From d15d3a05c63fad9db3dabac5005ae17b31be0d1f Mon Sep 17 00:00:00 2001 From: Flock-Li <863813609@qq.com> Date: Fri, 26 Mar 2021 12:50:13 +0800 Subject: [PATCH 1/5] add_source --- assignment-1/submission/18307130130/README.md | 0 assignment-1/submission/18307130130/source.py | 206 ++++++++++++++++++ 2 files changed, 206 insertions(+) create mode 100644 assignment-1/submission/18307130130/README.md create mode 100644 assignment-1/submission/18307130130/source.py diff --git a/assignment-1/submission/18307130130/README.md b/assignment-1/submission/18307130130/README.md new file mode 100644 index 0000000..e69de29 diff --git a/assignment-1/submission/18307130130/source.py b/assignment-1/submission/18307130130/source.py new file mode 100644 index 0000000..32b6f99 --- /dev/null +++ b/assignment-1/submission/18307130130/source.py @@ -0,0 +1,206 @@ +import numpy as np +import matplotlib.pyplot as plt + +class KNN: + + def __init__(self, k=5, p=2): + """ + When p = 1, this is equivalent to using manhattan_distance + , and euclidean_distance for p = 2. + """ + self.k = 5 + self.p = p + self.train_data = None + self.train_label = None + + def fit(self, train_data, train_label): + + # split train_data to validation_data + + train_label = train_label.reshape(-1, 1) + data = np.concatenate((train_data, train_label), axis=1) + np.random.shuffle(data) + + train_data = data[:, [0, 1]] + train_label = data[:, 2] + + v_ratio = 0.25 + length = train_data.shape[0] + label_len = data_len = round(length * (1 - v_ratio) ) + + self.train_data = t_data = train_data[:data_len,:] + self.train_label = t_label = train_label[:label_len] + + v_data = train_data[data_len:,:] + v_label = train_label[label_len:] + + acc_dict = dict() + for k in range(1, 20): + res = self._predict_by_k(t_data, t_label, v_data, k) + acc = np.mean(np.equal(res, v_label)) + print("k :", k, " acc: ", acc) + acc_dict[k] = acc + Max = 0 + select_k = 1 + for k, acc in acc_dict.items(): + if acc >= Max: + select_k = k + Max = acc + self.k = select_k + print("select k: ", select_k) + + def predict(self, test_data): + res = self._predict_by_k(self.train_data, self.train_label, test_data, self.k) + return np.array(res) + + def _predict_by_k(self, t_data, t_label, data, k): + res = [] + for d in data: + diff = t_data - d + dist = (np.sum(diff ** self.p, axis=1))**(1 / self.p) + topk = [t_label[x] for x in np.argsort(dist)[:k]] + cnt_dict = dict() + for x in topk: + if x in cnt_dict: + cnt_dict[x] += 1 + else: + cnt_dict[x] = 1 + sort_cnt = sorted(cnt_dict.items(), key=lambda x: x[1], reverse=True) + top_cnt = [] + Max_cnt = sort_cnt[0][1] + for number, cnt in sort_cnt: + if cnt >= Max_cnt: + top_cnt.append(number) + else: + break + i = np.random.randint(len(top_cnt)) + res.append(top_cnt[i]) + return res + + + +def GetGaussionSet(N, num, mean): + """ + N refer to number of dimensions, mean refer to mean of Gaussion, + number refer to number of data + """ + cov = np.eye(N) + x = np.random.multivariate_normal(mean, cov, num, 'raise') + return x + +def GenerateData(N, nums, means): + """ + Generate data according to nums and means + """ + dataset = dict() + for i in range(len(nums)): + # get the number as label + zeros = np.zeros((nums[i], 1)) + i + tmp = GetGaussionSet(N, nums[i], means[i]) + # concatenate the data and corresponding label + dataset[i] = np.concatenate((tmp, zeros), axis=1) + + ret = dataset[0] + for value in list(dataset.values())[1:]: + ret = np.concatenate((ret, value), axis=0) + + return ret + +def ShowFigure(dataset): + global nums + cmap = plt.cm.get_cmap("hsv", len(nums)) + + h = .02 + x_min, x_max = DataSet[:, 0].min() - 1, DataSet[:, 0].max() + 1 + y_min, y_max = DataSet[:, 1].min() - 1, DataSet[:, 1].max() + 1 + xx, yy = np.meshgrid(np.arange(x_min, x_max, h), + np.arange(y_min, y_max, h)) + + model = KNN() + model.fit(DataSet[:, [0, 1]], DataSet[:, 2]) + test_data = np.c_[xx.ravel(), yy.ravel()] + Z = model.predict(test_data) + Z = Z.reshape(xx.shape) + + plt.figure(12) + + plt.subplot(1, 2, 1) + plt.pcolormesh(xx, yy, Z, cmap=cmap, shading="auto") + + ax = plt.subplot(1,2,2) #界面只需显示一个视图 + ax.set_title('KNN separable data set') #视图名称,这里简单统一定这个名称吧 + plt.xlabel('X') #坐标轴名称 + plt.ylabel('Y') + + for i in range(len(nums)): + idx = np.where(dataset[:, 2] == i) + ax.scatter(dataset[idx,0], dataset[idx,1], marker='o', label=i, color=cmap(i), s=10) + #plt.scatter(dataset[:,0], dataset[:,1], marker='o', c=dataset[:,2], cmap=cmap, s=10) + + plt.legend(loc = 'upper right') #图例显示位置 + plt.show() + +def ShowAcc(train_data, test_data, Z): + global nums + cmap = plt.cm.get_cmap("hsv", len(nums)+1) + plt.figure(12) + ax = plt.subplot(1, 2, 1) + + ax.set_title('KNN train dataset') + plt.xlabel('X') #坐标轴名称 + plt.ylabel('Y') + + for i in range(len(nums)): + idx = np.where(train_data[:, 2] == i) + ax.scatter(train_data[idx, 0], train_data[idx, 1], marker='o', label=i, color=cmap(i), s=10) + + plt.legend(loc = 'upper right') #图例显示位置 + + ax = plt.subplot(1, 2, 2) + ax.set_title('KNN test dataset') + plt.xlabel('X') #坐标轴名称 + plt.ylabel('Y') + for i in range(len(nums)): + idx = np.where(test_data[:, 2] == i) + ax.scatter(test_data[idx,0], test_data[idx,1], marker='o', label=i, color=cmap(i), s=10) + + wrong_point = [] + for i in range(test_data.shape[0]): + if test_data[i][2] != Z[i]: + wrong_point.append([test_data[i][0], test_data[i][1]]) + if wrong_point != []: + wrong_point = np.array(wrong_point) + ax.scatter(wrong_point[:,0], wrong_point[:,1], marker='*', s=30) + + plt.legend(loc = 'upper right') #图例显示位置 + plt.show() + +if __name__ == "__main__": + N = 2 + # define two-dimension Gaussian distribution + means = [(1, 2), (1, 9), (4, 10), (9, 5), (7, 20)] + # define the number of each distribution + nums = [1000, 1000, 100, 1000, 100] + + # Generate DataSet according to N, nums, and means + DataSet = GenerateData(N, nums, means) + + # Randomly divide the data into 80% training set and 20% test set + np.random.shuffle(DataSet) + length = DataSet.shape[0] + train_len = round(length * 4 / 5) + train_data = DataSet[:train_len,:] + test_data = DataSet[train_len:,:] + + # start training and predict + model = KNN() + model.fit(train_data[:, [0, 1]], train_data[:, 2]) + Z = model.predict(test_data[:, [0, 1]]) + + # calculate the accuracy + print("acc = ", np.mean(np.equal(Z, test_data[:, 2]))) + + ShowAcc(train_data, test_data, Z) + + # visualize the reslut of KNN + # ShowFigure(DataSet) \ No newline at end of file -- Gitee From eb6820bac2000a3abf10e93b36c35ca4c9d5fa00 Mon Sep 17 00:00:00 2001 From: Flock-Li <863813609@qq.com> Date: Fri, 26 Mar 2021 15:00:10 +0800 Subject: [PATCH 2/5] add_readme --- assignment-1/submission/18307130130/README.md | 239 ++++++++++++++++++ assignment-1/submission/18307130130/source.py | 36 ++- 2 files changed, 256 insertions(+), 19 deletions(-) diff --git a/assignment-1/submission/18307130130/README.md b/assignment-1/submission/18307130130/README.md index e69de29..bda4dea 100644 --- a/assignment-1/submission/18307130130/README.md +++ b/assignment-1/submission/18307130130/README.md @@ -0,0 +1,239 @@ +# Assignment-1 Report + +

------李睿琛 18307130130

+## 一、数据集的生成与分割 + +### **数据集生成** + +`GenerateData`封装数据生成逻辑函数,修改参数数组,即可自定义分布特点。 + +> N:定义点的维度 +> +> means:定义分布均值 +> +> covs:定义分布协方差矩阵 +> +> nums:定义分布包含的点的数目 + +```python +# define two-dimension Gaussian distribution +N = 2 +means = [(1, 2), (1, 9), (4, 10), (9, 5), (7, 20)] +# define the number of each distribution +nums = [1000, 1000, 1000, 1000, 1000] +covs = [np.eye(N), np.eye(N), np.eye(N), np.eye(N), np.eye(N)] + +def GenerateData(N, nums, means, covs): + ... + GetGaussionSet(N, nums[i], means[i], covs[i]) + # concatenate the data and corresponding label + dataset[i] = np.concatenate((tmp, zeros), axis=1) + ... +``` + +`GetGaussionSet`根据给定数组生成高斯分布: + +```python +def GetGaussionSet(N, num, mean, cov): + """ + N refer to number of dimensions, mean refer to mean of Gaussion, + number refer to number of data + """ + x = np.random.multivariate_normal(mean, cov, num, 'raise') + return x +``` + +`GetGaussionSet`生成一个**以mean为均值,cov为协方差矩阵,包含num个点**的二维高斯分布的点集。 + +### **数据集分割** + +```python +# Randomly divide the data into 80% training set and 20% test set +np.random.shuffle(DataSet) +length = DataSet.shape[0] +train_len = round(length * 4 / 5) +train_data = DataSet[:train_len,:] +test_data = DataSet[train_len:,:] +``` + +打乱数据后,将数据随机划分为 80% 的训练集和 20% 的测试集。 + +## 二、KNN模型的拟合与预测 + +### 模型拟合 + +使用**交叉验证**确定合适**超参K**, 即把数据划分为训练集、验证集和测试集。一般的划分比例为6:2:2。 + +对80%的训练集进一步按6:2:2划分为60%训练集,20%验证集。 + +k值一般偏小,所以**遍历**确定正确性最高对应的k值: + +```python +v_ratio = 0.25 +length = train_data.shape[0] +label_len = data_len = round(length * (1 - v_ratio) ) +self.train_data = t_data = train_data[:data_len,:] +self.train_label = t_label = train_label[:label_len] +v_data = train_data[data_len:,:] +v_label = train_label[label_len:] + +# find the k with highest accuracy +for k in range(1, 20): + res = self._predict_by_k(t_data, t_label, v_data, k) +``` +输出如下: +``` +k : 1 acc: 0.984375 +k : 2 acc: 0.9828125 +... +k : 8 acc: 0.9890625 +k : 9 acc: 0.9890625 +k : 10 acc: 0.990625 +k : 11 acc: 0.9890625 +k : 12 acc: 0.990625 +k : 13 acc: 0.990625 +k : 14 acc: 0.9890625 +... +k : 18 acc: 0.9890625 +k : 19 acc: 0.9890625 +select k: 13 +``` + +即超参k设置为13时,在验证集上有最高准确性。 + +### **模型预测** + +```python +diff = t_data - d +dist = (np.sum(diff ** self.p, axis=1))**(1 / self.p) +topk = [t_label[x] for x in np.argsort(dist)[:k]] +``` + + 使用闵可夫斯基距离作为衡量: + +![img](https://img-blog.csdn.net/20170701211052055) + +```python +topk = [t_label[x] for x in np.argsort(dist)[:k]] +... +i = np.random.randint(len(top_cnt)) +res.append(top_cnt[i]) +``` + +根据距离从小到大排序,去前K个label,其中出现最频繁的即为预测结果。若有结果有多个,随机选取一个作为最终结果。 + +## 三、模型结果可视化 + +> N = 2 +> +> means = [(1, 2), (1, 9), (4, 10), (9, 5), (7, 20)] +> +> nums = [1000, 1000, 1000, 1000, 1000] +> +> covs = [np.eye(N), np.eye(N), np.eye(N), np.eye(N), np.eye(N)] + +K的选取: + +``` +k : 1 acc: 0.962 +k : 2 acc: 0.964 +k : 3 acc: 0.972 +k : 4 acc: 0.971 +k : 5 acc: 0.974 +k : 6 acc: 0.971 +k : 7 acc: 0.971 +k : 8 acc: 0.97 +k : 9 acc: 0.971 +k : 10 acc: 0.971 +k : 11 acc: 0.97 +k : 12 acc: 0.971 +k : 13 acc: 0.971 +k : 14 acc: 0.969 +k : 15 acc: 0.971 +k : 16 acc: 0.972 +k : 17 acc: 0.971 +k : 18 acc: 0.971 +k : 19 acc: 0.971 +select k: 5 +``` + +预测结果:左图可视化**训练集**分布,右图可视化**测试集**分布。星星符号标记了**预测错误**的点。 + +![1616737604559](C:\Users\lrc18\AppData\Roaming\Typora\typora-user-images\1616737604559.png) + +
图一
+## 四、实验探究 + +**设置对照组:** + +>means = [(1, 2), (1, 9), (4, 10)] +> +>nums = [1000, 1000, 1000] +> +>covs = [np.eye(N), np.eye(N), np.eye(N)] + +**acc = 0.9733333333333334** + +## ![1616738677599](C:\Users\lrc18\AppData\Roaming\Typora\typora-user-images\1616738677599.png) + +### 分布的距离 + +从图一中已经可以看到,黄色和绿色点集由于距离较近,预测错误率明显大于其他点。 + +而黄的与红色距离较远,基本没有出现预测错误的情况。 + +### 分布的方差 + +修改方差为: + +```python +covs = [np.array([ [5, 3], [3, 5] ]), np.eye(N), np.eye(N)] +``` + +**acc = 0.9583333333333334** + +![1616739122313](img/1.png) + +在二维高斯分布的协方差矩阵中: + +**正对角线代表每个变量的方差**,方差越大,数据波动越大; + +**副对角线代表不同变量之间的协方差**,协方差绝对值越大,变量相关性越大。 + +由图可见,`np.array([ [5, 3], [3, 5] ])`矩阵中方差为红色点集属性,方差为5,**数据波动,分布离散**;协方差为3,**数据分布呈现正相关**。这也导致数据混淆概率变大,预测准确率下降。 + +### 分布的数量 + +修改分布数量为: + +``` +nums = [1000, 5000, 1000] +``` + +![1616739948335](img/2.png) + +再次修改分布数量为: + +``` +nums = [1000, 10000, 1000] +``` + +![1616740079147](img/3.png) + +由于**绿色分布**数据量的增加,对于和**蓝色分布**重叠部分点的影响力增强,容易导致**过拟合**。 + +## 五、绘制KNN区域图 + +![1616741381345](img/4.png) + +```python +h = .02 +x_min, x_max = DataSet[:, 0].min() - 1, DataSet[:, 0].max() + 1 +y_min, y_max = DataSet[:, 1].min() - 1, DataSet[:, 1].max() + 1 +xx, yy = np.meshgrid(np.arange(x_min, x_max, h), + np.arange(y_min, y_max, h)) +``` + +**acc = 0.9775** + +生成网格点坐标,对每个点进行预测并绘制对应颜色。可以看见在区域交界处,颜色会出现部分**抖动**。 \ No newline at end of file diff --git a/assignment-1/submission/18307130130/source.py b/assignment-1/submission/18307130130/source.py index 32b6f99..f4e2b88 100644 --- a/assignment-1/submission/18307130130/source.py +++ b/assignment-1/submission/18307130130/source.py @@ -15,22 +15,19 @@ class KNN: def fit(self, train_data, train_label): - # split train_data to validation_data - train_label = train_label.reshape(-1, 1) data = np.concatenate((train_data, train_label), axis=1) np.random.shuffle(data) train_data = data[:, [0, 1]] train_label = data[:, 2] - + + # cross-validation v_ratio = 0.25 length = train_data.shape[0] label_len = data_len = round(length * (1 - v_ratio) ) - self.train_data = t_data = train_data[:data_len,:] self.train_label = t_label = train_label[:label_len] - v_data = train_data[data_len:,:] v_label = train_label[label_len:] @@ -66,29 +63,26 @@ class KNN: else: cnt_dict[x] = 1 sort_cnt = sorted(cnt_dict.items(), key=lambda x: x[1], reverse=True) - top_cnt = [] + top_cnt = sort_cnt[0][0] Max_cnt = sort_cnt[0][1] for number, cnt in sort_cnt: if cnt >= Max_cnt: - top_cnt.append(number) + top_cnt = number + Max_cnt = cnt else: break - i = np.random.randint(len(top_cnt)) - res.append(top_cnt[i]) + res.append(top_cnt) return res - - -def GetGaussionSet(N, num, mean): +def GetGaussionSet(N, num, mean, cov): """ N refer to number of dimensions, mean refer to mean of Gaussion, number refer to number of data """ - cov = np.eye(N) x = np.random.multivariate_normal(mean, cov, num, 'raise') return x -def GenerateData(N, nums, means): +def GenerateData(N, nums, means, covs): """ Generate data according to nums and means """ @@ -96,7 +90,7 @@ def GenerateData(N, nums, means): for i in range(len(nums)): # get the number as label zeros = np.zeros((nums[i], 1)) + i - tmp = GetGaussionSet(N, nums[i], means[i]) + tmp = GetGaussionSet(N, nums[i], means[i], covs[i]) # concatenate the data and corresponding label dataset[i] = np.concatenate((tmp, zeros), axis=1) @@ -180,10 +174,11 @@ if __name__ == "__main__": # define two-dimension Gaussian distribution means = [(1, 2), (1, 9), (4, 10), (9, 5), (7, 20)] # define the number of each distribution - nums = [1000, 1000, 100, 1000, 100] + nums = [400, 400, 400, 400, 400] + covs = [np.eye(N), np.eye(N), np.eye(N), np.eye(N), np.eye(N)] # Generate DataSet according to N, nums, and means - DataSet = GenerateData(N, nums, means) + DataSet = GenerateData(N, nums, means, covs) # Randomly divide the data into 80% training set and 20% test set np.random.shuffle(DataSet) @@ -200,7 +195,10 @@ if __name__ == "__main__": # calculate the accuracy print("acc = ", np.mean(np.equal(Z, test_data[:, 2]))) + model.train_label = model.train_label.reshape(-1, 1) + train_data = np.concatenate((model.train_data, model.train_label), axis=1) + # visualize the accuracy of KNN ShowAcc(train_data, test_data, Z) - # visualize the reslut of KNN - # ShowFigure(DataSet) \ No newline at end of file + # visualize the meshgraph of KNN + ShowFigure(DataSet) \ No newline at end of file -- Gitee From 45c15dc41f966581a46b6d65cf693eaf2a70bbbd Mon Sep 17 00:00:00 2001 From: Flock-Li <863813609@qq.com> Date: Mon, 29 Mar 2021 20:31:01 +0800 Subject: [PATCH 3/5] add_image --- assignment-1/submission/18307130130/img/1.png | Bin 0 -> 96066 bytes assignment-1/submission/18307130130/img/2.png | Bin 0 -> 118516 bytes assignment-1/submission/18307130130/img/3.png | Bin 0 -> 132285 bytes assignment-1/submission/18307130130/img/4.png | Bin 0 -> 75043 bytes 4 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/18307130130/img/1.png create mode 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    图一
    ## 四、实验探究 @@ -174,7 +174,7 @@ select k: 5 **acc = 0.9733333333333334** -## ![1616738677599](C:\Users\lrc18\AppData\Roaming\Typora\typora-user-images\1616738677599.png) +## ![1616738677599](img/5.png) ### 分布的距离 diff --git a/assignment-1/submission/18307130130/img/5.png b/assignment-1/submission/18307130130/img/5.png new file mode 100644 index 0000000000000000000000000000000000000000..2ee692c3ffec6ce0432b9e378a88a271a561eab8 GIT binary patch literal 90667 zcmeFZbySpJ+crFif{KWWfPjPoBCT{uNDe98pmYsLcPNSi0y1<94BgU=QqtWGA~|&D zyDz+d_j5n*^Q~{KZ+&aMf4%buYlgY5YwvyTGmhgpH~77hlfb=6auWuF;ld?F6=5(e z1Pq3WxQ+#WW1A}Y83v<-!9|6Yo#WOf-Q4f*)m&^jQO-WO`uoX&v{;Y-b^oi@*XY0f zO7$lUi|O%4h~+94FqXc4nQHz@D}!k4{C7RZ53P3LY{F}z#VYsSe*N~3(Ztc%QLnqjr-d_gG?b5M8T z(Z9jxxE2LQ-W}4irkTWISevX;6B82~t8~cjm&Ne@A_g4Jve=}XT*qZ0{21Jl>##ax z*7*6ZaGjv@=C?oHiPkGoc!H+|w>L0v# zwmRuFJvdQe2Zx-tULl&W>Z*EpF?^uVpoQIOU0aO?@uw?Z8jSW(6dH1StA%29yPXA0 z<|C)oM8*#v?BVgn7>m4KYtJ20^mLtIo&gwATOyczFyC{JAv>0I2s}y#J)J5YSulJ9 z8l5NTZSuqEuYI2wm@HjSY 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