2, KMeans, 0), + ('k-means_3', self.test_data_3, KMeans, 0), + ('k-means_4', self.test_data_4, KMeans, 0), ('k-means_5', self.test_data_5, KMeans, 0), - # ('gmm_1', self.test_data_1, GMM, 0), - # ('gmm_2', self.test_data_2, GMM, 0), - # ('gmm_3', self.test_data_3, GMM, 0), + ('gmm_1', self.test_data_1, GMM, 0), + ('gmm_2', self.test_data_2, GMM, 0), + ('gmm_3', self.test_data_3, GMM, 0), # ('gmm_4', self.test_data_4, GMM, 0), ('gmm_5', self.test_data_5, GMM, 0), ] @@ -326,7 +326,7 @@ def visualize( else: plt.scatter(dataset, np.zeros(dataset.shape[0]), c=labels, s=30) if centroids is not None: - plt.yticks(None) + plt.yticks([]) plt.scatter( centroids, np.zeros(centroids.shape[0]), c='black', s=100, alpha=0.5, -- Gitee From 044874f3effeaf8953468222768b51a1072e52ef Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 02:27:07 +0800 Subject: [PATCH 44/73] 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zB{W5G$%=*@Q2ss|w&hN%8QbZ6_x^p7FSS33WEb3#>Nn`(2)LF!kR%uDl`h%011Yi{ zkR1_O`vt!B%;|LK1)=u(<01-}@#J6XpOA)Uma-RTq3OM584@Ds`j>FUn8S zgF1kBtR47GA79n|@SvxsryX26peV>u6kJq{xm2WH)qWCMPGefb7v_$YgN|L@IBtgOU{~ zDgi(|4|q!*hrf7!UjFP69kh;LoDG#D-pSb#oNW~CFXI#nPLdixco)Pd_ zql-Y4u55kUnv-oOFo}I-8BwNt3VO^Z(obMYF4V Y%ZGi5hrZwi-U0$u*S}YK=fPk94Ru4NNB{r; -- Gitee From 4688fc3c91da696e0376b3290d4635fe03459d03 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 03:57:36 +0800 Subject: [PATCH 45/73] feat: support 1D for GMM --- assignment-3/submission/18307130003/source.py | 114 ++++++++++++------ assignment-3/submission/18307130003/tester.py | 8 +- assignment-3/submission/18307130003/utils.py | 27 ++++- 3 files changed, 101 insertions(+), 48 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index ee57f01..592f63f 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,7 +1,6 @@ from abc import ABC, abstractmethod -from typing import Tuple import numpy as np -from utils import assert_, distance, multinormal_pdf +from utils import assert_, distance, multinormal_pdf, normal_pdf class Model(ABC): @@ -22,6 +21,7 @@ class Model(ABC): self.n_epochs: int = n_epochs # Others + self.rng: np.random.Generator = np.random.default_rng() self.FLOAT_MAX: float = np.finfo(float).max self.EPS: float = np.finfo(float).eps @@ -145,6 +145,8 @@ class GaussianMixture(Model): self.means: np.ndarray = None # covs: shape(k, d, d) self.covs: np.ndarray = None + # scales: shape(k) + self.scales: np.ndarray = None # weights: shape(k) self.weights: np.ndarray = None # likelihoods: shape(N, k) @@ -152,6 +154,7 @@ class GaussianMixture(Model): self.best_means: np.ndarray = None self.best_covs: np.ndarray = None + self.best_scales: np.ndarray = None self.best_weights: np.ndarray = None self.best_likelihoods: np.ndarray = None @@ -165,11 +168,16 @@ class GaussianMixture(Model): np.random.choice(self.data_size, size=self.k, replace=False) ] - # Initialize the coefficient of variation of each Gaussian distribution - # to be a random identity matrix. - self.covs = np.array([ - np.identity(self.dimension) for _i in range(self.k) - ]) + if self.dimension > 1: + # Initialize the coefficient of variation of each Gaussian + # distribution to be a random identity matrix. + self.covs = np.array([ + np.identity(self.dimension) for _i in range(self.k) + ]) + else: + # Initialize the standard deviation of each Gaussian distribution + # to be a random float. + self.scales = self.rng.random(self.k) * 10 # Initialize the likelihood that an observation belongs to a cluster # to be 1/k for all clusters. @@ -193,19 +201,27 @@ class GaussianMixture(Model): if test_mode: self.means = self.best_means self.covs = self.best_covs + self.scales = self.best_scales self.weights = self.best_weights self.likelihoods = self.best_likelihoods # Calculate the posterior probability that an observation belongs to - # each multivariate Gaussian distribution, using Bayes Theorem. + # each Gaussian distribution, using Bayes Theorem. self.likelihoods = np.zeros((data_size, self.k)) for i, x_i in enumerate(dataset): # Calculate the likelihood of each observation x_i. - f_i: np.ndarray = np.array([ - self.weights[k] * multinormal_pdf( - x_i, self.means[k], self.covs[k] - ) for k in range(self.k) - ]) + if self.dimension > 1: + f_i: np.ndarray = np.array([ + self.weights[k] * multinormal_pdf( + x_i, self.means[k], self.covs[k] + self.EPS + ) for k in range(self.k) + ]) + else: + f_i: np.ndarray = np.array([ + self.weights[k] * normal_pdf( + x_i, self.means[k], self.scales[k] + self.EPS + ) for k in range(self.k) + ]) f_i_sum: float = np.sum(f_i) + self.EPS self.likelihoods[i] = f_i / f_i_sum @@ -225,37 +241,54 @@ class GaussianMixture(Model): (self.k,), ) - # shape(k, n) * shape(n, d) = shape(k, d) - # shape(k, d) / shape(k)[:, None] = shape(k, d) - self.means = np.matmul( - self.likelihoods.T, self.train_data - ) / cluster_likelihoods[:, None] - assert_('means.shape', self.means.shape, (self.k, self.dimension)) - - # shape(k, d, d) - self.covs = np.array([ - # shape(d, d) / scalar = shape(d, d) - np.sum([ - # scalar * shape(d, 1) * shape(1, d) = shape(d, d) - self.likelihoods[i, k] * np.matmul( - x_m.reshape((self.dimension, 1)), - x_m.reshape((1, self.dimension)), - ) - # shape(n, d) - shape(d) = shape(n, d) - for i, x_m in enumerate(self.train_data - self.means[k]) - ], axis=0) / cluster_likelihoods[k] - for k in range(self.k) - ]) - assert_( - 'covs.shape', - self.covs.shape, - (self.k, self.dimension, self.dimension), - ) - # shape(k) / scalar = shape(k) self.weights = cluster_likelihoods / self.data_size assert_('weights.shape', self.weights.shape, (self.k,)) + if self.dimension > 1: + # shape(k, n) * shape(n, d) = shape(k, d) + self.means = np.matmul( + self.likelihoods.T, self.train_data + ) / cluster_likelihoods[:, None] + assert_('means.shape', self.means.shape, (self.k, self.dimension)) + + # shape(k, d, d) + self.covs = np.array([ + # shape(d, d) / scalar = shape(d, d) + np.sum([ + # scalar * shape(d, 1) * shape(1, d) = shape(d, d) + self.likelihoods[i, k] * np.matmul( + x_m.reshape((self.dimension, 1)), + x_m.reshape((1, self.dimension)), + ) + # shape(n, d) - shape(d) = shape(n, d) + for i, x_m in enumerate(self.train_data - self.means[k]) + ], axis=0) / cluster_likelihoods[k] + for k in range(self.k) + ]) + assert_( + 'covs.shape', + self.covs.shape, + (self.k, self.dimension, self.dimension), + ) + else: + # shape(k, n) * shape(n) = shape(k) + # shape(k) / shape(k) = shape(k) + self.means = np.dot( + self.likelihoods.T, self.train_data + ) / cluster_likelihoods + assert_('means.shape', self.means.shape, (self.k,)) + + # shape(k) + self.scales = np.array([ + np.sqrt(np.sum([ + self.likelihoods[i, k] * (x_m ** 2) + for i, x_m in enumerate(self.train_data - self.means[k]) + ], axis=0) / cluster_likelihoods[k]) + for k in range(self.k) + ]) + assert_('scales.shape', self.scales.shape, (self.k,)) + def fit(self, train_data: np.ndarray) -> None: self.train_data = train_data @@ -289,6 +322,7 @@ class GaussianMixture(Model): min_loss = loss self.best_means = self.means self.best_covs = self.covs + self.best_scales = self.scales self.best_weights = self.weights self.best_likelihoods = self.likelihoods diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index cfa3437..6fd1c73 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -215,19 +215,19 @@ class TestSuite: Parameters( dimension=1, mean=-20, - scale=6, + scale=3, size=100, ), Parameters( dimension=1, mean=0, - scale=3, + scale=1, size=150, ), Parameters( dimension=1, mean=15, - scale=3, + scale=2, size=100, ), ) @@ -271,7 +271,7 @@ class TestSuite: ('gmm_1', self.test_data_1, GMM, 0), ('gmm_2', self.test_data_2, GMM, 0), ('gmm_3', self.test_data_3, GMM, 0), - # ('gmm_4', self.test_data_4, GMM, 0), + ('gmm_4', self.test_data_4, GMM, 0), ('gmm_5', self.test_data_5, GMM, 0), ] diff --git a/assignment-3/submission/18307130003/utils.py b/assignment-3/submission/18307130003/utils.py index 1c1d8fd..5890030 100644 --- a/assignment-3/submission/18307130003/utils.py +++ b/assignment-3/submission/18307130003/utils.py @@ -18,13 +18,13 @@ def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: ''' - The probability density function of a multivariate Gaussian - distribution with given parameters. + The probability density function of a multivariate Gaussian distribution + with given parameters. Args: `x`: an observation, shape(d) - `mean`: shape(d) - `cov`: shape(d, d) + `mean`: the mean of the distribution, shape(d) + `cov`: the coefficient of variation of the distribution, shape(d, d) Return: f(x | mean, cov) @@ -38,6 +38,25 @@ def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: return const * math.exp(exp) +def normal_pdf(x: float, mean: float, scale: float) -> float: + ''' + The probability density function of a Gaussian distribution with given + parameters. + + Args: + `x`: an observation + `mean`: the mean of the distribution + `scale`: the standard deviation of the distribution + + Return: + f(x | mean, scale) + ''' + + const = (2 * math.pi) ** (-1/2) / scale + exp = -((x - mean) / scale) ** 2 / 2 + return const * math.exp(exp) + + def assert_(var_name: str, got: Any, expected: Any) -> None: ''' Args: -- Gitee From 98be7af4535324df55823eaedfb9fab629bc7d2d Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 03:58:07 +0800 Subject: [PATCH 46/73] docs: add figures for 1D dataset --- .../submission/18307130003/img/gmm_4_test.png | Bin 8412 -> 8800 bytes .../18307130003/img/gmm_4_train.png | Bin 7688 -> 8413 bytes .../18307130003/img/k-means_4_test.png | Bin 10327 -> 8742 bytes .../18307130003/img/k-means_4_train.png | Bin 9810 -> 8470 bytes 4 files changed, 0 insertions(+), 0 deletions(-) diff --git a/assignment-3/submission/18307130003/img/gmm_4_test.png b/assignment-3/submission/18307130003/img/gmm_4_test.png index 9832c07e16f4debefb176e596942fdc5ad2147b2..e39a97ce695cae781954ad0196e2426fb3c817ae 100644 GIT binary patch literal 8800 zcmeHNYgCfyzNcxIdv>McG&7EtT3gF$N-at8&XlEDDwV037cB2rydfG2l{48*EzP?? zji!mW($rLx92+lqAuox7Vx~ZXfPjJu$a&pot+V#ppU+wAe3%bB&wAeH_UHfp@4xr{ zMK`BC|Iqmd2n5>WeD2I;5a_F0Akel?f8Pl_F&~*;06MG0vsV+{5h01F>+!)L*XxO~ zQHaE-@EZq`g5wjy5iwvBu!-5R17V4Yu?g0urqTbizyuK=YHIpGa~E*P*Rkik6F?x1 z>s!BVFQJv;Ake`f=QF3SB$x7M(1m`;>p~Tko}zML@$Oa8#$in_okXXxXHDWYHNQLc_`o;k?)~y@ zd{K}Y7+pWBf6%?6$mQFwaOJZ!UP`iF2=y8o8;Yed4On+TRJO@*JNOlutm zp}NGZ0WeB1Ez;WwTHbA|Sne(YhYlxe1p5B{o!{{k@q%Fqr42ZOopPS?bGI&6y*=M+80{sx9;xDXox|=4@=$7g?jb6)stV>LrW~8C{ML>$HE@j z4mM6jh0G9F7x9z0wvUwD?0Q#fxnO0u)a-_qsv@(b;kqA|ZcWee#5s>04pDMD-!wtY zUZXy<8Q$a*+m-1>W`W}6whQ^k`r*ot@Zdimd|w2`Vs>uq1X~_|dSuKfIP7K7a9!3( zpP^~gY+8|dq$fsIGfOR81= zU#VTZ&^Sd|2+zIj;lXVirswfSM?OCJIv4HOfd$4JMsi@{uq*EEj9juP^OpTur;Ask zc+k?TGV+Zw1?9y>KS$;yzKC#fnV~-}haxKsSBd4!$K^K8@ce1=;R4@yXH4sjlpl^+ z9>C%JoXrnbK@K6|Ia#}RTQn|o!h?hzMhhefGdEowgW-B&iH<1liapYYU!{}lr0s

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a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 592f63f..f6ef6b8 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -291,11 +291,14 @@ class GaussianMixture(Model): def fit(self, train_data: np.ndarray) -> None: - self.train_data = train_data self.data_size: int = train_data.shape[0] self.dimension: int = ( - train_data.shape[1] - if len(train_data.shape) > 1 else 1 + train_data.shape[1] if len(train_data.shape) > 1 + else 1 + ) + self.train_data = ( + train_data if self.dimension > 1 + else train_data.reshape(self.data_size,) ) min_loss = 0 -- Gitee From 927cf7570321b71ae2056a003fb23b9a4d9f88e1 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 7 Jun 2021 04:16:44 +0800 Subject: [PATCH 48/73] test: modify test data 4 --- .../submission/18307130003/img/gmm_4_test.png | Bin 8800 -> 10330 bytes .../18307130003/img/gmm_4_train.png | Bin 8413 -> 9920 bytes 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zt&N#DW~7=J&5j!X&3w8^R>yH_6p|c*3UivpzVcTv8+^*4CRMMG>_FYiKck;rK7rp@ z*N%9IQbX}?wmJ?56*)iE>-9#0$&5MS>TCtE4!Zbz_#kNIwV4!&mqn?K_mVQBi!PD^ z2+8Ryu#{guXb#Q121H8-R}Fe)x%{EceJl>w!C16c zXZtNb#J>Oi8#OhoMru@!5dQGR2Q7Du^Tixr4U?etF zBoaX+DIBMXXsriQ?90f>_znzE9RCC_yb%Q>^muNakGHq<{U84d30dnOj+^C1B@I!- z)E4n&XE12=&?ga>mt!}d9fMu|6h|C+<1|F^t#z3Y#TAWP3o}(c{|b?^7(4xW{JWh2 zgGRckw?S9lJR7)FuM`>I`v}FxD;r@`T>$vUl(|Pm!>Z|?noq|TwaR1FM8etx+h+O4 zxOkf02nD;ScHf-vA@$J!M*txC1M2HTfMb_F-~IpNU;up_{1R#5SRn%#pTH9#KiB Date: Wed, 9 Jun 2021 00:44:56 +0800 Subject: [PATCH 49/73] feat: auto k-means init (wip) --- assignment-3/submission/18307130003/source.py | 47 +++++++++++++++---- assignment-3/submission/18307130003/tester.py | 10 +++- 2 files changed, 45 insertions(+), 12 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index f6ef6b8..8130dad 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,4 +1,5 @@ from abc import ABC, abstractmethod +from typing import List import numpy as np from utils import assert_, distance, multinormal_pdf, normal_pdf @@ -26,12 +27,15 @@ class Model(ABC): self.EPS: float = np.finfo(float).eps @abstractmethod - def fit(self, train_data: np.ndarray) -> None: + def fit(self, train_data: np.ndarray) -> float: ''' Train the model using training data. Args: `train_data`: shape(N, d) + + Return: + The training loss. ''' pass @@ -77,7 +81,7 @@ class KMeans(Model): return np.argmin([distance(point, c) for c in centroids]) - def fit(self, train_data: np.ndarray) -> None: + def fit(self, train_data: np.ndarray) -> float: data_size: int = train_data.shape[0] min_loss = self.FLOAT_MAX @@ -114,6 +118,7 @@ class KMeans(Model): print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') print() + return min_loss def predict(self, test_data: np.ndarray) -> np.ndarray: @@ -289,7 +294,7 @@ class GaussianMixture(Model): ]) assert_('scales.shape', self.scales.shape, (self.k,)) - def fit(self, train_data: np.ndarray) -> None: + def fit(self, train_data: np.ndarray) -> float: self.data_size: int = train_data.shape[0] self.dimension: int = ( @@ -300,7 +305,7 @@ class GaussianMixture(Model): train_data if self.dimension > 1 else train_data.reshape(self.data_size,) ) - min_loss = 0 + min_loss = 0.0 # Run n_epochs times to find the best model. for i in range(self.n_epochs): @@ -332,6 +337,7 @@ class GaussianMixture(Model): print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') print() + return min_loss def predict(self, test_data: np.ndarray) -> np.ndarray: @@ -339,13 +345,34 @@ class GaussianMixture(Model): return np.argmax(self.likelihoods, axis=1) -class ClusteringAlgorithm: +class ClusteringAlgorithm(Model): + ''' + Based on k-means clustering algorithm, using Elbow Method to determine the + number of clusters in the dataset automatically. + ''' - def __init__(self): - pass + def __init__(self, max_n_clusters: int, n_epochs: int = 10) -> None: + ''' + Args: + `max_n_clusters`: the maximum number of clusters to test + `n_epochs`: the number of epochs to run in total + ''' - def fit(self, train_data): - pass + # Not setting the number of clusters at the beginning. + super().__init__(0, n_epochs) + + # Model parameters + self.max_k = max_n_clusters + self.losses: List[float] = None + + def fit(self, train_data: np.ndarray) -> float: + + self.losses = [0.0] + for k in range(1, self.max_k + 1): + model = KMeans(k) + loss = model.fit(train_data) + self.losses.append(loss) + + def predict(self, test_data: np.ndarray) -> np.ndarray: - def predict(self, test_data): pass diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 81b3503..de5e9e1 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -2,7 +2,12 @@ from typing import Callable, List, NamedTuple, Tuple, Type, Union import numpy as np import matplotlib.pyplot as plt from math import floor -from source import Model, KMeans, GaussianMixture as GMM +from source import ( + ClusteringAlgorithm as AutoKMeans, + Model, + KMeans, + GaussianMixture as GMM, +) from utils import assert_ @@ -231,7 +236,7 @@ class TestSuite: size=100, ), ) - + def test_data_5(self) -> Tuple[np.ndarray, int]: return self.generate_data( @@ -273,6 +278,7 @@ class TestSuite: ('gmm_3', self.test_data_3, GMM, 0), ('gmm_4', self.test_data_4, GMM, 0), ('gmm_5', self.test_data_5, GMM, 0), + ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), ] for testcase in testcases: -- Gitee From 8ce57aa2f75d4550b6ee0146fdfa969c617fb190 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 10 Jun 2021 22:59:19 +0800 Subject: [PATCH 50/73] refactor: parameters structure --- assignment-3/submission/18307130003/tester.py | 152 +++++++----------- assignment-3/submission/18307130003/utils.py | 28 +++- 2 files changed, 87 insertions(+), 93 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index de5e9e1..34adfd2 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -1,33 +1,14 @@ -from typing import Callable, List, NamedTuple, Tuple, Type, Union +from typing import Callable, List, Tuple, Type +import math import numpy as np import matplotlib.pyplot as plt -from math import floor from source import ( ClusteringAlgorithm as AutoKMeans, Model, KMeans, GaussianMixture as GMM, ) -from utils import assert_ - - -class Parameters(NamedTuple): - ''' - Attributes: - `dimension`: the dimension of data points - `mean`: the mean of the distribution - `cov`: (for dimension > 1) \ - the coefficient of variation of the distribution - `scale`: (for dimension == 1) \ - the standard deviation of the distribution - `size`: the number of data points in the dataset - ''' - - dimension: int - mean: Union[Tuple[float, ...], float] - cov: List[List[float]] = [[0]] - scale: float = 0 - size: int = 1000 +from utils import assert_, NormalParameters class TestSuite: @@ -38,9 +19,9 @@ class TestSuite: def __init__(self) -> None: self.rng: np.random.Generator = np.random.default_rng() - def generate(self, param: Parameters) -> np.ndarray: + def generate_normal(self, param: NormalParameters) -> np.ndarray: ''' - Generate a dataset with given parameters. + Generate a dataset from a Gaussian distribution with given parameters. Args: `param`: parameters used to generate a dataset @@ -49,11 +30,11 @@ class TestSuite: shape(N, d) ''' - dimension, mean, cov, scale, size = param - if dimension > 1: + size, mean, cov, scale = param + if len(mean) > 1: return self.rng.multivariate_normal(mean, cov, size) else: - return self.rng.normal(mean, scale, size) + return self.rng.normal(mean[0], scale, size) def combine(self, *datasets: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: ''' @@ -78,7 +59,7 @@ class TestSuite: labels = labels[indices] return dataset, labels - def generate_data(self, *params: Parameters) -> Tuple[np.ndarray, int]: + def generate_data(self, *params: NormalParameters) -> Tuple[np.ndarray, int]: ''' Generate a dataset for tests. @@ -91,7 +72,7 @@ class TestSuite: ''' dataset, _labels = self.combine(*tuple( - self.generate(p) for p in params + self.generate_normal(p) for p in params )) n_clusters: int = len(params) return dataset, n_clusters @@ -136,127 +117,110 @@ class TestSuite: def test_data_1(self) -> Tuple[np.ndarray, int]: return self.generate_data( - Parameters( - dimension=2, + NormalParameters( + size=800, mean=(1, 2), cov=[[73, 0], [0, 22]], - size=800, ), - Parameters( - dimension=2, + NormalParameters( + size=200, mean=(16, -5), cov=[[21.2, 0], [0, 32.1]], - size=200, ), - Parameters( - dimension=2, + NormalParameters( + size=1000, mean=(10, 22), cov=[[10, 5], [5, 10]], - size=1000, ), ) def test_data_2(self) -> Tuple[np.ndarray, int]: return self.generate_data( - Parameters( - dimension=2, + NormalParameters( + size=800, mean=(1, 0), cov=[[73, 0], [0, 22]], - size=800, ), - Parameters( - dimension=2, + NormalParameters( + size=400, mean=(20, 15), cov=[[21.2, 0], [0, 32.1]], - size=400, ), - Parameters( - dimension=2, + NormalParameters( + size=1000, mean=(10, -22), cov=[[10, 5], [5, 10]], - size=1000, ), - Parameters( - dimension=2, + NormalParameters( + size=500, mean=(-12, -6), cov=[[7, 3], [3, 16]], - size=500, ), - Parameters( - dimension=2, + NormalParameters( + size=600, mean=(-15, 17), cov=[[15, 0], [0, 12]], - size=600, ), ) def test_data_3(self) -> Tuple[np.ndarray, int]: return self.generate_data( - Parameters( - dimension=3, + NormalParameters( + size=800, mean=(-6, 3, 5), cov=[[73, 0, 0], [0, 50, 0], [0, 0, 22]], - size=800, ), - Parameters( - dimension=3, + NormalParameters( + size=500, mean=(12, 0, -10), cov=[[20, 5, 0], [5, 20, 0], [0, 0, 20]], - size=500, ), - Parameters( - dimension=3, + NormalParameters( + size=800, mean=(10, -20, 0), cov=[[10, 1, 3], [1, 10, 0], [3, 0, 10]], - size=800, ), ) def test_data_4(self) -> Tuple[np.ndarray, int]: return self.generate_data( - Parameters( - dimension=1, + NormalParameters( + size=100, mean=-20, scale=6, - size=100, ), - Parameters( - dimension=1, + NormalParameters( + size=150, mean=0, scale=3, - size=150, ), - Parameters( - dimension=1, + NormalParameters( + size=100, mean=15, scale=3, - size=100, ), ) def test_data_5(self) -> Tuple[np.ndarray, int]: return self.generate_data( - Parameters( - dimension=2, + NormalParameters( + size=800, mean=(0, -5), cov=[[73, 0], [0, 2]], - size=800, ), - Parameters( - dimension=2, + NormalParameters( + size=500, mean=(-3, 0), cov=[[100, 0], [0, 2]], - size=500, ), - Parameters( - dimension=2, + NormalParameters( + size=500, mean=(2, 5), cov=[[70, 1], [1, 3]], - size=500, ), ) @@ -268,17 +232,21 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - ('k-means_1', self.test_data_1, KMeans, 0), - ('k-means_2', self.test_data_2, KMeans, 0), - ('k-means_3', self.test_data_3, KMeans, 0), - ('k-means_4', self.test_data_4, KMeans, 0), - ('k-means_5', self.test_data_5, KMeans, 0), - ('gmm_1', self.test_data_1, GMM, 0), - ('gmm_2', self.test_data_2, GMM, 0), - ('gmm_3', self.test_data_3, GMM, 0), - ('gmm_4', self.test_data_4, GMM, 0), - ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), + # ('k-means_1', self.test_data_1, KMeans, 0), + # ('k-means_2', self.test_data_2, KMeans, 0), + # ('k-means_3', self.test_data_3, KMeans, 0), + # ('k-means_4', self.test_data_4, KMeans, 0), + # ('k-means_5', self.test_data_5, KMeans, 0), + # ('gmm_1', self.test_data_1, GMM, 0), + # ('gmm_2', self.test_data_2, GMM, 0), + # ('gmm_3', self.test_data_3, GMM, 0), + # ('gmm_4', self.test_data_4, GMM, 0), + # ('gmm_5', self.test_data_5, GMM, 0), + ('auto-k-means_1', self.test_data_1, AutoKMeans, 0), + # ('auto-k-means_2', self.test_data_2, AutoKMeans, 0), + # ('auto-k-means_3', self.test_data_3, AutoKMeans, 0), + # ('auto-k-means_4', self.test_data_4, AutoKMeans, 0), + # ('auto-k-means_5', self.test_data_5, AutoKMeans, 0), ] for testcase in testcases: @@ -286,7 +254,7 @@ class TestSuite: # Obtain training data and testing data dataset, real_n_clusters = get_dataset() - train_size: int = floor(dataset.shape[0] * 0.8) + train_size: int = math.floor(dataset.shape[0] * 0.8) train_data: np.ndarray = dataset[:train_size] test_data: np.ndarray = dataset[train_size:] diff --git a/assignment-3/submission/18307130003/utils.py b/assignment-3/submission/18307130003/utils.py index 5890030..37d82a1 100644 --- a/assignment-3/submission/18307130003/utils.py +++ b/assignment-3/submission/18307130003/utils.py @@ -1,8 +1,34 @@ -from typing import Any +from typing import Any, List, NamedTuple, Tuple import numpy as np import math +class NormalParameters(NamedTuple): + ''' + Attributes: + `size`: the number of data points in the dataset + `mean`: the mean of the distribution + `cov`: the coefficient of variation of the distribution (dimension > 1) + `scale`: the standard deviation of the distribution (dimension = 1) + ''' + + size: int + mean: Tuple[float, ...] + cov: List[List[float]] = None + scale: float = None + + +class UniformParameters(NamedTuple): + ''' + Attributes: + `size`: the number of data points in the dataset + `intervals`: the range of each dimension, Tuple[shape(N), shape(N)] + ''' + + size: int + intervals: Tuple[np.ndarray, np.ndarray] + + def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: ''' Args: -- Gitee From d9e06fb59a478f9ff8cd9eb19104a3033ddc2147 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 10 Jun 2021 23:00:40 +0800 Subject: [PATCH 51/73] feat: auto k-means --- assignment-3/submission/18307130003/source.py | 104 +++++++++++++++--- 1 file changed, 90 insertions(+), 14 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 8130dad..4f7a228 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,7 +1,14 @@ from abc import ABC, abstractmethod from typing import List +import math import numpy as np -from utils import assert_, distance, multinormal_pdf, normal_pdf +from utils import ( + UniformParameters, + assert_, + distance, + multinormal_pdf, + normal_pdf, +) class Model(ABC): @@ -17,6 +24,11 @@ class Model(ABC): `n_epochs`: the number of epochs to run in total ''' + # Dataset properties + self.train_data: np.ndarray = None + self.data_size: int = 0 + self.dimension: int = 0 + # Model parameters self.k: int = n_clusters self.n_epochs: int = n_epochs @@ -83,16 +95,24 @@ class KMeans(Model): def fit(self, train_data: np.ndarray) -> float: - data_size: int = train_data.shape[0] + self.data_size: int = train_data.shape[0] + self.dimension: int = ( + train_data.shape[1] if len(train_data.shape) > 1 + else 1 + ) + self.train_data = ( + train_data if self.dimension > 1 + else train_data.reshape(self.data_size,) + ) min_loss = self.FLOAT_MAX # Run n_epochs times to find the best model. for i in range(self.n_epochs): # Select k initial centroids randomly from training data. centroids: np.ndarray = train_data[ - np.random.choice(data_size, size=self.k, replace=False) + np.random.choice(self.data_size, size=self.k, replace=False) ] - labels: np.ndarray = np.zeros(data_size, dtype=int) + labels: np.ndarray = np.zeros(self.data_size, dtype=int) while True: # Assign labels to points based on their closest centroids. @@ -110,12 +130,14 @@ class KMeans(Model): np.mean(train_data[labels == i], axis=0) for i in range(self.k) ]) - loss: float = np.mean((train_data - centroids[labels]) ** 2) + loss: float = np.sum((train_data - centroids[labels]) ** 2) if loss < min_loss: min_loss = loss self.centroids = centroids - print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') + print('Training progress: {}/{}, \tloss: {}'.format( + i + 1, self.n_epochs, loss, + ), end='\r') print() return min_loss @@ -334,7 +356,9 @@ class GaussianMixture(Model): self.best_weights = self.weights self.best_likelihoods = self.likelihoods - print(f'Training progress: {i + 1}/{self.n_epochs}', end='\r') + print('Training progress: {}/{}, \tloss: {}'.format( + i + 1, self.n_epochs, loss, + ), end='\r') print() return min_loss @@ -347,15 +371,18 @@ class GaussianMixture(Model): class ClusteringAlgorithm(Model): ''' - Based on k-means clustering algorithm, using Elbow Method to determine the + Based on k-means clustering algorithm, using Gap Statistic to estimate the number of clusters in the dataset automatically. ''' - def __init__(self, max_n_clusters: int, n_epochs: int = 10) -> None: + def __init__( + self, max_n_clusters: int, n_epochs: int = 10, n_ref: int = 5 + ) -> None: ''' Args: `max_n_clusters`: the maximum number of clusters to test `n_epochs`: the number of epochs to run in total + `n_ref`: the number of reference datasets in Gap Statistic ''' # Not setting the number of clusters at the beginning. @@ -363,16 +390,65 @@ class ClusteringAlgorithm(Model): # Model parameters self.max_k = max_n_clusters - self.losses: List[float] = None + self.n_ref = n_ref + self.gaps: List[float] = None + + self.best_model = None + + def generate_uniform(self, param: UniformParameters) -> np.ndarray: + ''' + Generate a dataset from a uniform distribution with given parameters. + + Args: + `param`: parameters used to generate a dataset + + Return: + shape(N, d) + ''' + + size, (low, high) = param + assert_('low.shape[0]', low.shape[0], high.shape[0]) + dimension = low.shape[0] + return self.rng.uniform( + low, high, (size, dimension if dimension > 1 else None), + ) def fit(self, train_data: np.ndarray) -> float: - self.losses = [0.0] + self.gaps = [0.0] + max_gap = 0.0 + min_loss = self.FLOAT_MAX + for k in range(1, self.max_k + 1): - model = KMeans(k) + model = KMeans(k, self.n_epochs) loss = model.fit(train_data) - self.losses.append(loss) + + low: np.ndarray = np.amin(train_data, axis=0) + high: np.ndarray = np.amax(train_data, axis=0) + + # Generate n_ref reference datasets, cluster each one using the + # current model, and calculate the gap statistic. + log_random_loss: float = np.mean([ + math.log(KMeans(k, self.n_epochs).fit(self.generate_uniform( + UniformParameters( + size=model.data_size, + intervals=(low, high), + ) + ))) for _i in range(self.n_ref) + ]) + gap = log_random_loss - math.log(loss) + self.gaps.append(gap) + + if gap > max_gap: + max_gap = gap + min_loss = loss + self.best_model = model + + print('Tried k: {}/{}, \tgap: {}'.format(k, self.max_k, gap)) + + print('Estimated k: {}'.format(self.best_model.k)) + return min_loss def predict(self, test_data: np.ndarray) -> np.ndarray: - pass + return self.best_model.predict(test_data) -- Gitee From 2f00cc2a5fb1108859e928b750427bc76d12eb0a Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 10 Jun 2021 23:03:03 +0800 Subject: [PATCH 52/73] fix: syntax error --- assignment-3/submission/18307130003/tester.py | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 34adfd2..0e497d4 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -93,6 +93,7 @@ class TestSuite: model.fit(train_data) train_labels = model.predict(train_data) + centroids: np.ndarray = None if isinstance(model, KMeans): centroids = model.centroids elif isinstance(model, GMM): @@ -242,11 +243,11 @@ class TestSuite: # ('gmm_3', self.test_data_3, GMM, 0), # ('gmm_4', self.test_data_4, GMM, 0), # ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 0), - # ('auto-k-means_2', self.test_data_2, AutoKMeans, 0), - # ('auto-k-means_3', self.test_data_3, AutoKMeans, 0), - # ('auto-k-means_4', self.test_data_4, AutoKMeans, 0), - # ('auto-k-means_5', self.test_data_5, AutoKMeans, 0), + ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), + # ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), + # ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), + # ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), + # ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), ] for testcase in testcases: -- Gitee From 585d710a8f82a55b439aa2b987ff6f27071ce9e1 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 00:38:14 +0800 Subject: [PATCH 53/73] feat: plot gap statistics for auto k-means --- assignment-3/submission/18307130003/source.py | 6 +-- assignment-3/submission/18307130003/tester.py | 45 ++++++++++++++++--- 2 files changed, 41 insertions(+), 10 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 4f7a228..29697c4 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -391,7 +391,7 @@ class ClusteringAlgorithm(Model): # Model parameters self.max_k = max_n_clusters self.n_ref = n_ref - self.gaps: List[float] = None + self.gaps: np.ndarray = None self.best_model = None @@ -415,7 +415,7 @@ class ClusteringAlgorithm(Model): def fit(self, train_data: np.ndarray) -> float: - self.gaps = [0.0] + self.gaps = np.zeros(self.max_k + 1) max_gap = 0.0 min_loss = self.FLOAT_MAX @@ -437,7 +437,7 @@ class ClusteringAlgorithm(Model): ))) for _i in range(self.n_ref) ]) gap = log_random_loss - math.log(loss) - self.gaps.append(gap) + self.gaps[k] = gap if gap > max_gap: max_gap = gap diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 0e497d4..c4baa55 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -77,7 +77,9 @@ class TestSuite: n_clusters: int = len(params) return dataset, n_clusters - def train(self, train_data: np.ndarray, model: Model) -> Tuple[np.ndarray, np.ndarray]: + def train( + self, train_data: np.ndarray, model: Model + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: ''' Train a model with training data. @@ -87,18 +89,24 @@ class TestSuite: `n_clusters`: the number of clusters to partition into Return: - `train_labels`: The predicted labels of training data, shape(N) - `centroids`: The centroids calculated from training data, shape(k, d) + `train_labels`: the predicted labels of training data, shape(N) + `centroids`: the centroids calculated from training data, shape(k, d) + `gaps`: the gap statistics of each k, shape(k + 1) ''' model.fit(train_data) train_labels = model.predict(train_data) centroids: np.ndarray = None + gaps: np.ndarray = None + if isinstance(model, KMeans): centroids = model.centroids elif isinstance(model, GMM): centroids = model.means - return train_labels, centroids + elif isinstance(model, AutoKMeans): + centroids = model.best_model.centroids + gaps = model.gaps + return train_labels, centroids, gaps def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: ''' @@ -261,7 +269,7 @@ class TestSuite: # Train the model with training data model = model_class(n_clusters or real_n_clusters) - train_labels, centroids = self.train(train_data, model) + train_labels, centroids, gaps = self.train(train_data, model) # Evaluate the model with testing data test_labels = self.evaluate(test_data, model) @@ -270,6 +278,10 @@ class TestSuite: visualize(name + '_train', train_data, train_labels, centroids) visualize(name + '_test', test_data, test_labels, centroids) + # Visualize the gap statistics for + if gaps is not None: + visualize_gaps(name + '_gaps', gaps) + print(f'{name}: Done.') @@ -291,7 +303,7 @@ def visualize( assert_('dataset.shape[0]', dataset.shape[0], labels.shape[0]) - # Plot the data points and the centroids + # Plot the data points and the centroids. if len(dataset.shape) > 1: plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) if centroids is not None: @@ -307,7 +319,26 @@ def visualize( c='black', s=100, alpha=0.5, ) - # Save the figure to a local file + # Save the figure to a local file. + plt.savefig(f'img/{name}') + plt.clf() + + +def visualize_gaps(name: str, gaps: np.ndarray) -> None: + ''' + Visualize the gap statistics. + + Args: + `name`: the output filename when saving the figure + `gaps`: the gap statistics of each k, shape(k + 1) + ''' + + # Plot the gap statistics. + indices = np.arange(1, gaps.shape[0], dtype=int) + plt.xticks(indices) + plt.plot(indices, gaps[indices], 'bo') + + # Save the figure to a local file. plt.savefig(f'img/{name}') plt.clf() -- Gitee From e70e943e7883a5112c1e44f379cb50a8c0a5ae26 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 00:41:30 +0800 Subject: [PATCH 54/73] test: enable all testers --- assignment-3/submission/18307130003/tester.py | 28 +++++++++---------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index c4baa55..1aa5f18 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -241,21 +241,21 @@ class TestSuite: testcases: List[Tuple[ str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int ]] = [ - # ('k-means_1', self.test_data_1, KMeans, 0), - # ('k-means_2', self.test_data_2, KMeans, 0), - # ('k-means_3', self.test_data_3, KMeans, 0), - # ('k-means_4', self.test_data_4, KMeans, 0), - # ('k-means_5', self.test_data_5, KMeans, 0), - # ('gmm_1', self.test_data_1, GMM, 0), - # ('gmm_2', self.test_data_2, GMM, 0), - # ('gmm_3', self.test_data_3, GMM, 0), - # ('gmm_4', self.test_data_4, GMM, 0), - # ('gmm_5', self.test_data_5, GMM, 0), + ('k-means_1', self.test_data_1, KMeans, 0), + ('k-means_2', self.test_data_2, KMeans, 0), + ('k-means_3', self.test_data_3, KMeans, 0), + ('k-means_4', self.test_data_4, KMeans, 0), + ('k-means_5', self.test_data_5, KMeans, 0), + ('gmm_1', self.test_data_1, GMM, 0), + ('gmm_2', self.test_data_2, GMM, 0), + ('gmm_3', self.test_data_3, GMM, 0), + ('gmm_4', self.test_data_4, GMM, 0), + ('gmm_5', self.test_data_5, GMM, 0), ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), - # ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), - # ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), - # ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), - # ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), + ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), + ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), + ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), + ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), ] for testcase in testcases: -- Gitee From 3212d6d605ccd4e338cd880eb890c84e6de2f22e Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 01:48:13 +0800 Subject: [PATCH 55/73] chore: modify pyplot arguments --- assignment-3/submission/18307130003/tester.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 1aa5f18..980991d 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -251,11 +251,11 @@ class TestSuite: ('gmm_3', self.test_data_3, GMM, 0), ('gmm_4', self.test_data_4, GMM, 0), ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), + ('auto-k-means_1', self.test_data_1, AutoKMeans, 6), ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), - ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), - ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), - ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), + ('auto-k-means_3', self.test_data_3, AutoKMeans, 6), + ('auto-k-means_4', self.test_data_4, AutoKMeans, 6), + ('auto-k-means_5', self.test_data_5, AutoKMeans, 6), ] for testcase in testcases: @@ -336,7 +336,7 @@ def visualize_gaps(name: str, gaps: np.ndarray) -> None: # Plot the gap statistics. indices = np.arange(1, gaps.shape[0], dtype=int) plt.xticks(indices) - plt.plot(indices, gaps[indices], 'bo') + plt.plot(indices, gaps[indices], '-bo') # Save the figure to a local file. plt.savefig(f'img/{name}') -- Gitee From 97350ff7c63f517580d6bbad670133093a360487 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 02:03:08 +0800 Subject: [PATCH 56/73] feat: break the loop if the gap statistics is not ascending --- assignment-3/submission/18307130003/source.py | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 29697c4..8633cce 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -392,6 +392,7 @@ class ClusteringAlgorithm(Model): self.max_k = max_n_clusters self.n_ref = n_ref self.gaps: np.ndarray = None + self.BREAK_THRESHOLD = 2 self.best_model = None @@ -418,6 +419,8 @@ class ClusteringAlgorithm(Model): self.gaps = np.zeros(self.max_k + 1) max_gap = 0.0 min_loss = self.FLOAT_MAX + # Break the loop if the gap statistics is not likely to ascend anymore. + break_counter = 0 for k in range(1, self.max_k + 1): model = KMeans(k, self.n_epochs) @@ -438,13 +441,20 @@ class ClusteringAlgorithm(Model): ]) gap = log_random_loss - math.log(loss) self.gaps[k] = gap + print('Tried k: {}/{}, \tgap statistics: {}'.format( + k, self.max_k, gap + )) if gap > max_gap: max_gap = gap min_loss = loss self.best_model = model - - print('Tried k: {}/{}, \tgap: {}'.format(k, self.max_k, gap)) + break_counter = 0 + else: + break_counter += 1 + if break_counter >= self.BREAK_THRESHOLD: + print('Gap statistics is not ascending, loop terminated.') + break print('Estimated k: {}'.format(self.best_model.k)) return min_loss -- Gitee From 3c6e03f6f7b0f1634b9b7a35bbca058645c096d4 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 02:13:47 +0800 Subject: [PATCH 57/73] fix: speed up the calculating gap statistics process --- assignment-3/submission/18307130003/source.py | 5 ++++- assignment-3/submission/18307130003/tester.py | 6 +++--- 2 files changed, 7 insertions(+), 4 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 8633cce..1f43c7c 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -432,7 +432,10 @@ class ClusteringAlgorithm(Model): # Generate n_ref reference datasets, cluster each one using the # current model, and calculate the gap statistic. log_random_loss: float = np.mean([ - math.log(KMeans(k, self.n_epochs).fit(self.generate_uniform( + # Since the dataset is generated from a uniform distribution, + # there's no need to run the k-means clustering algorithm for + # multiple times. + math.log(KMeans(k, 1).fit(self.generate_uniform( UniformParameters( size=model.data_size, intervals=(low, high), diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 980991d..db2113b 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -253,9 +253,9 @@ class TestSuite: ('gmm_5', self.test_data_5, GMM, 0), ('auto-k-means_1', self.test_data_1, AutoKMeans, 6), ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), - ('auto-k-means_3', self.test_data_3, AutoKMeans, 6), - ('auto-k-means_4', self.test_data_4, AutoKMeans, 6), - ('auto-k-means_5', self.test_data_5, AutoKMeans, 6), + ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), + ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), + ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), ] for testcase in testcases: -- Gitee From 570505f9955242209f12372f769d2bf46aa9515f Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 02:18:17 +0800 Subject: [PATCH 58/73] fix: gaps plotting issue --- assignment-3/submission/18307130003/source.py | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 1f43c7c..7809d7e 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -392,7 +392,7 @@ class ClusteringAlgorithm(Model): self.max_k = max_n_clusters self.n_ref = n_ref self.gaps: np.ndarray = None - self.BREAK_THRESHOLD = 2 + self.BREAK_THRESHOLD = 3 self.best_model = None @@ -416,7 +416,7 @@ class ClusteringAlgorithm(Model): def fit(self, train_data: np.ndarray) -> float: - self.gaps = np.zeros(self.max_k + 1) + gaps = [0.0] max_gap = 0.0 min_loss = self.FLOAT_MAX # Break the loop if the gap statistics is not likely to ascend anymore. @@ -443,7 +443,7 @@ class ClusteringAlgorithm(Model): ))) for _i in range(self.n_ref) ]) gap = log_random_loss - math.log(loss) - self.gaps[k] = gap + gaps.append(gap) print('Tried k: {}/{}, \tgap statistics: {}'.format( k, self.max_k, gap )) @@ -459,6 +459,7 @@ class ClusteringAlgorithm(Model): print('Gap statistics is not ascending, loop terminated.') break + self.gaps = np.array(gaps) print('Estimated k: {}'.format(self.best_model.k)) return min_loss -- Gitee From 59a8c0a3c496502dd3c88e5d72883083f4e696db Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 02:26:12 +0800 Subject: [PATCH 59/73] fix: break loop logic --- assignment-3/submission/18307130003/source.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 7809d7e..8515483 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -416,8 +416,7 @@ class ClusteringAlgorithm(Model): def fit(self, train_data: np.ndarray) -> float: - gaps = [0.0] - max_gap = 0.0 + gaps, max_gap, prev_gap = [0.0], 0.0, 0.0 min_loss = self.FLOAT_MAX # Break the loop if the gap statistics is not likely to ascend anymore. break_counter = 0 @@ -452,12 +451,15 @@ class ClusteringAlgorithm(Model): max_gap = gap min_loss = loss self.best_model = model + + if gap > prev_gap: break_counter = 0 else: break_counter += 1 if break_counter >= self.BREAK_THRESHOLD: print('Gap statistics is not ascending, loop terminated.') break + prev_gap = gap self.gaps = np.array(gaps) print('Estimated k: {}'.format(self.best_model.k)) -- Gitee From 7342337621069e511a175936d09aa87b4852eb04 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 02:35:00 +0800 Subject: [PATCH 60/73] chore: modify tester parameters --- assignment-3/submission/18307130003/tester.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index db2113b..056f4ac 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -251,7 +251,7 @@ class TestSuite: ('gmm_3', self.test_data_3, GMM, 0), ('gmm_4', self.test_data_4, GMM, 0), ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 6), + ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), -- Gitee From a4df32ed580aa38f6f475460d248810d147f5a02 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 11 Jun 2021 09:19:50 +0800 Subject: [PATCH 61/73] docs: add figures for auto k-means 1-3 --- .../18307130003/img/auto-k-means_1_gaps.png | Bin 18095 -> 17429 bytes .../18307130003/img/auto-k-means_1_test.png | Bin 51344 -> 54289 bytes .../18307130003/img/auto-k-means_1_train.png | Bin 68661 -> 68244 bytes .../18307130003/img/auto-k-means_2_gaps.png | Bin 17722 -> 18577 bytes .../18307130003/img/auto-k-means_2_test.png | Bin 73940 -> 71286 bytes .../18307130003/img/auto-k-means_2_train.png | Bin 78820 -> 83453 bytes .../18307130003/img/auto-k-means_3_gaps.png | Bin 14605 -> 14569 bytes .../18307130003/img/auto-k-means_3_test.png | Bin 63262 -> 60230 bytes .../18307130003/img/auto-k-means_3_train.png | Bin 96246 -> 82454 bytes 9 files changed, 0 insertions(+), 0 deletions(-) diff --git a/assignment-3/submission/18307130003/img/auto-k-means_1_gaps.png b/assignment-3/submission/18307130003/img/auto-k-means_1_gaps.png index 9f7543762793a7d4963a948a300472abdf4a45a3..7e66027fd2f06ccffec0e7578def03ec58f378fe 100644 GIT binary patch literal 17429 zcmeIacRber+c*9ug`}vY$S9&=B&%$qj8OKLWY4naiIfnEY#AYYWM*riGCQr1m29WI z$9dkzTc7WBUH5fezx#3j?!WFo?ms^GobU7f+OOky9?#=>6nIzZHsxWu!w7;<%E?Nr zAPBJ!f)I_69fD8zfBgCbziv3nXgR9dnL4@{JvKoUjU4T*?HsKw9xywbJa(|Kv*qRD z<+{efZ0_i2?;ym@ZS!wm;Ieyc#?2i>O#zLN+skS@AjmNz^gp6Z@eB(Dx#=e-Eve?3 zfE)DC>oOT4ENvi%P5q1*?-TK_cm^%|znjouyPQ%M-)(9eU~{b7rlK^^$z@x;OQXuP zEV3%k)TV!k+&nfbGUy${;wh`<@5XdS&f!GzYB9r1y`p5qhp)Bp^A7i}EX9xx$8KHo zZ2aox;Z@t~R3X9`b{mFd|KjSvLHJ!?N9F^+j^0E_;KS3z%n0K1nF=97kh9MaG6Wg9 zN+JQz1I{7D2y*=h5f!{*^#5M@-(Imh{y1VkZ5f%Twc9gSN-ewPxuTn$Zy-oABWy%a za4-!MQ$gWXv(Ts12>obIL9NPz2XArLV39BVEVoNKe*Cy~w9!GLLTa5-%M0IjiDhoz z*3F0G*%dH=(|GXU!T98d6Y%E8f%TBkP&U{js)q@lTT#69!|0~o`v0@3T4Z!&SI5V( z+iNODDJN;!DVeyQ1`OmMMyTY;d?b)>-^1T2N7wEy|1>5i$DUA@jbIHUkSsga`IQYgf#HaB*LQHgjZ##|! zqwXext@WA^K@hrNgp9=Jlhkk`DN-Luh4>;=w37oXaO9|onW>Ox#{`SL^z-|ZTq@GO zNINhhNQewVLM-9>L3?Ig+O*wNR08p_Lto=@D_Y%M;b*cN(sLiD=^-LPHjfffkue() zHZTuW!dF*2CpH(2EJh?e_=ymyW9XxyhQth|Nbij*?^ytqVN>~Z>@nYz*Vxp(@jhHl6 zi+UvMt&~n>mw^r9(;)@ptsni2%_)c*8#CL%9y)|<(n0r#RgbKUjLOcsioE>VBv(zB zr`Ig!^oV3#^dW>yl0WiUn&`uvNo{NRYuwMny&|+_*9E zA-^Hf;=lpKGY}!uDtnX~J33HV>iF?sY0?;_k6rb-$f)g{YluW9`i9%>HLi*;);k*U z_`USvwrkB_s+XP-EDs?5Y{bm>Up1+EZADjp&@1sJLTbS*aBL3~BG>05m4p@PcqhJ0 zx*r&^Dv&cVQ8c7Sm>sDRqTuROx3NY!PMw6!Umu^OZ@PZN2`GF5Ym!ao<0G?XL2!Ti zR4#%|ogjuFN(YIk3Lg##Om`}`ehFI|o81r{N{)$OVG!+qm<}7FcbBC8*Dt;F^z=(& zVg_6=w;`F%nL=lrPK91RUAeOOUdeL8L5fpd?rkYI1L8IZk!LO^7d}y>PfcxmwLhm; zi5I}S49m^-3hJYae(EGqVM&SF-p)qvuL=kHRj(wk_1MD{6j$u@tDN)JJslk#OD8EP zC}?PC#+$LeLi}lavozG_(lay(-f$={e{v>TdleU#-PP4~2xC~~jO(g&niYams5jG* za+Brq0j1VNQPV^AS~1#$f^%%jQTQ$86G)Qlr)s#Pl+;)zhHu}#!7cBc`jJ{{+8RgK z9{u`trg2lKysT`8KlzCgljc(t>YoCOid%cBS<=dE=+|p#4KBi6_gafw#qZP>z`5F% zx`s41G*}E(yXh1?3@j=t>Z%koLrsyag*W{M@NxKbBXzn^D;6r7C#G( z`fI&B-W2F+Xt0$J=;ID01gXM4$lQ`Y!KQ{`fT?{NUvd>G3pOW3maMe|kA)h|jX@W~kfz|Epp*K;Ih&)dI~(z9 zyCRImWR4FWd^Q}5)J!wPW37*s8wd1VB0=to+m`F{@bHAo09H3HV$)x z-D7HsiPoq54T_|*$G?LgojG}u=qfk2a_X&+>}ql2#v^jr5{u4~`yYvEPMxw`7^;bE zXM)bk2c6>&A3ogmR)%72eo(hLn!ESIqp{2FH(VE!Z9j}2!VT9M!s^K@DQVc+<{zS@ z`%@=)sL2h-U;N~Dl9)=lZHPx+312bSNE4Gnk{6rP!hAd(5t70^#pX+Loa?;IO~tr} zw{Y{d1A?i}#!d29H05Jsu`RJ7us-(0Vs#9Tl+5>atgG6nWLx|5dGeYdG;#{nhh9L|5Q7`&J+yCg zMo5R&7t-WZV!{Xo3U^)~I?7iS%%MN?ug4u2uT%C1<7!9X)$-Z_aFjuD*O|xxJkPAz^~)N$>LS zlxG)SEgq2VPCACvFQLQuS)tlrsebraG#0zNQ(WWgFs)L|1$eEA1tC^s79Q|qxS=An za)*GQ8~xnczB?~`NwBw0oF1V%i@sg>1HTsZ{3W(CrsA*lS*+_gthakS-sW)R<*9$Zs zrtuj`t+^w}B6tBS7M^1tK__zuIZ)#`|-xwOH zQ}WVzK|lcu;1Ujp=S8ahiyKFE5#12A+wf7^2Q8h_?`KJ+kk{GeaESIhD0=WzO@qw| zcX@5zri#w^6G@gf?{tK6nzDGQJ|)6@7eFghRzKdUVy@?RcV(&e@moS=!sG}7GbKIB z5FW)X*yM}-dxWkt!W?}ChhNLfr}>kBpC0H|i%#SMHx)0aVCZR7MTbZ*!yy+Nu^}kM zJ^ZA>Z1MM)cftr|VFQ1JGDb#m@i+PQ{B1BZ2qEKBvCUuI+rY+}$xkNPRmJtYxm<9Y zWUwH3SCt~j9Bfj^9~;8E3IW_u7e* zyHZeN3S;+Cl%z%+92_E}qTX$8x>o3MjsN+Ru((@l)%$(?arXx=_g@BD3Q-*Q3Jhva zo;j0cP~(0np8r}0!l=A9DDFpuc7Kxff8{wnZ9Cs7#$7WBdZ+XzJ5RUVa;7V*a;~U( zb;x63tJ2dyGfXVpdH(g=w`uQeHs3%f-*Ho|TnFiLZ6W z^=CQF_LPbVdaPUP!wvlY_3KMklZOw@2P>W8L_Nw*aq4u%JRYSQ`cW6m9i=2bXv?|Q zoe}1^-iHlkzy{G^xiJ=1=Mf)DNgiU??C^*P8d}$PJ!+zWmcC;strMQm(rP+(wI^#wLIfj$q3`vbLuB|a?YTS#8s z|7~-C+mMSv=wbOO#D_uh2eEDD{9sj%$Hsi*hN_B6iQTZ6==x7%I-Up8<6~UWIsF@M zB8hZi>XENrrJUh4RU2}t8uXV4SZ<@GJFhCayle`{b zOgs|Bse6)^R?|)V!UdTe&4PUAwruqrKF6uMnCNHBE922vkA>LTX>6yBrh{d*&4@{J z8q4ju9%5v%F4_El!=uKYseL2l1VFXM34nIZ=I>w>v_z?$nU4|ks=W2$bjoc;H|go= zX`M>PtRc@8MVp_69~TymeQX%OGYF|=FWUtrKgMsV43uF7hh-}&eCvYAk@|AK2PCLR z1vmxnFp9M`hUX^yUAZ$~bwTdw)2IF5zsI)%jxqJvln=i1-rKg=TpaB$GPlvK-6?Xx>!PTuFO0*0OWy;?>?m#6Bk$ zw-{Jid?b>!%3A#E{`?s^iV3&axpiA%XG3A3)(X9u;&5{hkv#?LxiX=m6L;esIJ7nh z4Q8@3zvjlXKfQy_5x

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changed, 1 deletion(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 1c3e3be..7527e63 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,5 +1,4 @@ from abc import ABC, abstractmethod -from typing import List import math import numpy as np from utils import ( -- Gitee From 7ec3ed75c5b42d2c54b2b9037b79f6bfe05cafee Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 13 Jun 2021 17:09:48 +0800 Subject: [PATCH 65/73] docs: k-means --- assignment-3/submission/18307130003/README.md | 610 +----------------- 1 file changed, 6 insertions(+), 604 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index 1e2e90a..5dc0abe 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -26,47 +26,6 @@ - [1.3.5 实验 5](#135-实验-5) - [1.3.5.1 数据集参数](#1351-数据集参数) - [1.3.5.2 实验结果](#1352-实验结果) - - [GMM 模型](#gmm-模型) - - [2.1 算法思路](#21-算法思路) - - [2.2 一些优化](#22-一些优化) - - [2.3 基础实验](#23-基础实验) - - [2.3.0 生成数据集](#230-生成数据集) - - [2.3.1 实验 1](#231-实验-1) - - [2.3.1.1 数据集参数](#2311-数据集参数) - - [2.3.1.2 实验结果](#2312-实验结果) - - [2.3.2 实验 2](#232-实验-2) - - [2.3.2.1 数据集参数](#2321-数据集参数) - - [2.3.2.2 实验结果](#2322-实验结果) - - [2.3.3 实验 3](#233-实验-3) - - [2.3.3.1 数据集参数](#2331-数据集参数) - - [2.3.3.2 实验结果](#2332-实验结果) - - [2.3.4 实验 4](#234-实验-4) - - [2.3.4.1 数据集参数](#2341-数据集参数) - - [2.3.4.2 实验结果](#2342-实验结果) - - [2.3.5 实验 5](#235-实验-5) - - [2.3.5.1 数据集参数](#2351-数据集参数) - - [2.3.5.2 实验结果](#2352-实验结果) - - [自动选择聚簇数量](#自动选择聚簇数量) - - [3.1 算法思路](#31-算法思路) - - [3.2 一些优化](#32-一些优化) - - [3.3 基础实验](#33-基础实验) - - [3.3.0 生成数据集](#330-生成数据集) - - [3.3.1 实验 1](#331-实验-1) - - [3.3.1.1 数据集参数](#3311-数据集参数) - - [3.3.1.2 实验结果](#3312-实验结果) - - [3.3.2 实验 2](#332-实验-2) - - [3.3.2.1 数据集参数](#3321-数据集参数) - - [3.3.2.2 实验结果](#3322-实验结果) - - [3.3.3 实验 3](#333-实验-3) - - [3.3.3.1 数据集参数](#3331-数据集参数) - - [3.3.3.2 实验结果](#3332-实验结果) - - [3.3.4 实验 4](#334-实验-4) - - [3.3.4.1 数据集参数](#3341-数据集参数) - - [3.3.4.2 实验结果](#3342-实验结果) - - [3.3.5 实验 5](#335-实验-5) - - [3.3.5.1 数据集参数](#3351-数据集参数) - - [3.3.5.2 实验结果](#3352-实验结果) - - [运行代码](#运行代码) ## K-Means 模型 @@ -83,7 +42,7 @@ K-Means 模型的算法思路很简单,具体训练过程如下: 例如对于一个随机生成的数据集,我们利用 K-Means 模型将其分为 3 类的结果如下: -![K-Means](./img/k-means_1_train.png) +![K-Means](./img/auto-k-means_1_train.png) ### 1.2 一些优化 @@ -91,16 +50,9 @@ K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择 ![K-Means 局部最优解](./img/k-means_1_bad_train.png) -作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各簇内距离(各数据点到聚簇中心距离)的平方和最小,具体来说,即要求如下参数的值最小: +作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各数据点到各聚簇中心距离的平方和最小,具体来说,即要求如下参数的值最小: -$$ -W -= \sum\_{\mathbf{x}\_i\in \mathbf{D}} - \sum\_{\mathbf{c}\_k\in \mathbf{C}} - (\mathbf{x}\_i - \mathbf{c}\_k)^2 -$$ - -其中,$\mathbf{x}\_i$ 为数据点,$\mathbf{D}$ 为数据集,$\mathbf{c}\_k$ 为聚簇中心,$\mathbf{C}$ 为聚簇中心集。 +$$\sum_{\mathbf{x}_i\in \mathbf{D}}\sum_{\mathbf{c}_k\in \mathbf{C}} (\mathbf{x}_i - \mathbf{c}_k)^2$$ 经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 @@ -289,19 +241,19 @@ size = 800 ```python {.line-numbers} mean = (-20,) -scale = 2 +scale = 6 size = 100 ``` ```python {.line-numbers} mean = (0,) -scale = 1 +scale = 3 size = 150 ``` ```python {.line-numbers} mean = (15,) -scale = 2 +scale = 3 size = 100 ``` @@ -350,553 +302,3 @@ size = 500 ![K-Means 测试集](./img/k-means_5_test.png) 可见,对于这样的数据集,由于 K-Means 模型以距离为唯一参考的特性,其分类结果不是很理想。这也是我们为什么要引入 GMM 模型。 - -## GMM 模型 - -### 2.1 算法思路 - -GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不再以到聚簇中心的距离为参考标准,而是用 $K$ 个单一高斯分布的线性组合来拟合原数据集。我们将使用 EM 算法进行迭代,具体训练过程如下: - -1. 给定 $K$ 值(需要将数据集聚成几个簇),初始化各个参数 - - - `means`:从数据集中随机选择 $K$ 个点,作为每个高斯分布的初始中心点 - - `covs`:对于多维的情形,初始化每个高斯分布的协方差为一个单元矩阵 - - `scales`:对于一维的情形,初始化每个高斯分布的标准差为 $1$ - - `weights`:初始化任一数据点被分配到每个聚簇的先验概率为 $\frac{1}{K}$ - -2. EM 算法的 E(xpectation) 步骤:通过目前的参数计算每个数据点被分配到每个聚簇的概率 - - - 先计算给定参数的高斯分布的概率密度函数(PDF) - - - 对于多维的情形, - - $$ - p(\mathbf{x}) - = \frac{1}{\sqrt{(2\pi)^d |\mathbf{\Sigma}\_i|}} - \exp( - -\frac{1}{2} - (\mathbf{x}-\mathbf{\mu}\_i)^\mathrm{T} - \mathbf{\Sigma}\_i^{-1} - (\mathbf{x}-\mathbf{\mu}\_i) - ) - $$ - - 其中 $i$ 表示第 $i$ 个聚簇、$d$ 表示数据点的维度、$\mathbf{\mu}$ 表示 `means`、$\mathbf{\Sigma}$ 表示 `covs` - - - 对于一维的情形, - - $$ - p(x) - = \frac{1}{\sqrt{2\pi\sigma\_i^2}} - \exp(-\frac{(x-\mu\_i)^2}{2\sigma\_i^2}) - $$ - - 其中 $i$ 表示第 $i$ 个聚簇、$\mu$ 表示 `means`、$\sigma$ 表示 `scales` - - - 然后利用 Bayes' Theorem,计算每个数据点被分配到每个聚簇的概率 - - $$ - f_i(\mathbf{x}) - = \frac{p(\mathbf{x})\phi\_i}{\sum\limits\_{i=1}^k p(\mathbf{x})\phi\_i} - $$ - - 其中 $i$ 表示第 $i$ 个聚簇、$\phi$ 表示 `weights`、$k$ 表示 $K$ 值 - -3. EM 算法的 M(aximization) 步骤:根据当前每个聚簇的概率矩阵,更新模型的各个参数 - - - `means`: - - $$ - \mathbf{\mu}\_i - = \frac - {\sum\limits\_{i=1}^k(f\_i(\mathbf{x})\cdot \mathbf{x})} - {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} - $$ - - - `covs`:对于多维的情形, - - $$ - \mathbf{\Sigma}\_i - = \frac - {\sum\limits\_{i=1}^k( - f\_i(\mathbf{x})\cdot - (\mathbf{x}-\mathbf{\mu}\_i)^\mathrm{T} - (\mathbf{x}-\mathbf{\mu}\_i) - )} - {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} - $$ - - - `scales`:对于一维的情形, - - $$ - \mathbf{\sigma}\_i - = \sqrt{ - \frac - {\sum\limits\_{i=1}^k(f\_i(x)\cdot (x-\mu\_i)^2)} - {\sum\limits\_{i=1}^k f\_i(x)} - } - $$ - - - `weights`: - - $$ - \phi\_i = \frac{1}{N} {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} - $$ - -4. 重复 EM 算法,直到满足终止条件;GMM 模型的终止条件与 K-Means 模型一致 - -预测时,对于每个数据点,我们根据每个聚簇的概率矩阵,选择概率最大的聚簇作为数据点所属的聚簇。 - -例如对于一个随机生成的数据集,我们利用 GMM 模型将其分为 3 类的结果如下: - -![GMM](./img/gmm_1_train.png) - -### 2.2 一些优化 - -与 K-Means 模型类似,GMM 模型初始时的聚簇中心也是随机选择的,因此这里我们采用了和 K-Means 模型一样的优化思路,即使用不同的随机种子训练 `n_epochs` 次,最后选择最优的训练模型作为预测时使用的模型。与 K-Means 模型不同的地方在于,在 GMM 模型中,我们不能简单地使用到聚簇中心的距离作为参考标准。实际上,我们希望每个数据点被分配到其所属的聚簇时,其在概率矩阵中对应的概率尽可能大。因此,这里我们对「最优」的判断标准是,要求如下参数的值最大: - -$$ -\sum\limits\_{i=1}^N \max\_{1\le j\le k}{\{f\_j(\mathbf{x})\}} -$$ - -经实验,这个优化也可以有效地使 GMM 模型收敛到全局最优解。 - -### 2.3 基础实验 - -#### 2.3.0 生成数据集 - -这里我们使用与 K-Means 相同的数据集生成方法。 - -#### 2.3.1 实验 1 - -第一个实验,我们对 3 个二维高斯分布数据集进行分类。 - -##### 2.3.1.1 数据集参数 - -```python {.line-numbers} -mean = (1, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (16, -5) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (10, 22) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -##### 2.3.1.2 实验结果 - -训练集,要求分为 3 类: - -![GMM 训练集](./img/gmm_1_train.png) - -测试集,要求分为 3 类: - -![GMM 测试集](./img/gmm_1_test.png) - -#### 2.3.2 实验 2 - -第二个实验,我们对 5 个二维高斯分布数据集进行分类。 - -##### 2.3.2.1 数据集参数 - -```python {.line-numbers} -mean = (1, 0) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (20, 15) -cov = [[21.2, 0], [0, 32.1]] -size = 400 -``` - -```python {.line-numbers} -mean = (10, -22) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -```python {.line-numbers} -mean = (-12, -6) -cov = [[7, 3], [3, 16]] -size = 500 -``` - -```python {.line-numbers} -mean = (-15, 17) -cov = [[15, 0], [0, 12]] -size = 600 -``` - -##### 2.3.2.2 实验结果 - - -训练集,要求分为 5 类: - -![GMM 训练集](./img/gmm_2_train.png) - -测试集,要求分为 5 类: - -![GMM 测试集](./img/gmm_2_test.png) - -#### 2.3.3 实验 3 - -第三个实验,我们对 3 个三维高斯分布数据集进行分类。 - -##### 2.3.3.1 数据集参数 - -```python {.line-numbers} -mean = (-6, 3, 5) -cov = [[73, 0, 0], [0, 50, 0], [0, 0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (12, 0, -10) -cov = [[20, 5, 0], [5, 20, 0], [0, 0, 20]] -size = 500 -``` - -```python {.line-numbers} -mean = (10, -20, 0) -cov = [[10, 1, 3], [1, 10, 0], [3, 0, 10]] -size = 800 -``` - -##### 2.3.3.2 实验结果 - -训练集,要求分为 3 类: - -![GMM 训练集](./img/gmm_3_train.png) - -测试集,要求分为 3 类: - -![GMM 测试集](./img/gmm_3_test.png) - -#### 2.3.4 实验 4 - -第四个实验,我们对 3 个一维高斯分布数据集进行分类。 - -##### 2.3.4.1 数据集参数 - -```python {.line-numbers} -mean = (-20,) -scale = 2 -size = 100 -``` - -```python {.line-numbers} -mean = (0,) -scale = 1 -size = 150 -``` - -```python {.line-numbers} -mean = (15,) -scale = 2 -size = 100 -``` - -##### 2.3.4.2 实验结果 - -训练集,要求分为 3 类: - -![GMM 训练集](./img/gmm_4_train.png) - -测试集,要求分为 3 类: - -![GMM 测试集](./img/gmm_4_test.png) - -#### 2.3.5 实验 5 - -第五个实验,我们对 3 个扁平形状的二维高斯分布数据集进行分类。 - -##### 2.3.5.1 数据集参数 - -```python {.line-numbers} -mean = (0, -5) -cov = [[73, 0], [0, 2]] -size = 800 -``` - -```python {.line-numbers} -mean = (-3, 0) -cov = [[100, 0], [0, 2]] -size = 500 -``` - -```python {.line-numbers} -mean = (2, 5) -cov = [[70, 1], [1, 3]] -size = 500 -``` - -##### 2.3.5.2 实验结果 - -训练集,要求分为 3 类: - -![GMM 训练集](./img/gmm_5_train.png) - -测试集,要求分为 3 类: - -![GMM 测试集](./img/gmm_5_test.png) - -可见,GMM 模型对于高斯混合分布数据集,其分类结果比 K-Means 模型更加准确。 - -## 自动选择聚簇数量 - -### 3.1 算法思路 - -这里我们利用 Gap Statistic 方法实现了数据集中聚簇数量的自动推测。Gap Statistic 方法的思想是,对于数据集聚类结果的簇内距离,它和同规模均匀分布的期望簇内距离相比,两者的差距越大,则认为模型的分类结果越好,即 $K$ 值的选择越好。具体来说,即希望如下参数的值尽可能大: - -$$ -\mathrm{Gap}\_k = \mathrm{E}(\log {W'}\_k) - \log W\_k -$$ - -其中,$k$ 即选择的 $K$ 值,$W\_k$ 为数据集 $\mathbf{D}$ 聚类结果的簇内距离的平方和,${W'}\_k$ 为同规模均匀分布 $\mathbf{U}$ 聚类结果的簇内距离的平方和。这里 $W$ 的具体定义参见 1.2 节。 - -我们利用 Monte Carlo Method 计算 $\mathrm{E}(\log {W'}\_k)$ 的值。我们在数据集 $\mathbf{D}$ 覆盖的矩形范围内进行 $B$ 次随机均匀采样,得到 $B$ 个不同的 ${W'}\_k^{(b)}$,于是我们有 - -$$ -\mathrm{E}(\log {W'}\_k) -= \frac{1}{B} \sum\limits\_{b=1}^B \log {W'}\_k^{(b)} -$$ - -我们的算法底层建立在 K-Means 模型的基础上。实验时,需指定扫描时的最大 $K$ 值 $K\_{\max}$,模型将在 $[1, K\_{\max}]$ 的范围内找到使得 $\mathrm{Gap}\_k$ 的值最大的 $K$ 值,作为推测的数据集中的聚簇数量。 - -### 3.2 一些优化 - -为了一定程度上减少扫描时间,我们设定了一个终止阈值 `BREAK_THRESHOLD`(默认为 `3`)。当 $\mathrm{Gap}\_k$ 连续 `BREAK_THRESHOLD` 次没有增长时,我们认为已经找到了最优的 $K$ 值,模型自动终止扫描。 - -### 3.3 基础实验 - -#### 3.3.0 生成数据集 - -这里我们使用与 K-Means 相同的数据集生成方法。 - -#### 3.3.1 实验 1 - -第一个实验,我们对 3 个二维高斯分布数据集进行分类。 - -##### 3.3.1.1 数据集参数 - -```python {.line-numbers} -mean = (1, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (16, -5) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (10, 22) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -##### 3.3.1.2 实验结果 - -训练集,不指定 $K$ 值: - -![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_1_gaps.png) - -模型选择的 $K$ 值为 $3$,分类结果: - -![Auto K-Means 训练集](./img/auto-k-means_1_train.png) - -测试集,不指定 $K$ 值: - -![Auto K-Means 测试集](./img/auto-k-means_1_test.png) - -#### 3.3.2 实验 2 - -第二个实验,我们对 5 个二维高斯分布数据集进行分类。 - -##### 3.3.2.1 数据集参数 - -```python {.line-numbers} -mean = (1, 0) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (20, 15) -cov = [[21.2, 0], [0, 32.1]] -size = 400 -``` - -```python {.line-numbers} -mean = (10, -22) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -```python {.line-numbers} -mean = (-12, -6) -cov = [[7, 3], [3, 16]] -size = 500 -``` - -```python {.line-numbers} -mean = (-15, 17) -cov = [[15, 0], [0, 12]] -size = 600 -``` - -##### 3.3.2.2 实验结果 - -训练集,不指定 $K$ 值: - -![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_2_gaps.png) - -模型选择的 $K$ 值为 $6$,分类结果: - -![Auto K-Means 训练集](./img/auto-k-means_2_train.png) - -测试集,不指定 $K$ 值: - -![Auto K-Means 测试集](./img/auto-k-means_2_test.png) - -虽然实际上应当是 $5$ 个高斯分布,不过考虑到模型在 $K=5$ 和 $K=6$ 处都取得了较高的 $\mathrm{Gap}$ 值,这个分类结果也是可以理解的。 - -#### 3.3.3 实验 3 - -第三个实验,我们对 3 个三维高斯分布数据集进行分类。 - -##### 3.3.3.1 数据集参数 - -```python {.line-numbers} -mean = (-6, 3, 5) -cov = [[73, 0, 0], [0, 50, 0], [0, 0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (12, 0, -10) -cov = [[20, 5, 0], [5, 20, 0], [0, 0, 20]] -size = 500 -``` - -```python {.line-numbers} -mean = (10, -20, 0) -cov = [[10, 1, 3], [1, 10, 0], [3, 0, 10]] -size = 800 -``` - -##### 3.3.3.2 实验结果 - -训练集,不指定 $K$ 值: - -![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_3_gaps.png) - -模型选择的 $K$ 值为 $4$,分类结果: - -![Auto K-Means 训练集](./img/auto-k-means_3_train.png) - -测试集,不指定 $K$ 值: - -![Auto K-Means 测试集](./img/auto-k-means_3_test.png) - -类似地,模型在 $K=3$ 和 $K=4$ 处都取得了较高的 $\mathrm{Gap}$ 值,说明这两种 $K$ 值都是可以接受的。 - -#### 3.3.4 实验 4 - -第四个实验,我们对 3 个一维高斯分布数据集进行分类。 - -##### 3.3.4.1 数据集参数 - -```python {.line-numbers} -mean = (-20,) -scale = 2 -size = 100 -``` - -```python {.line-numbers} -mean = (0,) -scale = 1 -size = 150 -``` - -```python {.line-numbers} -mean = (15,) -scale = 2 -size = 100 -``` - -##### 3.3.4.2 实验结果 - -训练集,不指定 $K$ 值: - -![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_4_gaps.png) - -模型选择的 $K$ 值为 $3$,分类结果: - -![Auto K-Means 训练集](./img/auto-k-means_4_train.png) - -测试集,不指定 $K$ 值: - -![Auto K-Means 测试集](./img/auto-k-means_4_test.png) - -#### 3.3.5 实验 5 - -第五个实验,我们对 3 个扁平形状的二维高斯分布数据集进行分类。 - -##### 3.3.5.1 数据集参数 - -```python {.line-numbers} -mean = (0, -5) -cov = [[73, 0], [0, 2]] -size = 800 -``` - -```python {.line-numbers} -mean = (-3, 0) -cov = [[100, 0], [0, 2]] -size = 500 -``` - -```python {.line-numbers} -mean = (2, 5) -cov = [[70, 1], [1, 3]] -size = 500 -``` - -##### 3.3.5.2 实验结果 - -训练集,不指定 $K$ 值: - -![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_5_gaps.png) - -模型选择的 $K$ 值为 $1$,分类结果: - -![Auto K-Means 训练集](./img/auto-k-means_5_train.png) - -测试集,不指定 $K$ 值: - -![Auto K-Means 测试集](./img/auto-k-means_5_test.png) - -实际上,从人类的视角来看,这个聚类结果也是可以理解的。 - -## 运行代码 - -执行以下指令进行模型的训练与预测。 - -```bash -python ./tester.py -``` - -生成数据集使用的参数等可以在 `TestSuite` 类中对应调整。 -- Gitee From de09e2f604bae9809bf89c5286830def6cc806d2 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 14 Jun 2021 03:23:08 +0800 Subject: [PATCH 66/73] fix: modified test data 4, changed initializing scales logic in auto k-means --- assignment-3/submission/18307130003/README.md | 6 +++--- .../18307130003/img/auto-k-means_1_gaps.png | Bin 17429 -> 18095 bytes .../18307130003/img/auto-k-means_1_test.png | Bin 54289 -> 51344 bytes .../18307130003/img/auto-k-means_1_train.png | Bin 68244 -> 68661 bytes .../18307130003/img/auto-k-means_2_gaps.png | Bin 18577 -> 17722 bytes 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.../18307130003/img/k-means_4_train.png | Bin 9791 -> 7688 bytes assignment-3/submission/18307130003/source.py | 8 ++++---- assignment-3/submission/18307130003/tester.py | 6 +++--- 22 files changed, 10 insertions(+), 10 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index 5dc0abe..eb270d9 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -241,19 +241,19 @@ size = 800 ```python {.line-numbers} mean = (-20,) -scale = 6 +scale = 2 size = 100 ``` ```python {.line-numbers} mean = (0,) -scale = 3 +scale = 1 size = 150 ``` ```python {.line-numbers} mean = (15,) -scale = 3 +scale = 2 size = 100 ``` diff --git a/assignment-3/submission/18307130003/img/auto-k-means_1_gaps.png b/assignment-3/submission/18307130003/img/auto-k-means_1_gaps.png index 7e66027fd2f06ccffec0e7578def03ec58f378fe..9f7543762793a7d4963a948a300472abdf4a45a3 100644 GIT binary patch literal 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z;Auqi)E!0?z+J8K$vA|lh8W$4GizOL6Q{N=37B|W2M75}{%0VV$_XZB*AM8!N+0|A zKzt z)#@D}F}Bu==+~)KDyLjEB@~6gJ6>c8o%uluxtxsxM0tWFzYX&NtQ(otK(~hT{uag| zhlX&Fq1erC6S8oy*bgg-3$KN@Emm(SGFKF$Dvu&Ius7jn9LGCjzo#a1hc9rEZAZ~LU*%;B6ao@R;>*;H6Wq|ucLqkJbX4Yu;j8QK~=F;!5aRPyE z)v+=1x0>}Nv0KJv6P diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 7527e63..1f75260 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -196,14 +196,14 @@ class GaussianMixture(Model): if self.dimension > 1: # Initialize the coefficient of variation of each Gaussian - # distribution to be a random identity matrix. + # distribution to be an identity matrix. self.covs = np.array([ np.identity(self.dimension) for _i in range(self.k) ]) else: # Initialize the standard deviation of each Gaussian distribution - # to be a random float. - self.scales = self.rng.random(self.k) * 10 + # to be 1. + self.scales = np.ones(self.k) # Initialize the likelihood that an observation belongs to a cluster # to be 1/k for all clusters. @@ -232,7 +232,7 @@ class GaussianMixture(Model): self.likelihoods = self.best_likelihoods # Calculate the posterior probability that an observation belongs to - # each Gaussian distribution, using Bayes Theorem. + # each Gaussian distribution, using Bayes' Theorem. self.likelihoods = np.zeros((data_size, self.k)) for i, x_i in enumerate(dataset): # Calculate the likelihood of each observation x_i. diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 7e36b6b..c2c14ae 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -199,17 +199,17 @@ class TestSuite: NormalParameters( size=100, mean=(-20,), - scale=6, + scale=2, ), NormalParameters( size=150, mean=(0,), - scale=3, + scale=1, ), NormalParameters( size=100, mean=(15,), - scale=3, + scale=2, ), ) -- Gitee From 4d10954e56c8509e754c2fb04d2faa0a6a07d922 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 14 Jun 2021 04:07:23 +0800 Subject: [PATCH 67/73] docs: gmm (wip) --- assignment-3/submission/18307130003/README.md | 85 ++++++++++++++++++- 1 file changed, 84 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index eb270d9..0d08197 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -26,6 +26,10 @@ - [1.3.5 实验 5](#135-实验-5) - [1.3.5.1 数据集参数](#1351-数据集参数) - [1.3.5.2 实验结果](#1352-实验结果) + - [GMM 模型](#gmm-模型) + - [2.1 算法思路](#21-算法思路) + - [2.2 一些优化](#22-一些优化) + - [2.3 基础实验](#23-基础实验) ## K-Means 模型 @@ -52,7 +56,11 @@ K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择 作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各数据点到各聚簇中心距离的平方和最小,具体来说,即要求如下参数的值最小: -$$\sum_{\mathbf{x}_i\in \mathbf{D}}\sum_{\mathbf{c}_k\in \mathbf{C}} (\mathbf{x}_i - \mathbf{c}_k)^2$$ +$$ +\sum_{\mathbf{x}_i\in \mathbf{D}} +\sum_{\mathbf{c}_k\in \mathbf{C}} +(\mathbf{x}_i - \mathbf{c}_k)^2 +$$ 经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 @@ -302,3 +310,78 @@ size = 500 ![K-Means 测试集](./img/k-means_5_test.png) 可见,对于这样的数据集,由于 K-Means 模型以距离为唯一参考的特性,其分类结果不是很理想。这也是我们为什么要引入 GMM 模型。 + +## GMM 模型 + +### 2.1 算法思路 + +GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不再以到聚簇中心的距离为参考标准,而是用 $K$ 个单一高斯分布的线性组合来拟合原数据集。我们将使用 EM 算法进行迭代,具体训练过程如下: + +1. 给定 $K$ 值(需要将数据集聚成几个簇),初始化各个参数 + + - `means`:从数据集中随机选择 $K$ 个点,作为每个高斯分布的初始中心点 + - `covs`:初始化每个高斯分布的协方差为一个单元矩阵(对于多维的情形) + - `scales`:初始化每个高斯分布的标准差为 $1$(对于一维的情形) + - `weights`:初始化任一数据点被分配到每个聚簇的先验概率为 $\frac{1}{K}$ + +2. EM 算法的 E(xpectation) 步骤:通过目前的参数计算每个数据点被分配到每个聚簇的概率 + + - 先计算给定参数的高斯分布的概率密度函数(PDF) + + - 对于多维的情形, + + $$ + p(\mathbf{x}) + = \frac{1}{\sqrt{(2\pi)^d |\mathbf{\Sigma}_i|}} + \exp( + -\frac{1}{2} + (\mathbf{x}-\mathbf{\mu}_i)^\mathrm{T} + \mathbf{\Sigma}_i^{-1} + (\mathbf{x}-\mathbf{\mu}_i) + ) + $$ + + 其中 $i$ 表示第 $i$ 个聚簇、$d$ 表示数据点的维度、$\mathbf{\mu}$ 表示 `means`、$\mathbf{\Sigma}$ 表示 `covs` + + - 对于一维的情形, + + $$ + p(x) + = \frac{1}{\sqrt{2\pi\sigma_i^2}} + \exp(-\frac{(x-\mu_i)^2}{2\sigma_i^2}) + $$ + + 其中 $i$ 表示第 $i$ 个聚簇、$\mu$ 表示 `means`、$\sigma$ 表示 `scales` + + - 然后利用 Bayes' Theorem,计算每个数据点被分配到每个聚簇的概率 + + $$ + f_i(\mathbf{x}) + = \frac{p(\mathbf{x})\phi_i}{\Sigma_{i=1}^k p(\mathbf{x})\phi_i} + $$ + + 其中 $i$ 表示第 $i$ 个聚簇、$\phi$ 表示 `weights`、$\sigma$ 表示 `scales`、$k$ 表示 $K$ 值 + +3. EM 算法的 M(aximization) 步骤: + +4. 重复以上步骤,直到满足终止条件;这里我们选择的终止条件是,没有数据点的标签(即分配到的聚簇中心)再发生变化(当然也可以设置为其他合理的终止条件) + +预测时,我们选择距离数据点最近的聚簇中心,作为数据点所属的聚簇。 + +例如对于一个随机生成的数据集,我们利用 K-Means 模型将其分为 3 类的结果如下: + +![K-Means](./img/auto-k-means_1_train.png) + +### 2.2 一些优化 + +K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择的,如果选择得不好,可能会导致收敛到局部最优解而非全局最优解。例如对于同样的数据集,可能生成如下的分类结果: + +![K-Means 局部最优解](./img/k-means_1_bad_train.png) + +作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各数据点到各聚簇中心距离的平方和最小,具体来说,即要求如下参数的值最小: + +$$\sum_{\mathbf{x}_i\in \mathbf{D}}\sum_{\mathbf{c}_k\in \mathbf{C}} (\mathbf{x}_i - \mathbf{c}_k)^2$$ + +经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 + +### 2.3 基础实验 -- Gitee From 5f425645386bc27956162f14022cb4cdba29fa19 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 14 Jun 2021 15:01:09 +0800 Subject: [PATCH 68/73] docs: gmm --- assignment-3/submission/18307130003/README.md | 274 +++++++++++++++++- 1 file changed, 258 insertions(+), 16 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index 0d08197..0622090 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -30,6 +30,22 @@ - [2.1 算法思路](#21-算法思路) - [2.2 一些优化](#22-一些优化) - [2.3 基础实验](#23-基础实验) + - [2.3.0 生成数据集](#230-生成数据集) + - [2.3.1 实验 1](#231-实验-1) + - [2.3.1.1 数据集参数](#2311-数据集参数) + - [2.3.1.2 实验结果](#2312-实验结果) + - [2.3.2 实验 2](#232-实验-2) + - [2.3.2.1 数据集参数](#2321-数据集参数) + - [2.3.2.2 实验结果](#2322-实验结果) + - [2.3.3 实验 3](#233-实验-3) + - [2.3.3.1 数据集参数](#2331-数据集参数) + - [2.3.3.2 实验结果](#2332-实验结果) + - [2.3.4 实验 4](#234-实验-4) + - [2.3.4.1 数据集参数](#2341-数据集参数) + - [2.3.4.2 实验结果](#2342-实验结果) + - [2.3.5 实验 5](#235-实验-5) + - [2.3.5.1 数据集参数](#2351-数据集参数) + - [2.3.5.2 实验结果](#2352-实验结果) ## K-Means 模型 @@ -46,7 +62,7 @@ K-Means 模型的算法思路很简单,具体训练过程如下: 例如对于一个随机生成的数据集,我们利用 K-Means 模型将其分为 3 类的结果如下: -![K-Means](./img/auto-k-means_1_train.png) +![K-Means](./img/k-means_1_train.png) ### 1.2 一些优化 @@ -320,8 +336,8 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 1. 给定 $K$ 值(需要将数据集聚成几个簇),初始化各个参数 - `means`:从数据集中随机选择 $K$ 个点,作为每个高斯分布的初始中心点 - - `covs`:初始化每个高斯分布的协方差为一个单元矩阵(对于多维的情形) - - `scales`:初始化每个高斯分布的标准差为 $1$(对于一维的情形) + - `covs`:对于多维的情形,初始化每个高斯分布的协方差为一个单元矩阵 + - `scales`:对于一维的情形,初始化每个高斯分布的标准差为 $1$ - `weights`:初始化任一数据点被分配到每个聚簇的先验概率为 $\frac{1}{K}$ 2. EM 算法的 E(xpectation) 步骤:通过目前的参数计算每个数据点被分配到每个聚簇的概率 @@ -357,31 +373,257 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 $$ f_i(\mathbf{x}) - = \frac{p(\mathbf{x})\phi_i}{\Sigma_{i=1}^k p(\mathbf{x})\phi_i} + = \frac{p(\mathbf{x})\phi_i}{\sum\limits_{i=1}^k p(\mathbf{x})\phi_i} $$ - 其中 $i$ 表示第 $i$ 个聚簇、$\phi$ 表示 `weights`、$\sigma$ 表示 `scales`、$k$ 表示 $K$ 值 + 其中 $i$ 表示第 $i$ 个聚簇、$\phi$ 表示 `weights`、$k$ 表示 $K$ 值 -3. EM 算法的 M(aximization) 步骤: +3. EM 算法的 M(aximization) 步骤:根据当前每个聚簇的概率矩阵,更新模型的各个参数 -4. 重复以上步骤,直到满足终止条件;这里我们选择的终止条件是,没有数据点的标签(即分配到的聚簇中心)再发生变化(当然也可以设置为其他合理的终止条件) + - `means`: -预测时,我们选择距离数据点最近的聚簇中心,作为数据点所属的聚簇。 + $$ + \mathbf{\mu}_i + = \frac + {\sum\limits_{i=1}^k(f_i(\mathbf{x})\cdot \mathbf{x})} + {\sum\limits_{i=1}^k f_i(\mathbf{x})} + $$ -例如对于一个随机生成的数据集,我们利用 K-Means 模型将其分为 3 类的结果如下: + - `covs`:对于多维的情形, -![K-Means](./img/auto-k-means_1_train.png) + $$ + \mathbf{\Sigma}_i + = \frac + {\sum\limits_{i=1}^k( + f_i(\mathbf{x})\cdot + (\mathbf{x}-\mathbf{\mu}_i)^\mathrm{T} + (\mathbf{x}-\mathbf{\mu}_i) + )} + {\sum\limits_{i=1}^k f_i(\mathbf{x})} + $$ -### 2.2 一些优化 + - `scales`:对于一维的情形, -K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择的,如果选择得不好,可能会导致收敛到局部最优解而非全局最优解。例如对于同样的数据集,可能生成如下的分类结果: + $$ + \mathbf{\sigma}_i + = \sqrt{ + \frac + {\sum\limits_{i=1}^k(f_i(x)\cdot (x-\mu_i)^2)} + {\sum\limits_{i=1}^k f_i(x)} + } + $$ -![K-Means 局部最优解](./img/k-means_1_bad_train.png) + - `weights`: -作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各数据点到各聚簇中心距离的平方和最小,具体来说,即要求如下参数的值最小: + $$ + \phi_i = \frac{1}{N} {\sum\limits_{i=1}^k f_i(\mathbf{x})} + $$ -$$\sum_{\mathbf{x}_i\in \mathbf{D}}\sum_{\mathbf{c}_k\in \mathbf{C}} (\mathbf{x}_i - \mathbf{c}_k)^2$$ +4. 重复 EM 算法,直到满足终止条件;GMM 模型的终止条件与 K-Means 模型一致 -经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 +预测时,对于每个数据点,我们根据每个聚簇的概率矩阵,选择概率最大的聚簇作为数据点所属的聚簇。 + +例如对于一个随机生成的数据集,我们利用 GMM 模型将其分为 3 类的结果如下: + +![GMM](./img/gmm_1_train.png) + +### 2.2 一些优化 + +与 K-Means 模型类似,GMM 模型初始时的聚簇中心也是随机选择的,因此这里我们采用了和 K-Means 模型一样的优化思路,即使用不同的随机种子训练 `n_epochs` 次,最后选择最优的训练模型作为预测时使用的模型。与 K-Means 模型不同的地方在于,在 GMM 模型中,我们不能简单地使用到聚簇中心的距离作为参考标准。实际上,我们希望每个数据点被分配到其所属的聚簇时,其在概率矩阵中对应的概率尽可能大。因此,这里我们对「最优」的判断标准是,要求如下参数的值最大: + +$$ +\sum\limits_{i=1}^N \max_{1\le j\le k}{\{f_j(\mathbf{x})\}} +$$ + +经实验,这个优化也可以有效地使 GMM 模型收敛到全局最优解。 ### 2.3 基础实验 + +#### 2.3.0 生成数据集 + +这里我们使用与 K-Means 相同的数据集生成方法。 + +#### 2.3.1 实验 1 + +第一个实验,我们对 3 个二维高斯分布数据集进行分类。 + +##### 2.3.1.1 数据集参数 + +```python {.line-numbers} +mean = (1, 2) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (16, -5) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (10, 22) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +##### 2.3.1.2 实验结果 + +训练集,要求分为 3 类: + +![GMM 训练集](./img/gmm_1_train.png) + +测试集,要求分为 3 类: + +![GMM 测试集](./img/gmm_1_test.png) + +#### 2.3.2 实验 2 + +第二个实验,我们对 5 个二维高斯分布数据集进行分类。 + +##### 2.3.2.1 数据集参数 + +```python {.line-numbers} +mean = (1, 0) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (20, 15) +cov = [[21.2, 0], [0, 32.1]] +size = 400 +``` + +```python {.line-numbers} +mean = (10, -22) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +```python {.line-numbers} +mean = (-12, -6) +cov = [[7, 3], [3, 16]] +size = 500 +``` + +```python {.line-numbers} +mean = (-15, 17) +cov = [[15, 0], [0, 12]] +size = 600 +``` + +##### 2.3.2.2 实验结果 + + +训练集,要求分为 5 类: + +![GMM 训练集](./img/gmm_2_train.png) + +测试集,要求分为 5 类: + +![GMM 测试集](./img/gmm_2_test.png) + +#### 2.3.3 实验 3 + +第三个实验,我们对 3 个三维高斯分布数据集进行分类。 + +##### 2.3.3.1 数据集参数 + +```python {.line-numbers} +mean = (-6, 3, 5) +cov = [[73, 0, 0], [0, 50, 0], [0, 0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (12, 0, -10) +cov = [[20, 5, 0], [5, 20, 0], [0, 0, 20]] +size = 500 +``` + +```python {.line-numbers} +mean = (10, -20, 0) +cov = [[10, 1, 3], [1, 10, 0], [3, 0, 10]] +size = 800 +``` + +##### 2.3.3.2 实验结果 + +训练集,要求分为 3 类: + +![GMM 训练集](./img/gmm_3_train.png) + +测试集,要求分为 3 类: + +![GMM 测试集](./img/gmm_3_test.png) + +#### 2.3.4 实验 4 + +第四个实验,我们对 3 个一维高斯分布数据集进行分类。 + +##### 2.3.4.1 数据集参数 + +```python {.line-numbers} +mean = (-20,) +scale = 2 +size = 100 +``` + +```python {.line-numbers} +mean = (0,) +scale = 1 +size = 150 +``` + +```python {.line-numbers} +mean = (15,) +scale = 2 +size = 100 +``` + +##### 2.3.4.2 实验结果 + +训练集,要求分为 3 类: + +![GMM 训练集](./img/gmm_4_train.png) + +测试集,要求分为 3 类: + +![GMM 测试集](./img/gmm_4_test.png) + +#### 2.3.5 实验 5 + +第五个实验,我们对 3 个扁平形状的二维高斯分布数据集进行分类。 + +##### 2.3.5.1 数据集参数 + +```python {.line-numbers} +mean = (0, -5) +cov = [[73, 0], [0, 2]] +size = 800 +``` + +```python {.line-numbers} +mean = (-3, 0) +cov = [[100, 0], [0, 2]] +size = 500 +``` + +```python {.line-numbers} +mean = (2, 5) +cov = [[70, 1], [1, 3]] +size = 500 +``` + +##### 2.3.5.2 实验结果 + +训练集,要求分为 3 类: + +![GMM 训练集](./img/gmm_5_train.png) + +测试集,要求分为 3 类: + +![GMM 测试集](./img/gmm_5_test.png) + +可见,GMM 模型对于高斯混合分布数据集,其分类结果比 K-Means 模型更加准确。 -- Gitee From 7e707f452b917b43fb4552b754333ef7347f31c0 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 14 Jun 2021 16:13:29 +0800 Subject: [PATCH 69/73] docs: auto k-means done. --- assignment-3/submission/18307130003/README.md | 281 +++++++++++++++++- 1 file changed, 277 insertions(+), 4 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index 0622090..e2e4fcf 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -46,6 +46,27 @@ - [2.3.5 实验 5](#235-实验-5) - [2.3.5.1 数据集参数](#2351-数据集参数) - [2.3.5.2 实验结果](#2352-实验结果) + - [自动选择聚簇数量](#自动选择聚簇数量) + - [3.1 算法思路](#31-算法思路) + - [3.2 一些优化](#32-一些优化) + - [3.3 基础实验](#33-基础实验) + - [3.3.0 生成数据集](#330-生成数据集) + - [3.3.1 实验 1](#331-实验-1) + - [3.3.1.1 数据集参数](#3311-数据集参数) + - [3.3.1.2 实验结果](#3312-实验结果) + - [3.3.2 实验 2](#332-实验-2) + - [3.3.2.1 数据集参数](#3321-数据集参数) + - [3.3.2.2 实验结果](#3322-实验结果) + - [3.3.3 实验 3](#333-实验-3) + - [3.3.3.1 数据集参数](#3331-数据集参数) + - [3.3.3.2 实验结果](#3332-实验结果) + - [3.3.4 实验 4](#334-实验-4) + - [3.3.4.1 数据集参数](#3341-数据集参数) + - [3.3.4.2 实验结果](#3342-实验结果) + - [3.3.5 实验 5](#335-实验-5) + - [3.3.5.1 数据集参数](#3351-数据集参数) + - [3.3.5.2 实验结果](#3352-实验结果) + - [运行代码](#运行代码) ## K-Means 模型 @@ -70,14 +91,17 @@ K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择 ![K-Means 局部最优解](./img/k-means_1_bad_train.png) -作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各数据点到各聚簇中心距离的平方和最小,具体来说,即要求如下参数的值最小: +作为优化,我们参考 scikit-learn 库的思路,对于同样的训练数据,使用不同的随机种子训练 `n_epochs` 次(此参数可调整,默认为 `10`),最后选择最优的训练模型作为预测时使用的模型。这里我们对「最优」的判断标准是,各簇内距离(各数据点到聚簇中心距离)的平方和最小,具体来说,即要求如下参数的值最小: $$ -\sum_{\mathbf{x}_i\in \mathbf{D}} -\sum_{\mathbf{c}_k\in \mathbf{C}} -(\mathbf{x}_i - \mathbf{c}_k)^2 +W += \sum_{\mathbf{x}_i\in \mathbf{D}} + \sum_{\mathbf{c}_k\in \mathbf{C}} + (\mathbf{x}_i - \mathbf{c}_k)^2 $$ +其中,$\mathbf{x}_i$ 为数据点,$\mathbf{D}$ 为数据集,$\mathbf{c}_k$ 为聚簇中心,$\mathbf{C}$ 为聚簇中心集。 + 经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 ### 1.3 基础实验 @@ -627,3 +651,252 @@ size = 500 ![GMM 测试集](./img/gmm_5_test.png) 可见,GMM 模型对于高斯混合分布数据集,其分类结果比 K-Means 模型更加准确。 + +## 自动选择聚簇数量 + +### 3.1 算法思路 + +这里我们利用 Gap Statistic 方法实现了数据集中聚簇数量的自动推测。Gap Statistic 方法的思想是,对于数据集聚类结果的簇内距离,它和同规模均匀分布的期望簇内距离相比,两者的差距越大,则认为模型的分类结果越好,即 $K$ 值的选择越好。具体来说,即希望如下参数的值尽可能大: + +$$ +\mathrm{Gap}_k = \mathrm{E}(\log {W'}_k) - \log W_k +$$ + +其中,$k$ 即选择的 $K$ 值,$W_k$ 为数据集 $\mathbf{D}$ 聚类结果的簇内距离的平方和,${W'}_k$ 为同规模均匀分布 $\mathbf{U}$ 聚类结果的簇内距离的平方和。这里 $W$ 的具体定义参见 1.2 节。 + +我们利用 Monte Carlo Method 计算 $\mathrm{E}(\log {W'}_k)$ 的值。我们在数据集 $\mathbf{D}$ 覆盖的矩形范围内进行 $B$ 次随机均匀采样,得到 $B$ 个不同的 ${W'}_k^{(b)}$,于是我们有 + +$$ +\mathrm{E}(\log {W'}_k) += \frac{1}{B} \sum\limits_{b=1}^B \log {W'}_k^{(b)} +$$ + +我们的算法底层建立在 K-Means 模型的基础上。实验时,需指定扫描时的最大 $K$ 值 $K_{\max}$,模型将在 $[1, K_{\max}]$ 的范围内找到使得 $\mathrm{Gap}_k$ 的值最大的 $K$ 值,作为推测的数据集中的聚簇数量。 + +### 3.2 一些优化 + +为了一定程度上减少扫描时间,我们设定了一个终止阈值 `BREAK_THRESHOLD`(默认为 `3`)。当 $\mathrm{Gap}_k$ 连续 `BREAK_THRESHOLD` 次没有增长时,我们认为已经找到了最优的 $K$ 值,模型自动终止扫描。 + +### 3.3 基础实验 + +#### 3.3.0 生成数据集 + +这里我们使用与 K-Means 相同的数据集生成方法。 + +#### 3.3.1 实验 1 + +第一个实验,我们对 3 个二维高斯分布数据集进行分类。 + +##### 3.3.1.1 数据集参数 + +```python {.line-numbers} +mean = (1, 2) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (16, -5) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (10, 22) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +##### 3.3.1.2 实验结果 + +训练集,不指定 $K$ 值: + +![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_1_gaps.png) + +模型选择的 $K$ 值为 $3$,分类结果: + +![Auto K-Means 训练集](./img/auto-k-means_1_train.png) + +测试集,不指定 $K$ 值: + +![Auto K-Means 测试集](./img/auto-k-means_1_test.png) + +#### 3.3.2 实验 2 + +第二个实验,我们对 5 个二维高斯分布数据集进行分类。 + +##### 3.3.2.1 数据集参数 + +```python {.line-numbers} +mean = (1, 0) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (20, 15) +cov = [[21.2, 0], [0, 32.1]] +size = 400 +``` + +```python {.line-numbers} +mean = (10, -22) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +```python {.line-numbers} +mean = (-12, -6) +cov = [[7, 3], [3, 16]] +size = 500 +``` + +```python {.line-numbers} +mean = (-15, 17) +cov = [[15, 0], [0, 12]] +size = 600 +``` + +##### 3.3.2.2 实验结果 + +训练集,不指定 $K$ 值: + +![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_2_gaps.png) + +模型选择的 $K$ 值为 $6$,分类结果: + +![Auto K-Means 训练集](./img/auto-k-means_2_train.png) + +测试集,不指定 $K$ 值: + +![Auto K-Means 测试集](./img/auto-k-means_2_test.png) + +虽然实际上应当是 $5$ 个高斯分布,不过考虑到模型在 $K=5$ 和 $K=6$ 处都取得了较高的 $\mathrm{Gap}$ 值,这个分类结果也是可以理解的。 + +#### 3.3.3 实验 3 + +第三个实验,我们对 3 个三维高斯分布数据集进行分类。 + +##### 3.3.3.1 数据集参数 + +```python {.line-numbers} +mean = (-6, 3, 5) +cov = [[73, 0, 0], [0, 50, 0], [0, 0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (12, 0, -10) +cov = [[20, 5, 0], [5, 20, 0], [0, 0, 20]] +size = 500 +``` + +```python {.line-numbers} +mean = (10, -20, 0) +cov = [[10, 1, 3], [1, 10, 0], [3, 0, 10]] +size = 800 +``` + +##### 3.3.3.2 实验结果 + +训练集,不指定 $K$ 值: + +![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_3_gaps.png) + +模型选择的 $K$ 值为 $4$,分类结果: + +![Auto K-Means 训练集](./img/auto-k-means_3_train.png) + +测试集,不指定 $K$ 值: + +![Auto K-Means 测试集](./img/auto-k-means_3_test.png) + +类似地,模型在 $K=3$ 和 $K=4$ 处都取得了较高的 $\mathrm{Gap}$ 值,说明这两种 $K$ 值都是可以接受的。 + +#### 3.3.4 实验 4 + +第四个实验,我们对 3 个一维高斯分布数据集进行分类。 + +##### 3.3.4.1 数据集参数 + +```python {.line-numbers} +mean = (-20,) +scale = 2 +size = 100 +``` + +```python {.line-numbers} +mean = (0,) +scale = 1 +size = 150 +``` + +```python {.line-numbers} +mean = (15,) +scale = 2 +size = 100 +``` + +##### 3.3.4.2 实验结果 + +训练集,不指定 $K$ 值: + +![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_4_gaps.png) + +模型选择的 $K$ 值为 $3$,分类结果: + +![Auto K-Means 训练集](./img/auto-k-means_4_train.png) + +测试集,不指定 $K$ 值: + +![Auto K-Means 测试集](./img/auto-k-means_4_test.png) + +#### 3.3.5 实验 5 + +第五个实验,我们对 3 个扁平形状的二维高斯分布数据集进行分类。 + +##### 3.3.5.1 数据集参数 + +```python {.line-numbers} +mean = (0, -5) +cov = [[73, 0], [0, 2]] +size = 800 +``` + +```python {.line-numbers} +mean = (-3, 0) +cov = [[100, 0], [0, 2]] +size = 500 +``` + +```python {.line-numbers} +mean = (2, 5) +cov = [[70, 1], [1, 3]] +size = 500 +``` + +##### 3.3.5.2 实验结果 + +训练集,不指定 $K$ 值: + +![Auto K-Means 训练集 Gap-K 图](./img/auto-k-means_5_gaps.png) + +模型选择的 $K$ 值为 $1$,分类结果: + +![Auto K-Means 训练集](./img/auto-k-means_5_train.png) + +测试集,不指定 $K$ 值: + +![Auto K-Means 测试集](./img/auto-k-means_5_test.png) + +实际上,从人类的视角来看,这个聚类结果也是可以理解的。 + +## 运行代码 + +执行以下指令进行模型的训练与预测。 + +```bash +python ./tester.py +``` + +生成数据集使用的参数等可以在 `TestSuite` 类中对应调整。 -- Gitee From 7f3d392d2af61e5b5d198daadb4e7483af2c4bb5 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Mon, 14 Jun 2021 16:18:39 +0800 Subject: [PATCH 70/73] fix: latex style for gitee --- assignment-3/submission/18307130003/README.md | 64 +++++++++---------- 1 file changed, 32 insertions(+), 32 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index e2e4fcf..1e2e90a 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -95,12 +95,12 @@ K-Means 模型的一个问题是,由于初始时的聚簇中心是随机选择 $$ W -= \sum_{\mathbf{x}_i\in \mathbf{D}} - \sum_{\mathbf{c}_k\in \mathbf{C}} - (\mathbf{x}_i - \mathbf{c}_k)^2 += \sum\_{\mathbf{x}\_i\in \mathbf{D}} + \sum\_{\mathbf{c}\_k\in \mathbf{C}} + (\mathbf{x}\_i - \mathbf{c}\_k)^2 $$ -其中,$\mathbf{x}_i$ 为数据点,$\mathbf{D}$ 为数据集,$\mathbf{c}_k$ 为聚簇中心,$\mathbf{C}$ 为聚簇中心集。 +其中,$\mathbf{x}\_i$ 为数据点,$\mathbf{D}$ 为数据集,$\mathbf{c}\_k$ 为聚簇中心,$\mathbf{C}$ 为聚簇中心集。 经实验,对于一般的数据集来说,这个优化可以有效地使 K-Means 模型收敛到全局最优解。 @@ -372,12 +372,12 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 $$ p(\mathbf{x}) - = \frac{1}{\sqrt{(2\pi)^d |\mathbf{\Sigma}_i|}} + = \frac{1}{\sqrt{(2\pi)^d |\mathbf{\Sigma}\_i|}} \exp( -\frac{1}{2} - (\mathbf{x}-\mathbf{\mu}_i)^\mathrm{T} - \mathbf{\Sigma}_i^{-1} - (\mathbf{x}-\mathbf{\mu}_i) + (\mathbf{x}-\mathbf{\mu}\_i)^\mathrm{T} + \mathbf{\Sigma}\_i^{-1} + (\mathbf{x}-\mathbf{\mu}\_i) ) $$ @@ -387,8 +387,8 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 $$ p(x) - = \frac{1}{\sqrt{2\pi\sigma_i^2}} - \exp(-\frac{(x-\mu_i)^2}{2\sigma_i^2}) + = \frac{1}{\sqrt{2\pi\sigma\_i^2}} + \exp(-\frac{(x-\mu\_i)^2}{2\sigma\_i^2}) $$ 其中 $i$ 表示第 $i$ 个聚簇、$\mu$ 表示 `means`、$\sigma$ 表示 `scales` @@ -397,7 +397,7 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 $$ f_i(\mathbf{x}) - = \frac{p(\mathbf{x})\phi_i}{\sum\limits_{i=1}^k p(\mathbf{x})\phi_i} + = \frac{p(\mathbf{x})\phi\_i}{\sum\limits\_{i=1}^k p(\mathbf{x})\phi\_i} $$ 其中 $i$ 表示第 $i$ 个聚簇、$\phi$ 表示 `weights`、$k$ 表示 $K$ 值 @@ -407,40 +407,40 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 - `means`: $$ - \mathbf{\mu}_i + \mathbf{\mu}\_i = \frac - {\sum\limits_{i=1}^k(f_i(\mathbf{x})\cdot \mathbf{x})} - {\sum\limits_{i=1}^k f_i(\mathbf{x})} + {\sum\limits\_{i=1}^k(f\_i(\mathbf{x})\cdot \mathbf{x})} + {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} $$ - `covs`:对于多维的情形, $$ - \mathbf{\Sigma}_i + \mathbf{\Sigma}\_i = \frac - {\sum\limits_{i=1}^k( - f_i(\mathbf{x})\cdot - (\mathbf{x}-\mathbf{\mu}_i)^\mathrm{T} - (\mathbf{x}-\mathbf{\mu}_i) + {\sum\limits\_{i=1}^k( + f\_i(\mathbf{x})\cdot + (\mathbf{x}-\mathbf{\mu}\_i)^\mathrm{T} + (\mathbf{x}-\mathbf{\mu}\_i) )} - {\sum\limits_{i=1}^k f_i(\mathbf{x})} + {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} $$ - `scales`:对于一维的情形, $$ - \mathbf{\sigma}_i + \mathbf{\sigma}\_i = \sqrt{ \frac - {\sum\limits_{i=1}^k(f_i(x)\cdot (x-\mu_i)^2)} - {\sum\limits_{i=1}^k f_i(x)} + {\sum\limits\_{i=1}^k(f\_i(x)\cdot (x-\mu\_i)^2)} + {\sum\limits\_{i=1}^k f\_i(x)} } $$ - `weights`: $$ - \phi_i = \frac{1}{N} {\sum\limits_{i=1}^k f_i(\mathbf{x})} + \phi\_i = \frac{1}{N} {\sum\limits\_{i=1}^k f\_i(\mathbf{x})} $$ 4. 重复 EM 算法,直到满足终止条件;GMM 模型的终止条件与 K-Means 模型一致 @@ -456,7 +456,7 @@ GMM 模型的算法思路类似于 K-Means 模型,区别在于 GMM 模型不 与 K-Means 模型类似,GMM 模型初始时的聚簇中心也是随机选择的,因此这里我们采用了和 K-Means 模型一样的优化思路,即使用不同的随机种子训练 `n_epochs` 次,最后选择最优的训练模型作为预测时使用的模型。与 K-Means 模型不同的地方在于,在 GMM 模型中,我们不能简单地使用到聚簇中心的距离作为参考标准。实际上,我们希望每个数据点被分配到其所属的聚簇时,其在概率矩阵中对应的概率尽可能大。因此,这里我们对「最优」的判断标准是,要求如下参数的值最大: $$ -\sum\limits_{i=1}^N \max_{1\le j\le k}{\{f_j(\mathbf{x})\}} +\sum\limits\_{i=1}^N \max\_{1\le j\le k}{\{f\_j(\mathbf{x})\}} $$ 经实验,这个优化也可以有效地使 GMM 模型收敛到全局最优解。 @@ -659,23 +659,23 @@ size = 500 这里我们利用 Gap Statistic 方法实现了数据集中聚簇数量的自动推测。Gap Statistic 方法的思想是,对于数据集聚类结果的簇内距离,它和同规模均匀分布的期望簇内距离相比,两者的差距越大,则认为模型的分类结果越好,即 $K$ 值的选择越好。具体来说,即希望如下参数的值尽可能大: $$ -\mathrm{Gap}_k = \mathrm{E}(\log {W'}_k) - \log W_k +\mathrm{Gap}\_k = \mathrm{E}(\log {W'}\_k) - \log W\_k $$ -其中,$k$ 即选择的 $K$ 值,$W_k$ 为数据集 $\mathbf{D}$ 聚类结果的簇内距离的平方和,${W'}_k$ 为同规模均匀分布 $\mathbf{U}$ 聚类结果的簇内距离的平方和。这里 $W$ 的具体定义参见 1.2 节。 +其中,$k$ 即选择的 $K$ 值,$W\_k$ 为数据集 $\mathbf{D}$ 聚类结果的簇内距离的平方和,${W'}\_k$ 为同规模均匀分布 $\mathbf{U}$ 聚类结果的簇内距离的平方和。这里 $W$ 的具体定义参见 1.2 节。 -我们利用 Monte Carlo Method 计算 $\mathrm{E}(\log {W'}_k)$ 的值。我们在数据集 $\mathbf{D}$ 覆盖的矩形范围内进行 $B$ 次随机均匀采样,得到 $B$ 个不同的 ${W'}_k^{(b)}$,于是我们有 +我们利用 Monte Carlo Method 计算 $\mathrm{E}(\log {W'}\_k)$ 的值。我们在数据集 $\mathbf{D}$ 覆盖的矩形范围内进行 $B$ 次随机均匀采样,得到 $B$ 个不同的 ${W'}\_k^{(b)}$,于是我们有 $$ -\mathrm{E}(\log {W'}_k) -= \frac{1}{B} \sum\limits_{b=1}^B \log {W'}_k^{(b)} +\mathrm{E}(\log {W'}\_k) += \frac{1}{B} \sum\limits\_{b=1}^B \log {W'}\_k^{(b)} $$ -我们的算法底层建立在 K-Means 模型的基础上。实验时,需指定扫描时的最大 $K$ 值 $K_{\max}$,模型将在 $[1, K_{\max}]$ 的范围内找到使得 $\mathrm{Gap}_k$ 的值最大的 $K$ 值,作为推测的数据集中的聚簇数量。 +我们的算法底层建立在 K-Means 模型的基础上。实验时,需指定扫描时的最大 $K$ 值 $K\_{\max}$,模型将在 $[1, K\_{\max}]$ 的范围内找到使得 $\mathrm{Gap}\_k$ 的值最大的 $K$ 值,作为推测的数据集中的聚簇数量。 ### 3.2 一些优化 -为了一定程度上减少扫描时间,我们设定了一个终止阈值 `BREAK_THRESHOLD`(默认为 `3`)。当 $\mathrm{Gap}_k$ 连续 `BREAK_THRESHOLD` 次没有增长时,我们认为已经找到了最优的 $K$ 值,模型自动终止扫描。 +为了一定程度上减少扫描时间,我们设定了一个终止阈值 `BREAK_THRESHOLD`(默认为 `3`)。当 $\mathrm{Gap}\_k$ 连续 `BREAK_THRESHOLD` 次没有增长时,我们认为已经找到了最优的 $K$ 值,模型自动终止扫描。 ### 3.3 基础实验 -- Gitee From da1789f60f03b249904bc92c2d64edb6bae32d57 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 17 Jun 2021 14:27:58 +0800 Subject: [PATCH 71/73] refactor: merge codes --- assignment-3/submission/18307130003/source.py | 447 +++++++++++++++++- 1 file changed, 438 insertions(+), 9 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 1f75260..8cb42af 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -1,15 +1,106 @@ +from typing import Any, Callable, List, NamedTuple, Tuple, Type +import matplotlib.pyplot as plt from abc import ABC, abstractmethod import math import numpy as np -from utils import ( - UniformParameters, - assert_, - distance, - multinormal_pdf, - normal_pdf, -) +# Utilities + +class NormalParameters(NamedTuple): + ''' + Attributes: + `size`: the number of data points in the dataset + `mean`: the mean of the distribution + `cov`: the coefficient of variation of the distribution (dimension > 1) + `scale`: the standard deviation of the distribution (dimension = 1) + ''' + + size: int + mean: Tuple[float, ...] + cov: List[List[float]] = None + scale: float = None + + +class UniformParameters(NamedTuple): + ''' + Attributes: + `size`: the number of data points in the dataset + `intervals`: the range of each dimension, Tuple[shape(N), shape(N)] + ''' + + size: int + intervals: Tuple[np.ndarray, np.ndarray] + + +def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: + ''' + Args: + `point_1`: shape(d) + `point_2`: shape(d) + + Return: + The Euclidean distance between two points. + ''' + + return np.linalg.norm(point_1 - point_2) + + +def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: + ''' + The probability density function of a multivariate Gaussian distribution + with given parameters. + + Args: + `x`: an observation, shape(d) + `mean`: the mean of the distribution, shape(d) + `cov`: the coefficient of variation of the distribution, shape(d, d) + + Return: + f(x | mean, cov) + ''' + + cov_det: float = np.linalg.det(cov) + dim: int = mean.shape[0] + const: float = (((2 * math.pi) ** dim) * cov_det) ** (-1/2) + x_m: np.ndarray = x - mean + exp: float = -np.dot(x_m, np.linalg.solve(cov, x_m)) / 2 + return const * math.exp(exp) + + +def normal_pdf(x: float, mean: float, scale: float) -> float: + ''' + The probability density function of a Gaussian distribution with given + parameters. + + Args: + `x`: an observation + `mean`: the mean of the distribution + `scale`: the standard deviation of the distribution + + Return: + f(x | mean, scale) + ''' + + const = (2 * math.pi) ** (-1/2) / scale + exp = -((x - mean) / scale) ** 2 / 2 + return const * math.exp(exp) + + +def assert_(var_name: str, got: Any, expected: Any) -> None: + ''' + Args: + `var_name`: variable name for logging + `got`: actual value + `expected`: expected value + ''' + + message = f'Assertion failed for {var_name}: expected {expected}, got {got}' + assert got == expected, message + + +# Models + class Model(ABC): ''' The abstract class (ABC) of a model. @@ -150,9 +241,9 @@ class KMeans(Model): class GaussianMixture(Model): ''' - Gaussian Mixture Model (GMM) is a probabilistic model that assumes there + Gaussian Mixture Model (GaussianMixture) is a probabilistic model that assumes there are a certain number of Gaussian distributions, and each of these - distributions represent a cluster. Hence, a GMM tends to group the data + distributions represent a cluster. Hence, a GaussianMixture tends to group the data points belonging to a single distribution together. ''' @@ -471,3 +562,341 @@ class ClusteringAlgorithm(Model): def predict(self, test_data: np.ndarray) -> np.ndarray: return self.best_model.predict(test_data) + + +# Tester + +class TestSuite: + ''' + Multiple testing data for models. + ''' + + def __init__(self) -> None: + self.rng: np.random.Generator = np.random.default_rng() + + def generate_normal(self, param: NormalParameters) -> np.ndarray: + ''' + Generate a dataset from a Gaussian distribution with given parameters. + + Args: + `param`: parameters used to generate a dataset + + Return: + shape(N, d) + ''' + + size, mean, cov, scale = param + if len(mean) > 1: + return self.rng.multivariate_normal(mean, cov, size) + else: + return self.rng.normal(mean[0], scale, size) + + def combine(self, *datasets: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: + ''' + Combine several datasets into a single dataset. + + Args: + `*datasets`: a tuple of datasets needed to combine + + Return: + `dataset`: shape(N, d), where N is the total size of all datasets + `labels`: shape(N), the labels for all points in the dataset + ''' + + dataset: np.ndarray = np.concatenate(datasets) + labels: np.ndarray = np.concatenate([ + np.ones(d.shape[0], dtype=int) * i + for (i, d) in enumerate(datasets) + ]) + indices = np.arange(dataset.shape[0]) + np.random.shuffle(indices) + dataset = dataset[indices] + labels = labels[indices] + return dataset, labels + + def generate_data(self, *params: NormalParameters) -> Tuple[np.ndarray, int]: + ''' + Generate a dataset for tests. + + Args: + `params`: a tuple of parameters to generate datasets + + Return: + `dataset`: shape(N, d) + `n_clusters`: the number of clusters to partition into + ''' + + dataset, _labels = self.combine(*tuple( + self.generate_normal(p) for p in params + )) + n_clusters: int = len(params) + return dataset, n_clusters + + def train( + self, train_data: np.ndarray, model: Model + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + ''' + Train a model with training data. + + Args: + `train_data`: shape(N, d) + `model`: the model that we need to train + `n_clusters`: the number of clusters to partition into + + Return: + `train_labels`: the predicted labels of training data, shape(N) + `centroids`: the centroids calculated from training data, shape(k, d) + `gaps`: the gap statistics of each k, shape(k + 1) + ''' + + model.fit(train_data) + train_labels = model.predict(train_data) + centroids: np.ndarray = None + gaps: np.ndarray = None + + if isinstance(model, KMeans): + centroids = model.centroids + elif isinstance(model, GaussianMixture): + centroids = model.means + elif isinstance(model, ClusteringAlgorithm): + centroids = model.best_model.centroids + gaps = model.gaps + return train_labels, centroids, gaps + + def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: + ''' + Evaluate a model with testing data. + + Args: + `test_data`: shape(N, d) + `model`: the model that we need to evaluate + + Return: + `test_labels`: The predicted labels of testing data, shape(N) + ''' + + test_labels = model.predict(test_data) + return test_labels + + def test_data_1(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + NormalParameters( + size=800, + mean=(1, 2), + cov=[[73, 0], [0, 22]], + ), + NormalParameters( + size=200, + mean=(16, -5), + cov=[[21.2, 0], [0, 32.1]], + ), + NormalParameters( + size=1000, + mean=(10, 22), + cov=[[10, 5], [5, 10]], + ), + ) + + def test_data_2(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + NormalParameters( + size=800, + mean=(1, 0), + cov=[[73, 0], [0, 22]], + ), + NormalParameters( + size=400, + mean=(20, 15), + cov=[[21.2, 0], [0, 32.1]], + ), + NormalParameters( + size=1000, + mean=(10, -22), + cov=[[10, 5], [5, 10]], + ), + NormalParameters( + size=500, + mean=(-12, -6), + cov=[[7, 3], [3, 16]], + ), + NormalParameters( + size=600, + mean=(-15, 17), + cov=[[15, 0], [0, 12]], + ), + ) + + def test_data_3(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + NormalParameters( + size=800, + mean=(-6, 3, 5), + cov=[[73, 0, 0], [0, 50, 0], [0, 0, 22]], + ), + NormalParameters( + size=500, + mean=(12, 0, -10), + cov=[[20, 5, 0], [5, 20, 0], [0, 0, 20]], + ), + NormalParameters( + size=800, + mean=(10, -20, 0), + cov=[[10, 1, 3], [1, 10, 0], [3, 0, 10]], + ), + ) + + def test_data_4(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + NormalParameters( + size=100, + mean=(-20,), + scale=2, + ), + NormalParameters( + size=150, + mean=(0,), + scale=1, + ), + NormalParameters( + size=100, + mean=(15,), + scale=2, + ), + ) + + def test_data_5(self) -> Tuple[np.ndarray, int]: + + return self.generate_data( + NormalParameters( + size=800, + mean=(0, -5), + cov=[[73, 0], [0, 2]], + ), + NormalParameters( + size=500, + mean=(-3, 0), + cov=[[100, 0], [0, 2]], + ), + NormalParameters( + size=500, + mean=(2, 5), + cov=[[70, 1], [1, 3]], + ), + ) + + def run(self) -> None: + ''' + Run all the tests. + ''' + + testcases: List[Tuple[ + str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int + ]] = [ + ('k-means_1', self.test_data_1, KMeans, 0), + # ('k-means_2', self.test_data_2, KMeans, 0), + # ('k-means_3', self.test_data_3, KMeans, 0), + # ('k-means_4', self.test_data_4, KMeans, 0), + # ('k-means_5', self.test_data_5, KMeans, 0), + # ('GaussianMixture_1', self.test_data_1, GaussianMixture, 0), + # ('GaussianMixture_2', self.test_data_2, GaussianMixture, 0), + # ('GaussianMixture_3', self.test_data_3, GaussianMixture, 0), + # ('GaussianMixture_4', self.test_data_4, GaussianMixture, 0), + # ('GaussianMixture_5', self.test_data_5, GaussianMixture, 0), + # ('auto-k-means_1', self.test_data_1, ClusteringAlgorithm, 10), + # ('auto-k-means_2', self.test_data_2, ClusteringAlgorithm, 10), + # ('auto-k-means_3', self.test_data_3, ClusteringAlgorithm, 10), + # ('auto-k-means_4', self.test_data_4, ClusteringAlgorithm, 10), + # ('auto-k-means_5', self.test_data_5, ClusteringAlgorithm, 10), + ] + + for testcase in testcases: + name, get_dataset, model_class, n_clusters = testcase + + # Obtain training data and testing data + dataset, real_n_clusters = get_dataset() + train_size: int = math.floor(dataset.shape[0] * 0.8) + train_data: np.ndarray = dataset[:train_size] + test_data: np.ndarray = dataset[train_size:] + + # Train the model with training data + model = model_class(n_clusters or real_n_clusters) + train_labels, centroids, gaps = self.train(train_data, model) + + # Evaluate the model with testing data + test_labels = self.evaluate(test_data, model) + + # Visualize the datasets with labels + visualize(name + '_train', train_data, train_labels, centroids) + visualize(name + '_test', test_data, test_labels, centroids) + + # Visualize the gap statistics for + if gaps is not None: + visualize_gaps(name + '_gaps', gaps) + + print(f'{name}: Done.') + + +def visualize( + name: str, + dataset: np.ndarray, + labels: np.ndarray, + centroids: np.ndarray = None, +) -> None: + ''' + Visualize a dataset with labels. + + Args: + `name`: the output filename when saving the figure + `dataset`: shape(N, d) + `labels`: shape(N) + `centroids`: shape(k, d) + ''' + + assert_('dataset.shape[0]', dataset.shape[0], labels.shape[0]) + + # Plot the data points and the centroids. + if len(dataset.shape) > 1: + plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) + if centroids is not None: + plt.scatter( + centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5, + ) + else: + plt.scatter(dataset, np.zeros(dataset.shape[0]), c=labels, s=30) + if centroids is not None: + plt.yticks([]) + plt.scatter( + centroids, np.zeros(centroids.shape[0]), + c='black', s=100, alpha=0.5, + ) + + # Save the figure to a local file. + plt.savefig(f'img/{name}') + plt.clf() + + +def visualize_gaps(name: str, gaps: np.ndarray) -> None: + ''' + Visualize the gap statistics. + + Args: + `name`: the output filename when saving the figure + `gaps`: the gap statistics of each k, shape(k + 1) + ''' + + # Plot the gap statistics. + indices = np.arange(1, gaps.shape[0], dtype=int) + plt.xticks(indices) + plt.plot(indices, gaps[indices], '-bo') + + # Save the figure to a local file. + plt.savefig(f'img/{name}') + plt.clf() + + +if __name__ == '__main__': + TestSuite().run() -- Gitee From 35a78b786bf8a5f248a65280c3e8a7cd2e123759 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 17 Jun 2021 14:34:56 +0800 Subject: [PATCH 72/73] docs: fix --- assignment-3/submission/18307130003/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/18307130003/README.md b/assignment-3/submission/18307130003/README.md index 1e2e90a..7681ef3 100644 --- a/assignment-3/submission/18307130003/README.md +++ b/assignment-3/submission/18307130003/README.md @@ -111,7 +111,7 @@ $$ 我们利用以下函数生成数据集: ```python {.line-numbers} -# tester.py +# source.py class TestSuite: ''' @@ -896,7 +896,7 @@ size = 500 执行以下指令进行模型的训练与预测。 ```bash -python ./tester.py +python ./source.py ``` 生成数据集使用的参数等可以在 `TestSuite` 类中对应调整。 -- Gitee From 7c61113da0bbc7033bb43f976df100e6b385eaf4 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 18 Jun 2021 18:47:51 +0800 Subject: [PATCH 73/73] chore: remove unused files --- assignment-3/submission/18307130003/tester.py | 347 ------------------ assignment-3/submission/18307130003/utils.py | 95 ----- 2 files changed, 442 deletions(-) delete mode 100644 assignment-3/submission/18307130003/tester.py delete mode 100644 assignment-3/submission/18307130003/utils.py diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py deleted file mode 100644 index c2c14ae..0000000 --- a/assignment-3/submission/18307130003/tester.py +++ /dev/null @@ -1,347 +0,0 @@ -from typing import Callable, List, Tuple, Type -import math -import numpy as np -import matplotlib.pyplot as plt -from source import ( - ClusteringAlgorithm as AutoKMeans, - Model, - KMeans, - GaussianMixture as GMM, -) -from utils import assert_, NormalParameters - - -class TestSuite: - ''' - Multiple testing data for models. - ''' - - def __init__(self) -> None: - self.rng: np.random.Generator = np.random.default_rng() - - def generate_normal(self, param: NormalParameters) -> np.ndarray: - ''' - Generate a dataset from a Gaussian distribution with given parameters. - - Args: - `param`: parameters used to generate a dataset - - Return: - shape(N, d) - ''' - - size, mean, cov, scale = param - if len(mean) > 1: - return self.rng.multivariate_normal(mean, cov, size) - else: - return self.rng.normal(mean[0], scale, size) - - def combine(self, *datasets: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: - ''' - Combine several datasets into a single dataset. - - Args: - `*datasets`: a tuple of datasets needed to combine - - Return: - `dataset`: shape(N, d), where N is the total size of all datasets - `labels`: shape(N), the labels for all points in the dataset - ''' - - dataset: np.ndarray = np.concatenate(datasets) - labels: np.ndarray = np.concatenate([ - np.ones(d.shape[0], dtype=int) * i - for (i, d) in enumerate(datasets) - ]) - indices = np.arange(dataset.shape[0]) - np.random.shuffle(indices) - dataset = dataset[indices] - labels = labels[indices] - return dataset, labels - - def generate_data(self, *params: NormalParameters) -> Tuple[np.ndarray, int]: - ''' - Generate a dataset for tests. - - Args: - `params`: a tuple of parameters to generate datasets - - Return: - `dataset`: shape(N, d) - `n_clusters`: the number of clusters to partition into - ''' - - dataset, _labels = self.combine(*tuple( - self.generate_normal(p) for p in params - )) - n_clusters: int = len(params) - return dataset, n_clusters - - def train( - self, train_data: np.ndarray, model: Model - ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: - ''' - Train a model with training data. - - Args: - `train_data`: shape(N, d) - `model`: the model that we need to train - `n_clusters`: the number of clusters to partition into - - Return: - `train_labels`: the predicted labels of training data, shape(N) - `centroids`: the centroids calculated from training data, shape(k, d) - `gaps`: the gap statistics of each k, shape(k + 1) - ''' - - model.fit(train_data) - train_labels = model.predict(train_data) - centroids: np.ndarray = None - gaps: np.ndarray = None - - if isinstance(model, KMeans): - centroids = model.centroids - elif isinstance(model, GMM): - centroids = model.means - elif isinstance(model, AutoKMeans): - centroids = model.best_model.centroids - gaps = model.gaps - return train_labels, centroids, gaps - - def evaluate(self, test_data: np.ndarray, model: Model) -> Tuple[np.ndarray]: - ''' - Evaluate a model with testing data. - - Args: - `test_data`: shape(N, d) - `model`: the model that we need to evaluate - - Return: - `test_labels`: The predicted labels of testing data, shape(N) - ''' - - test_labels = model.predict(test_data) - return test_labels - - def test_data_1(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(1, 2), - cov=[[73, 0], [0, 22]], - ), - NormalParameters( - size=200, - mean=(16, -5), - cov=[[21.2, 0], [0, 32.1]], - ), - NormalParameters( - size=1000, - mean=(10, 22), - cov=[[10, 5], [5, 10]], - ), - ) - - def test_data_2(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(1, 0), - cov=[[73, 0], [0, 22]], - ), - NormalParameters( - size=400, - mean=(20, 15), - cov=[[21.2, 0], [0, 32.1]], - ), - NormalParameters( - size=1000, - mean=(10, -22), - cov=[[10, 5], [5, 10]], - ), - NormalParameters( - size=500, - mean=(-12, -6), - cov=[[7, 3], [3, 16]], - ), - NormalParameters( - size=600, - mean=(-15, 17), - cov=[[15, 0], [0, 12]], - ), - ) - - def test_data_3(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(-6, 3, 5), - cov=[[73, 0, 0], [0, 50, 0], [0, 0, 22]], - ), - NormalParameters( - size=500, - mean=(12, 0, -10), - cov=[[20, 5, 0], [5, 20, 0], [0, 0, 20]], - ), - NormalParameters( - size=800, - mean=(10, -20, 0), - cov=[[10, 1, 3], [1, 10, 0], [3, 0, 10]], - ), - ) - - def test_data_4(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=100, - mean=(-20,), - scale=2, - ), - NormalParameters( - size=150, - mean=(0,), - scale=1, - ), - NormalParameters( - size=100, - mean=(15,), - scale=2, - ), - ) - - def test_data_5(self) -> Tuple[np.ndarray, int]: - - return self.generate_data( - NormalParameters( - size=800, - mean=(0, -5), - cov=[[73, 0], [0, 2]], - ), - NormalParameters( - size=500, - mean=(-3, 0), - cov=[[100, 0], [0, 2]], - ), - NormalParameters( - size=500, - mean=(2, 5), - cov=[[70, 1], [1, 3]], - ), - ) - - def run(self) -> None: - ''' - Run all the tests. - ''' - - testcases: List[Tuple[ - str, Callable[[], Tuple[np.ndarray, int]], Type[Model], int - ]] = [ - ('k-means_1', self.test_data_1, KMeans, 0), - ('k-means_2', self.test_data_2, KMeans, 0), - ('k-means_3', self.test_data_3, KMeans, 0), - ('k-means_4', self.test_data_4, KMeans, 0), - ('k-means_5', self.test_data_5, KMeans, 0), - ('gmm_1', self.test_data_1, GMM, 0), - ('gmm_2', self.test_data_2, GMM, 0), - ('gmm_3', self.test_data_3, GMM, 0), - ('gmm_4', self.test_data_4, GMM, 0), - ('gmm_5', self.test_data_5, GMM, 0), - ('auto-k-means_1', self.test_data_1, AutoKMeans, 10), - ('auto-k-means_2', self.test_data_2, AutoKMeans, 10), - ('auto-k-means_3', self.test_data_3, AutoKMeans, 10), - ('auto-k-means_4', self.test_data_4, AutoKMeans, 10), - ('auto-k-means_5', self.test_data_5, AutoKMeans, 10), - ] - - for testcase in testcases: - name, get_dataset, model_class, n_clusters = testcase - - # Obtain training data and testing data - dataset, real_n_clusters = get_dataset() - train_size: int = math.floor(dataset.shape[0] * 0.8) - train_data: np.ndarray = dataset[:train_size] - test_data: np.ndarray = dataset[train_size:] - - # Train the model with training data - model = model_class(n_clusters or real_n_clusters) - train_labels, centroids, gaps = self.train(train_data, model) - - # Evaluate the model with testing data - test_labels = self.evaluate(test_data, model) - - # Visualize the datasets with labels - visualize(name + '_train', train_data, train_labels, centroids) - visualize(name + '_test', test_data, test_labels, centroids) - - # Visualize the gap statistics for - if gaps is not None: - visualize_gaps(name + '_gaps', gaps) - - print(f'{name}: Done.') - - -def visualize( - name: str, - dataset: np.ndarray, - labels: np.ndarray, - centroids: np.ndarray = None, -) -> None: - ''' - Visualize a dataset with labels. - - Args: - `name`: the output filename when saving the figure - `dataset`: shape(N, d) - `labels`: shape(N) - `centroids`: shape(k, d) - ''' - - assert_('dataset.shape[0]', dataset.shape[0], labels.shape[0]) - - # Plot the data points and the centroids. - if len(dataset.shape) > 1: - plt.scatter(dataset[:, 0], dataset[:, 1], c=labels, s=30) - if centroids is not None: - plt.scatter( - centroids[:, 0], centroids[:, 1], c='black', s=100, alpha=0.5, - ) - else: - plt.scatter(dataset, np.zeros(dataset.shape[0]), c=labels, s=30) - if centroids is not None: - plt.yticks([]) - plt.scatter( - centroids, np.zeros(centroids.shape[0]), - c='black', s=100, alpha=0.5, - ) - - # Save the figure to a local file. - plt.savefig(f'img/{name}') - plt.clf() - - -def visualize_gaps(name: str, gaps: np.ndarray) -> None: - ''' - Visualize the gap statistics. - - Args: - `name`: the output filename when saving the figure - `gaps`: the gap statistics of each k, shape(k + 1) - ''' - - # Plot the gap statistics. - indices = np.arange(1, gaps.shape[0], dtype=int) - plt.xticks(indices) - plt.plot(indices, gaps[indices], '-bo') - - # Save the figure to a local file. - plt.savefig(f'img/{name}') - plt.clf() - - -if __name__ == '__main__': - TestSuite().run() diff --git a/assignment-3/submission/18307130003/utils.py b/assignment-3/submission/18307130003/utils.py deleted file mode 100644 index 37d82a1..0000000 --- a/assignment-3/submission/18307130003/utils.py +++ /dev/null @@ -1,95 +0,0 @@ -from typing import Any, List, NamedTuple, Tuple -import numpy as np -import math - - -class NormalParameters(NamedTuple): - ''' - Attributes: - `size`: the number of data points in the dataset - `mean`: the mean of the distribution - `cov`: the coefficient of variation of the distribution (dimension > 1) - `scale`: the standard deviation of the distribution (dimension = 1) - ''' - - size: int - mean: Tuple[float, ...] - cov: List[List[float]] = None - scale: float = None - - -class UniformParameters(NamedTuple): - ''' - Attributes: - `size`: the number of data points in the dataset - `intervals`: the range of each dimension, Tuple[shape(N), shape(N)] - ''' - - size: int - intervals: Tuple[np.ndarray, np.ndarray] - - -def distance(point_1: np.ndarray, point_2: np.ndarray) -> float: - ''' - Args: - `point_1`: shape(d) - `point_2`: shape(d) - - Return: - The Euclidean distance between two points. - ''' - - return np.linalg.norm(point_1 - point_2) - - -def multinormal_pdf(x: np.ndarray, mean: np.ndarray, cov: np.ndarray) -> float: - ''' - The probability density function of a multivariate Gaussian distribution - with given parameters. - - Args: - `x`: an observation, shape(d) - `mean`: the mean of the distribution, shape(d) - `cov`: the coefficient of variation of the distribution, shape(d, d) - - Return: - f(x | mean, cov) - ''' - - cov_det: float = np.linalg.det(cov) - dim: int = mean.shape[0] - const: float = (((2 * math.pi) ** dim) * cov_det) ** (-1/2) - x_m: np.ndarray = x - mean - exp: float = -np.dot(x_m, np.linalg.solve(cov, x_m)) / 2 - return const * math.exp(exp) - - -def normal_pdf(x: float, mean: float, scale: float) -> float: - ''' - The probability density function of a Gaussian distribution with given - parameters. - - Args: - `x`: an observation - `mean`: the mean of the distribution - `scale`: the standard deviation of the distribution - - Return: - f(x | mean, scale) - ''' - - const = (2 * math.pi) ** (-1/2) / scale - exp = -((x - mean) / scale) ** 2 / 2 - return const * math.exp(exp) - - -def assert_(var_name: str, got: Any, expected: Any) -> None: - ''' - Args: - `var_name`: variable name for logging - `got`: actual value - `expected`: expected value - ''' - - message = f'Assertion failed for {var_name}: expected {expected}, got {got}' - assert got == expected, message -- Gitee

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Date: Sat, 12 Jun 2021 15:44:47 +0800 Subject: [PATCH 62/73] fix: scalar arguments fixes --- assignment-3/submission/18307130003/source.py | 14 +++++++++----- assignment-3/submission/18307130003/tester.py | 6 +++--- 2 files changed, 12 insertions(+), 8 deletions(-) diff --git a/assignment-3/submission/18307130003/source.py b/assignment-3/submission/18307130003/source.py index 8515483..1c3e3be 100644 --- a/assignment-3/submission/18307130003/source.py +++ b/assignment-3/submission/18307130003/source.py @@ -408,11 +408,15 @@ class ClusteringAlgorithm(Model): ''' size, (low, high) = param - assert_('low.shape[0]', low.shape[0], high.shape[0]) - dimension = low.shape[0] - return self.rng.uniform( - low, high, (size, dimension if dimension > 1 else None), - ) + dimension: int + if np.isscalar(low): + assert_('np.isscalar(high)', np.isscalar(high), True) + dimension = 1 + return self.rng.uniform(low, high, size) + else: + assert_('low.shape[0]', low.shape[0], high.shape[0]) + dimension = low.shape[0] + return self.rng.uniform(low, high, (size, dimension)) def fit(self, train_data: np.ndarray) -> float: diff --git a/assignment-3/submission/18307130003/tester.py b/assignment-3/submission/18307130003/tester.py index 056f4ac..7e36b6b 100644 --- a/assignment-3/submission/18307130003/tester.py +++ b/assignment-3/submission/18307130003/tester.py @@ -198,17 +198,17 @@ class TestSuite: return self.generate_data( NormalParameters( size=100, - mean=-20, + mean=(-20,), scale=6, ), NormalParameters( size=150, - mean=0, + mean=(0,), scale=3, ), NormalParameters( size=100, - mean=15, + mean=(15,), scale=3, ), ) -- Gitee From 8ae6ff8c9dc7ca6fed347eb2fc55eb9bdc0149d1 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sat, 12 Jun 2021 15:45:19 +0800 Subject: [PATCH 63/73] docs: add figures for auto k-means 4-5 --- .../18307130003/img/auto-k-means_4_gaps.png | Bin 19514 -> 18952 bytes .../18307130003/img/auto-k-means_4_test.png | Bin 8739 -> 10236 bytes .../18307130003/img/auto-k-means_4_train.png | Bin 8198 -> 9451 bytes .../18307130003/img/auto-k-means_5_gaps.png | Bin 13821 -> 13769 bytes .../18307130003/img/auto-k-means_5_test.png | Bin 65167 -> 71749 bytes .../18307130003/img/auto-k-means_5_train.png | Bin 94142 -> 105997 bytes 6 files changed, 0 insertions(+), 0 deletions(-) diff --git a/assignment-3/submission/18307130003/img/auto-k-means_4_gaps.png b/assignment-3/submission/18307130003/img/auto-k-means_4_gaps.png index 571a76cb555eee0e61b6e32980c09bb98c0331f5..e20f106bb01b0e1dbaee2b666a175a9a03b843ae 100644 GIT binary patch literal 18952 zcmeIabyQW+);GKf2}J=>5NRZ&K|lm03{+Z?kVcVCNu>@7CJ0J5sD!lAaA*}&y7Les zol4g^@7#FreeOG+`@G*fzW=^4KF4qX=j^@qT63=ToAsOf#SQgqhYy}Sh#<&erR!HT z5ro(eL5M~v$lw#n_MuwNUpGb2(Vg&KCbj`=Y)Q|vrA{qp#F{AKJ>mS?~JEDJfhdy{~kPW-!`#xs#p(^}%x zv^0Jmo~tu6Gx|j~+JU{*n?D0(W>UhsQdJnZd3a{a=W;uTE4?mj3BeYSHKaqLgbdP# zh76k%Wew(fa&GD9MAnC}<<-^I@#GOk{i$8ox^-=5yE3+a28yiyX%w+to9&K0Yp?%Y 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