From 1ef588b6b3ed0f000d82687558cd9219c723d835 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:23:48 +0800 Subject: [PATCH 01/84] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2018340246016?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/18340246016/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/18340246016/.keep diff --git a/assignment-1/submission/18340246016/.keep b/assignment-1/submission/18340246016/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 5ca46c0e2e2a6b2a27e8a210e7ff9a982d9a68c3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:24:27 +0800 Subject: [PATCH 02/84] add assignment-1/submission/18340246016. --- assignment-1/submission/18340246016/source.py | 3 +++ 1 file changed, 3 insertions(+) create mode 100644 assignment-1/submission/18340246016/source.py diff --git a/assignment-1/submission/18340246016/source.py b/assignment-1/submission/18340246016/source.py new file mode 100644 index 0000000..6da0614 --- /dev/null +++ b/assignment-1/submission/18340246016/source.py @@ -0,0 +1,3 @@ +import numpy as np +import matplotlib.pyplot as plt + -- Gitee From 9275105f3472ae128e23398a7d7a6aeeaa4e7a17 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:24:52 +0800 Subject: [PATCH 03/84] update assignment-1/submission/18340246016/source.py. --- assignment-1/submission/18340246016/source.py | 97 +++++++++++++++++++ 1 file changed, 97 insertions(+) diff --git a/assignment-1/submission/18340246016/source.py b/assignment-1/submission/18340246016/source.py index 6da0614..ceb7e79 100644 --- a/assignment-1/submission/18340246016/source.py +++ b/assignment-1/submission/18340246016/source.py @@ -1,3 +1,100 @@ import numpy as np import matplotlib.pyplot as plt +class KNN: + + def __init__(self): + self.train_data = None + self.train_labels = None + self.k = None + + def train_test_split(self,x,y,rate): + shuffled_indexes = np.random.permutation(len(x)) + test_size = int(len(x) * rate) + train_index = shuffled_indexes[test_size:] + test_index = shuffled_indexes[:test_size] + return x[train_index], x[test_index], y[train_index], y[test_index] + + def distance(self,v1,v2): + + weight_array = (v1-v2)**2 + weight_array_sum = np.sum(weight_array) + return weight_array_sum**(0.5) + + def fit(self, train_data, train_label): + + # 归一化 + mu = np.mean(train_data, axis=0) + sigma = np.std(train_data, axis=0) + train_data = (train_data - mu) / sigma + #train_data = train_data / np.sqrt(np.sum(train_data**2)) + + # 划分训练集/验证集 with rate =0.3 + X_train, X_test, Y_train, Y_test = self.train_test_split(train_data,train_label,0.3) + + # 对于不同的K[1-0.5*len(train)]，计算验证集到训练集的欧氏距离 + best_k=0 + k_candi=0; + for k in range(1,int(0.5*len(X_train))+1): + + true_couter=0 + for test_counter in range(0,len(X_test)): + pos_vec_list=[] + + for train_counter in range(0,len(X_train)): + pos_vec = np.array([self.distance(X_test[test_counter],X_train[train_counter]),Y_train[train_counter]]) + pos_vec_list.append(pos_vec) + + #对距离list根据距离排序 + pos_vec_list = np.array(pos_vec_list) + pos_vec_list_sorted = pos_vec_list[np.lexsort(pos_vec_list[:,::-1].T)] + #k-近邻结果列表 + result_list = pos_vec_list_sorted[:k][:,1] + + + + #test预测结果 + label = int(result_list[np.argmax(result_list)]) + + + #检验本次test在给定k下是否正确 + if (label == Y_test[test_counter] ): + true_couter=true_couter+1 + + + #最优K取值 + if (true_couter >= best_k): + best_k = true_couter + k_candi = k + + self.k = k_candi + self.train_data = train_data + self.train_labels = train_label + return self.k + + def predict(self, test_data): + test_label=[] + result_list=[] + + # 归一化 + mu = np.mean(test_data, axis=0) + sigma = np.std(test_data, axis=0) + test_data = (test_data - mu) / sigma + #test_data = test_data / np.sqrt(np.sum(test_data**2)) + + for i in range (0,len(test_data)): + pos_vec_list=[] + for m in range(0,len(self.train_data)): + pos_vec = np.array([self.distance(self.train_data[m],test_data[i]),self.train_labels[m]]) + pos_vec_list.append(pos_vec) + + + + pos_vec_list = np.array(pos_vec_list) + pos_vec_list_sorted = pos_vec_list[np.lexsort(pos_vec_list[:,::-1].T)] + + result_list = pos_vec_list_sorted[:(self.k)][:,1] + test_label.append(result_list[np.argmax(result_list)]) + + return test_label + \ No newline at end of file -- Gitee From 169edea5f44dd38eef04a63b55fb618c164cd560 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:25:43 +0800 Subject: [PATCH 04/84] add assignment-1/submission/18340246016. --- assignment-1/submission/18340246016/README.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/18340246016/README.md diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md new file mode 100644 index 0000000..e69de29 -- Gitee From 3c12a1eb9998381e7c1bccb5f8b0adf173b58104 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:26:49 +0800 Subject: [PATCH 05/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index e69de29..8e40f5c 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -0,0 +1 @@ +![输入图片说明](https://images.gitee.com/uploads/images/2021/0331/222640_06e435c4_8823823.png "屏幕截图.png") \ No newline at end of file -- Gitee From dbd75c0b8593ca3cd168fbfed5e05228159dc47f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Wed, 31 Mar 2021 22:38:14 +0800 Subject: [PATCH 06/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 8e40f5c..cd15cf2 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1 +1,13 @@ -![输入图片说明](https://images.gitee.com/uploads/images/2021/0331/222640_06e435c4_8823823.png "屏幕截图.png") \ No newline at end of file +1. 解释一下实现过程 +1.1 sup +1.2 fit +1.3 predict +2. 高斯分布探究试验 +2.1 mean集中 + xy分散 = 对应的k +2.2 mean集中 + xy集中 = 对应的k +2.3 mean分散 + xy分散 = 对应的k +2.4 mean分散 + xy集中 = 对应的k +3.K值 +3.1 不同量下的best_k +3.2 不同K下的锯齿图 +3.3 不同K下的acc \ No newline at end of file -- Gitee From 45c6c5da81bd7a0f0bf59cb519a9303ec99ca570 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 09:59:57 +0800 Subject: [PATCH 07/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index cd15cf2..374abde 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1,5 +1,5 @@ -1. 解释一下实现过程 -1.1 sup + **1. KNN实现过程 +** 1.1 sup 1.2 fit 1.3 predict 2. 高斯分布探究试验 -- Gitee From 5a3180ff238da453a133b97fcecd85f455163dc8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:01:49 +0800 Subject: [PATCH 08/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 374abde..0c41536 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1,5 +1,15 @@ - **1. KNN实现过程 -** 1.1 sup +1. KNN实现过程 +1.1 sup + +``` +# 这里我们用train_test_split实现训练集与验证集以给定的比例划分与打乱 +def train_test_split(self,x,y,rate): + shuffled_indexes = np.random.permutation(len(x)) + test_size = int(len(x) * rate) + train_index = shuffled_indexes[test_size:] + test_index = shuffled_indexes[:test_size] + return x[train_index], x[test_index], y[train_index], y[test_index]``` + 1.2 fit 1.3 predict 2. 高斯分布探究试验 -- Gitee From ab8bfc81ae4732eddffe0e627f814b9f61322965 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:02:31 +0800 Subject: [PATCH 09/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 0c41536..9b1dba0 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -8,7 +8,8 @@ def train_test_split(self,x,y,rate): test_size = int(len(x) * rate) train_index = shuffled_indexes[test_size:] test_index = shuffled_indexes[:test_size] - return x[train_index], x[test_index], y[train_index], y[test_index]``` + return x[train_index], x[test_index], y[train_index], y[test_index] +``` 1.2 fit 1.3 predict -- Gitee From e6cc90b27f5dc9b7f479e7c0c4ef95d9862e5dfa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:04:15 +0800 Subject: [PATCH 10/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 17 +++++++++++++++-- 1 file changed, 15 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 9b1dba0..4add29c 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1,5 +1,6 @@ -1. KNN实现过程 -1.1 sup + **1. KNN实现过程 +** +1.1 辅助方法的实现 ``` # 这里我们用train_test_split实现训练集与验证集以给定的比例划分与打乱 @@ -11,6 +12,18 @@ def train_test_split(self,x,y,rate): return x[train_index], x[test_index], y[train_index], y[test_index] ``` + +``` +# 用distance方法计算两组向量之间的欧式距离 +def distance(self,v1,v2): + + weight_array = (v1-v2)**2 + weight_array_sum = np.sum(weight_array) + return weight_array_sum**(0.5) +``` + + + 1.2 fit 1.3 predict 2. 高斯分布探究试验 -- Gitee From e0b06a6434b7ffa9a3f40ec02cf04baa3d411e13 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:04:36 +0800 Subject: [PATCH 11/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 4add29c..967769b 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1,5 +1,5 @@ - **1. KNN实现过程 -** + **1. KNN实现过程** + 1.1 辅助方法的实现 ``` -- Gitee From 686121c8207506ad63a461b9e4e0574c5ead6678 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:05:24 +0800 Subject: [PATCH 12/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 967769b..ec767fd 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -1,6 +1,6 @@ **1. KNN实现过程** -1.1 辅助方法的实现 +*1.1 辅助方法的实现* ``` # 这里我们用train_test_split实现训练集与验证集以给定的比例划分与打乱 -- Gitee From 539d4afd793a3b9a08ec92c0211294001f1d271e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:09:14 +0800 Subject: [PATCH 13/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 58 ++++++++++++++++++- 1 file changed, 57 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index ec767fd..e701704 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -24,7 +24,63 @@ def distance(self,v1,v2): -1.2 fit +*1.2 fit* + + +``` +# 我们用fit方法实现 1. 对训练数据的归一化 2. 训练数据内部subdivide为训练集与测试集，取最优K值 3. 将训练数据赋值self.data +def fit(self, train_data, train_label): + + # 归一化 + mu = np.mean(train_data, axis=0) + sigma = np.std(train_data, axis=0) + train_data = (train_data - mu) / sigma + + # 划分训练集/验证集 with rate =0.3 + X_train, X_test, Y_train, Y_test = self.train_test_split(train_data,train_label,0.3) + + # 对于不同的K[1-0.5*len(train)]，计算验证集到训练集的欧氏距离 + best_k=0 + k_candi=0; + for k in range(1,int(0.5*len(X_train))+1): + + true_couter=0 + for test_counter in range(0,len(X_test)): + pos_vec_list=[] + + for train_counter in range(0,len(X_train)): + pos_vec = np.array([self.distance(X_test[test_counter],X_train[train_counter]),Y_train[train_counter]]) + pos_vec_list.append(pos_vec) + + #对距离list根据距离排序 + pos_vec_list = np.array(pos_vec_list) + pos_vec_list_sorted = pos_vec_list[np.lexsort(pos_vec_list[:,::-1].T)] + #k-近邻结果列表 + result_list = pos_vec_list_sorted[:k][:,1] + + + + #test预测结果 + label = int(result_list[np.argmax(result_list)]) + + + #检验本次test在给定k下是否正确 + if (label == Y_test[test_counter] ): + true_couter=true_couter+1 + + + #最优K取值 + if (true_couter >= best_k): + best_k = true_couter + k_candi = k + + self.k = k_candi + self.train_data = train_data + self.train_labels = train_label + return self.k +``` + + 1.3 predict 2. 高斯分布探究试验 2.1 mean集中 + xy分散 = 对应的k -- Gitee From 2832e09057af7e54527b51fa37605e67a5e5bfb1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:12:50 +0800 Subject: [PATCH 14/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 35 +++++++++++++++++-- 1 file changed, 33 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index e701704..e153822 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -24,7 +24,7 @@ def distance(self,v1,v2): -*1.2 fit* +*1.2 fit方法的实现* ``` @@ -81,7 +81,38 @@ def fit(self, train_data, train_label): ``` -1.3 predict +*1.3 predict方法的实现* + +``` + # 根据fit方法带入的数据data以及训练结果K，预测test_label + def predict(self, test_data): + test_label=[] + result_list=[] + + # 归一化原始训练数据 + mu = np.mean(test_data, axis=0) + sigma = np.std(test_data, axis=0) + test_data = (test_data - mu) / sigma + + for i in range (0,len(test_data)): + pos_vec_list=[] + for m in range(0,len(self.train_data)): + pos_vec = np.array([self.distance(self.train_data[m],test_data[i]),self.train_labels[m]]) + pos_vec_list.append(pos_vec) + + + # KNN结果列表 + pos_vec_list = np.array(pos_vec_list) + pos_vec_list_sorted = pos_vec_list[np.lexsort(pos_vec_list[:,::-1].T)] + + result_list = pos_vec_list_sorted[:(self.k)][:,1] + test_label.append(result_list[np.argmax(result_list)]) + + return test_label +``` + + + 2. 高斯分布探究试验 2.1 mean集中 + xy分散 = 对应的k 2.2 mean集中 + xy集中 = 对应的k -- Gitee From 95423483bff247c6a7d86058859f44336f4e91bf Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:25:56 +0800 Subject: [PATCH 15/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 22 +++++++++++++++++-- 1 file changed, 20 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index e153822..be84c79 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -113,8 +113,26 @@ def fit(self, train_data, train_label): -2. 高斯分布探究试验 -2.1 mean集中 + xy分散 = 对应的k + **2. 高斯分布探究试验** + +*2.1 均值集中 + xy分布分散 = 对应的k* + +$$cov= +\left\{ + \begin{matrix} + a & b \\ + f & g \\ + + \end{matrix} +\right\} +? + +作者：xxq2dream +链接：https://juejin.cn/post/6844903650024767501 +来源：掘金 +著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。 + + 2.2 mean集中 + xy集中 = 对应的k 2.3 mean分散 + xy分散 = 对应的k 2.4 mean分散 + xy集中 = 对应的k -- Gitee From 12060eec5f19b3a955b411ebae5e31c9734d1f3f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:27:08 +0800 Subject: [PATCH 16/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 21 +++++++------------ 1 file changed, 7 insertions(+), 14 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index be84c79..f9a1184 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -117,20 +117,13 @@ def fit(self, train_data, train_label): *2.1 均值集中 + xy分布分散 = 对应的k* -$$cov= -\left\{ - \begin{matrix} - a & b \\ - f & g \\ - - \end{matrix} -\right\} -? - -作者：xxq2dream -链接：https://juejin.cn/post/6844903650024767501 -来源：掘金 -著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。 +$$ + \begin{matrix} + 1 & 2 & 3 \\ + 4 & 5 & 6 \\ + 7 & 8 & 9 + \end{matrix} \tag{1} +$$ 2.2 mean集中 + xy集中 = 对应的k -- Gitee From dbe92ea7cd043b86e1eb0287c9ac3e98524e242a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:45:24 +0800 Subject: [PATCH 17/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 18 +++++++++++------- 1 file changed, 11 insertions(+), 7 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index f9a1184..c499215 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -115,18 +115,22 @@ def fit(self, train_data, train_label): **2. 高斯分布探究试验** -*2.1 均值集中 + xy分布分散 = 对应的k* +*2.1 均值集中 + xy分布集中 = 对应的k* $$ - \begin{matrix} - 1 & 2 & 3 \\ - 4 & 5 & 6 \\ - 7 & 8 & 9 - \end{matrix} \tag{1} +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +35 & 0 \\\\ +0 & 23 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +13 & 4 +\end{array}\right] +\end{array} $$ -2.2 mean集中 + xy集中 = 对应的k +2.2 mean集中 + xy分散 = 对应的k 2.3 mean分散 + xy分散 = 对应的k 2.4 mean分散 + xy集中 = 对应的k 3.K值 -- Gitee From 3801048141d20a7647300f181fc7a9a9769cb458 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:47:21 +0800 Subject: [PATCH 18/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 34 +++++++++++++++++-- 1 file changed, 31 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index c499215..14bb501 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -120,15 +120,43 @@ def fit(self, train_data, train_label): $$ \begin{array}{l} \Sigma=\left[\begin{array}{cc} -35 & 0 \\\\ -0 & 23 +1 & 0 \\\\ +0 & 1 \end{array}\right] \\\\ \mu=\left[\begin{array}{ll} -13 & 4 +10 & 10 \end{array}\right] \end{array} $$ +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 0 \\\\ +0 & 1 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +8 & 8 +\end{array}\right] +\end{array} +$$ + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 1 \\\\ +1 & 1 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +12 & 12 +\end{array}\right] +\end{array} +$$ + + + + + 2.2 mean集中 + xy分散 = 对应的k 2.3 mean分散 + xy分散 = 对应的k -- Gitee From 14d1d4e31825f461c74fdf2ac42a994c1dd5844a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:48:28 +0800 Subject: [PATCH 19/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 14bb501..bd7b2bc 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -134,7 +134,8 @@ $$ \Sigma=\left[\begin{array}{cc} 2 & 0 \\\\ 0 & 1 -\end{array}\right] \\\\ +\end{array}\right] + \mu=\left[\begin{array}{ll} 8 & 8 \end{array}\right] @@ -146,7 +147,7 @@ $$ \Sigma=\left[\begin{array}{cc} 2 & 1 \\\\ 1 & 1 -\end{array}\right] \\\\ +\end{array}\right] \mu=\left[\begin{array}{ll} 12 & 12 \end{array}\right] -- Gitee From b6b2531f6ae5b73d48462c76e483ce1e117b41d9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:49:28 +0800 Subject: [PATCH 20/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index bd7b2bc..fb5a0e2 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -122,20 +122,20 @@ $$ \Sigma=\left[\begin{array}{cc} 1 & 0 \\\\ 0 & 1 -\end{array}\right] \\\\ +\end{array}\right] \mu=\left[\begin{array}{ll} 10 & 10 \end{array}\right] \end{array} $$ + $$ \begin{array}{l} \Sigma=\left[\begin{array}{cc} 2 & 0 \\\\ 0 & 1 -\end{array}\right] - +\end{array}\right] \mu=\left[\begin{array}{ll} 8 & 8 \end{array}\right] -- Gitee From 1011ce111e717a9cdd19f47eb8a4e0dbb73020f9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:50:38 +0800 Subject: [PATCH 21/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index fb5a0e2..ba03e39 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -155,8 +155,8 @@ $$ $$ - - +![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") +![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") 2.2 mean集中 + xy分散 = 对应的k -- Gitee From fede853ada5c1c5df0325141eea076a2d3365b9b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:52:09 +0800 Subject: [PATCH 22/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index ba03e39..cfb6d7e 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -155,8 +155,8 @@ $$ $$ -![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") -![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") +[训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") +[测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") 2.2 mean集中 + xy分散 = 对应的k -- Gitee From 4e48ea5a162cbc234609bfa4a73e6814de0ca7e8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:52:45 +0800 Subject: [PATCH 23/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index cfb6d7e..46d3cef 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -154,8 +154,9 @@ $$ \end{array} $$ - +训练集分布 [训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") +测试集分布 [测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") -- Gitee From 25af1019ff636595e0d333c4ba2be1dcae2e420b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:53:07 +0800 Subject: [PATCH 24/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 46d3cef..e1f3828 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -155,9 +155,9 @@ $$ $$ 训练集分布 -[训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") +![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") 测试集分布 -[测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") +![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") 2.2 mean集中 + xy分散 = 对应的k -- Gitee From 9194b762ef77c7ec05c307d378806a7034df6ff9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:53:48 +0800 Subject: [PATCH 25/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index e1f3828..d8481ae 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -154,9 +154,12 @@ $$ \end{array} $$ -训练集分布 +*训练集分布* + ![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") -测试集分布 + +*测试集分布* + ![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") -- Gitee From 8d7ab95f9350f3c7b8c0cbd7b66ea0c0704e1a6e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 10:55:12 +0800 Subject: [PATCH 26/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index d8481ae..f1e58dd 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -156,12 +156,11 @@ $$ *训练集分布* -![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105007_0d3f874d_8823823.png "屏幕截图.png") +![训练集分布](https://images.gitee.com/uploads/images/2021/0401/105433_e7ec4619_8823823.png "屏幕截图.png") *测试集分布* -![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105032_733d6b01_8823823.png "屏幕截图.png") - +![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105459_56af4a90_8823823.png "屏幕截图.png") 2.2 mean集中 + xy分散 = 对应的k 2.3 mean分散 + xy分散 = 对应的k -- Gitee From 03702af752031b5fcb57db3d82f1304a11d2b7cc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:06:21 +0800 Subject: [PATCH 27/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 68 +++++++++++++++++++ 1 file changed, 68 insertions(+) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index f1e58dd..fb194d0 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -115,6 +115,74 @@ def fit(self, train_data, train_label): **2. 高斯分布探究试验** +*2.0 生成以及展示函数* + + +``` +# 赋值矩阵 +mean = (10, 10) +cov = np.array([[1,0], [0, 1]]) +x = np.random.multivariate_normal(mean, cov, (200,)) + +mean = (8, 8) +cov = np.array([[2, 0], [0, 1]]) +y = np.random.multivariate_normal(mean, cov, (200,)) + +mean = (12, 12) +cov = np.array([[2,1],[1,1]]) +z = np.random.multivariate_normal(mean, cov, (400,)) + +# 合并xyz三组函数 +data = np.concatenate([x,y,z]) +# 为xyz打标签 +label = np.concatenate([ + np.zeros((200,),dtype=int), + np.ones((200,),dtype=int), + np.ones((400,),dtype=int)*2 + ]) +# 按8：2的比例分割训练集与测试集 +X_train, X_test, Y_train, Y_test = model.train_test_split(data,label,0.2) + +``` + + +``` +# 展示函数 +def display(x,y): + type1_x = []; type1_y = [] + type2_x = []; type2_y = [] + type3_x = []; type3_y = [] + + plt.figure(figsize=(8,6)) + + for i in range(0,len(x)): + if(y[i]==0): + type1_x.append(x[i][0]) + type1_y.append(x[i][1]) + if(y[i]==1): + type2_x.append(x[i][0]) + type2_y.append(x[i][1]) + if(y[i]==2): + type3_x.append(x[i][0]) + type3_y.append(x[i][1]) + + fig = plt.figure(figsize = (10, 6)) + ax = fig.add_subplot(111) + + type1 = ax.scatter(type1_x, type1_y, s = 30, c = 'brown') + type2 = ax.scatter(type2_x, type2_y, s = 30, c = 'lime') + type3 = ax.scatter(type3_x, type3_y, s = 30, c = "darkviolet") + + + + ax.legend((type1, type2, type3), ("A", "B", "C"), loc = 0) + + plt.show() + +``` + + + *2.1 均值集中 + xy分布集中 = 对应的k* $$ -- Gitee From 51b9ab10652cda0db8da897675f20572235cfaf9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:13:34 +0800 Subject: [PATCH 28/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index fb194d0..94b5226 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -230,6 +230,11 @@ $$ ![测试集分布](https://images.gitee.com/uploads/images/2021/0401/105459_56af4a90_8823823.png "屏幕截图.png") +*K与准确率结果* +| k | 准确率 | +| ---------------- | ------ | +| 1 | 78.75% | + 2.2 mean集中 + xy分散 = 对应的k 2.3 mean分散 + xy分散 = 对应的k 2.4 mean分散 + xy集中 = 对应的k -- Gitee From 737f72377b45ffa45f5d22672b36aad59ab8c530 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:19:18 +0800 Subject: [PATCH 29/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 55 ++++++++++++++++++- 1 file changed, 53 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 94b5226..2aba0a1 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -185,6 +185,55 @@ def display(x,y): *2.1 均值集中 + xy分布集中 = 对应的k* +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +4 & 0 \\\\ +0 & 2 +\end{array}\right] +\mu=\left[\begin{array}{ll} +10 & 10 +\end{array}\right] +\end{array} +$$ + + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 0 \\\\ +0 & 4 +\end{array}\right] +\mu=\left[\begin{array}{ll} +8 & 8 +\end{array}\right] +\end{array} +$$ + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +8 & 1 \\\\ +1 & 6 +\end{array}\right] +\mu=\left[\begin{array}{ll} +12 & 12 +\end{array}\right] +\end{array} +$$ + +*训练集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/111859_687c068b_8823823.png "屏幕截图.png") +*测试集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/111906_d0e2e134_8823823.png "屏幕截图.png") +*K与准确率结果* +| k | 准确率 | +| ---------------- | ------ | +| 1 | 78.75% | + +*2.2 mean集中 + xy分散 = 对应的k* $$ \begin{array}{l} \Sigma=\left[\begin{array}{cc} @@ -235,10 +284,12 @@ $$ | ---------------- | ------ | | 1 | 78.75% | -2.2 mean集中 + xy分散 = 对应的k + 2.3 mean分散 + xy分散 = 对应的k 2.4 mean分散 + xy集中 = 对应的k -3.K值 + +**3.K值** + 3.1 不同量下的best_k 3.2 不同K下的锯齿图 3.3 不同K下的acc \ No newline at end of file -- Gitee From 14eab53ac5f492e17dc93538c008893c9fcce9ac Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:21:27 +0800 Subject: [PATCH 30/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 2aba0a1..9a18ef1 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -183,7 +183,7 @@ def display(x,y): -*2.1 均值集中 + xy分布集中 = 对应的k* +*2.1 均值集中 + xy分布分散 = 对应的k* $$ \begin{array}{l} @@ -222,18 +222,20 @@ $$ \end{array} $$ + *训练集分布* ![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/111859_687c068b_8823823.png "屏幕截图.png") + *测试集分布* ![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/111906_d0e2e134_8823823.png "屏幕截图.png") *K与准确率结果* | k | 准确率 | | ---------------- | ------ | -| 1 | 78.75% | +| 4 | 62.5% | -*2.2 mean集中 + xy分散 = 对应的k* +*2.2 mean集中 + xy集中 = 对应的k* $$ \begin{array}{l} \Sigma=\left[\begin{array}{cc} -- Gitee From 95ac2d2371d7de6a57f2c8e57008cc89b5b66e4d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:25:31 +0800 Subject: [PATCH 31/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 56 ++++++++++++++++++- 1 file changed, 55 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 9a18ef1..9aab188 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -287,7 +287,61 @@ $$ | 1 | 78.75% | -2.3 mean分散 + xy分散 = 对应的k +***2.3 mean分散 + xy分散 = 对应的k*** + + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +4 & 0 \\\\ +0 & 2 +\end{array}\right] +\mu=\left[\begin{array}{ll} +2 & 2 +\end{array}\right] +\end{array} +$$ + + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 0 \\\\ +0 & 4 +\end{array}\right] +\mu=\left[\begin{array}{ll} +4 & 6 +\end{array}\right] +\end{array} +$$ + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +8 & 1 \\\\ +1 & 6 +\end{array}\right] +\mu=\left[\begin{array}{ll} +10 & 10 +\end{array}\right] +\end{array} +$$ + + +*训练集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112426_09535d36_8823823.png "屏幕截图.png") + +*测试集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112437_53a32eec_8823823.png "屏幕截图.png")*K与准确率结果* + + +| k | 准确率 | +| ---------------- | ------ | +| 2 | 86.25% | + + 2.4 mean分散 + xy集中 = 对应的k **3.K值** -- Gitee From 7c88f32407cf34e8ed2e855bf59f479bca89755b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:29:07 +0800 Subject: [PATCH 32/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 63 ++++++++++++++++++- 1 file changed, 61 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 9aab188..2c150ce 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -334,7 +334,9 @@ $$ *测试集分布* -![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112437_53a32eec_8823823.png "屏幕截图.png")*K与准确率结果* +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112437_53a32eec_8823823.png "屏幕截图.png") + +*K与准确率结果* | k | 准确率 | @@ -342,7 +344,64 @@ $$ | 2 | 86.25% | -2.4 mean分散 + xy集中 = 对应的k +*2.4 mean分散 + xy集中 = 对应的k* + + + + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +1 & 0 \\\\ +0 & 1 +\end{array}\right] +\mu=\left[\begin{array}{ll} +2 & 2 +\end{array}\right] +\end{array} +$$ + + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 0 \\\\ +0 & 2 +\end{array}\right] +\mu=\left[\begin{array}{ll} +4 & 6 +\end{array}\right] +\end{array} +$$ + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 1 \\\\ +1 & 3 +\end{array}\right] +\mu=\left[\begin{array}{ll} +10 & 10 +\end{array}\right] +\end{array} +$$ + + +*训练集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112759_754208e4_8823823.png "屏幕截图.png") + +*测试集分布* + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/112810_ca9d4230_8823823.png "屏幕截图.png") + +*K与准确率结果* + + +| k | 准确率 | +| ---------------- | ------ | +| 1 | 95.625% | + **3.K值** -- Gitee From 09c735138f878a03a47d6d4283f058c09a17fac6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:30:28 +0800 Subject: [PATCH 33/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 2c150ce..ddd781c 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -183,7 +183,7 @@ def display(x,y): -*2.1 均值集中 + xy分布分散 = 对应的k* +***2.1 均值集中 + xy分布分散 = 对应的k*** $$ \begin{array}{l} @@ -230,12 +230,14 @@ $$ *测试集分布* ![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/111906_d0e2e134_8823823.png "屏幕截图.png") + *K与准确率结果* | k | 准确率 | | ---------------- | ------ | | 4 | 62.5% | -*2.2 mean集中 + xy集中 = 对应的k* +***2.2 mean集中 + xy集中 = 对应的k*** + $$ \begin{array}{l} \Sigma=\left[\begin{array}{cc} @@ -344,7 +346,7 @@ $$ | 2 | 86.25% | -*2.4 mean分散 + xy集中 = 对应的k* +***2.4 mean分散 + xy集中 = 对应的k*** -- Gitee From 34088143a60d7ec6900d6ecf51e0075f4924853b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:39:51 +0800 Subject: [PATCH 34/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index ddd781c..61877f6 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -405,6 +405,12 @@ $$ | 1 | 95.625% | +***2.5 有关高斯分布的结论*** +1. 与直观体会到的类似，模型准确率与高斯分布均值离散程度正相关，与xy方差负相关 +2. 模型在均值分散，方差集中的情况下表现最好，在均值集中，方差分散的情况下表现最差 +3. 最佳K的取值与准确率无直接联系，准确性更多取决于分布情况 + + **3.K值** 3.1 不同量下的best_k -- Gitee From ee9ac51821f0ce42029f2aaeea5b3fe0cf95c8df Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 11:47:50 +0800 Subject: [PATCH 35/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 54 ++++++++++--------- 1 file changed, 30 insertions(+), 24 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 61877f6..a1b275d 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -119,29 +119,30 @@ def fit(self, train_data, train_label): ``` -# 赋值矩阵 -mean = (10, 10) -cov = np.array([[1,0], [0, 1]]) -x = np.random.multivariate_normal(mean, cov, (200,)) +def generate (amount_1,amount_2,amount_3): -mean = (8, 8) -cov = np.array([[2, 0], [0, 1]]) -y = np.random.multivariate_normal(mean, cov, (200,)) - -mean = (12, 12) -cov = np.array([[2,1],[1,1]]) -z = np.random.multivariate_normal(mean, cov, (400,)) - -# 合并xyz三组函数 -data = np.concatenate([x,y,z]) -# 为xyz打标签 -label = np.concatenate([ - np.zeros((200,),dtype=int), - np.ones((200,),dtype=int), - np.ones((400,),dtype=int)*2 - ]) -# 按8：2的比例分割训练集与测试集 -X_train, X_test, Y_train, Y_test = model.train_test_split(data,label,0.2) + mean = (2, 2) + cov = np.array([[1,0], [0, 1]]) + x = np.random.multivariate_normal(mean, cov, (amount_1,)) + + mean = (4, 6) + cov = np.array([[2, 0], [0, 2]]) + y = np.random.multivariate_normal(mean, cov, (amount_2,)) + + mean = (10, 10) + cov = np.array([[2,1],[1,3]]) + z = np.random.multivariate_normal(mean, cov, (amount_3,)) + + + data = np.concatenate([x,y,z]) + + label = np.concatenate([ + np.zeros((amount_1,),dtype=int), + np.ones((amount_2,),dtype=int), + np.ones((amount_3,),dtype=int)*2 + ]) + + return model.train_test_split(data,label,0.2) ``` @@ -411,8 +412,13 @@ $$ 3. 最佳K的取值与准确率无直接联系，准确性更多取决于分布情况 -**3.K值** -3.1 不同量下的best_k +** +3. K值 +** + +***3.1 不同量下的best_k*** + + 3.2 不同K下的锯齿图 3.3 不同K下的acc \ No newline at end of file -- Gitee From 979ab862116ae3f5039d310ef1393d0f97660677 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 12:03:22 +0800 Subject: [PATCH 36/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 28 +++++++++++++++++++ 1 file changed, 28 insertions(+) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index a1b275d..2feaf97 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -419,6 +419,34 @@ $$ ***3.1 不同量下的best_k*** +（这里以2.4高斯分布为例） + +``` +# 准备数据集维度 +amount_list = [[10,10,10],[50,50,50],[100,100,100],[150,50,200],[200,200,200],[250,300,400]] +k_list=[] +aug_amount = [30,150,300,400,600,950] + +# 在不同数据集量下训练最佳k值 +for i in range (0,len(amount_list)): + model = KNN() + X_train, X_test, Y_train, Y_test = generate(amount_list[i][0],amount_list[i][1],amount_list[i][2]) + k_list.append(model.fit(X_train, Y_train)) + +# 画图 +l1=plt.plot(aug_amount,k_list,'r--',label='Best-K-Value') +plt.title('The relationship between # elements and |K|') +plt.xlabel('Total # of elements') +plt.ylabel('K-value') +plt.legend() + +``` +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/120033_088f8aa7_8823823.png "屏幕截图.png") + + +1. K取值与元素数量无关 +2. 最佳K会趋向于一个较小的值，所以在fit时考虑遍历[1,10]，无需遍历更大的K（导致额外无用运算） + 3.2 不同K下的锯齿图 3.3 不同K下的acc \ No newline at end of file -- Gitee From 59ba14c2d14761e6d5ff2b323fb8ed9c73280a24 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 12:04:35 +0800 Subject: [PATCH 37/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index 2feaf97..d9e68d0 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -413,9 +413,7 @@ $$ -** -3. K值 -** +**3. K值 ** ***3.1 不同量下的best_k*** -- Gitee From 0bf9f950a569592a6b0f694632897248bef8fa1b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 12:25:38 +0800 Subject: [PATCH 38/84] update assignment-1/submission/18340246016/README.md. --- assignment-1/submission/18340246016/README.md | 39 ++++++++++++++++++- 1 file changed, 37 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18340246016/README.md b/assignment-1/submission/18340246016/README.md index d9e68d0..c998960 100644 --- a/assignment-1/submission/18340246016/README.md +++ b/assignment-1/submission/18340246016/README.md @@ -446,5 +446,40 @@ plt.legend() 2. 最佳K会趋向于一个较小的值，所以在fit时考虑遍历[1,10]，无需遍历更大的K（导致额外无用运算） -3.2 不同K下的锯齿图 -3.3 不同K下的acc \ No newline at end of file +**3.2 不同K下的acc** + + +``` +# 因为我实现的KNN函数没有K参数（学习最优K），这里采用SKlearn数据库中的KNeighborsClassifier来做本次探究 +from sklearn.datasets import load_iris +from sklearn.model_selection import train_test_split +from sklearn.neighbors import KNeighborsClassifier + +# 导入sklearn iris数据库并分类 +iris = load_iris() +X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size = 0.25, random_state = 33) + +# 在不同k值下计算accuracy +acc_list=[] + +for i in range (1,100): + + + knc = KNeighborsClassifier(n_neighbors=i) + knc.fit(X_train, y_train) + y_predict = knc.predict(X_test) + + acc_list.append(knc.score(X_test, y_test)) + +# 画图 +l1=plt.plot(range(1,100),acc_list,'green',label='Accuracy') +plt.title('The relationship between K-choice and Accuracy') +plt.xlabel('K-Value') +plt.ylabel('Accuracy') +plt.legend() + +``` +![输入图片说明](https://images.gitee.com/uploads/images/2021/0401/122104_30809a7a_8823823.png "屏幕截图.png") + +1. 同3.1结论[2]，最佳K的取值会聚焦于一个较小的值 +2. iris数据集大小为150，可以看到超过0.5*len 之后准确率锁定在50%（几乎约等于瞎猜） -- Gitee From 995af67ca45c3e02d0286696b32538e31fe08f7f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=AD=9F=E7=84=95=E7=84=B6?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 12:27:33 +0800 Subject: [PATCH 39/84] update assignment-1/submission/18340246016/source.py. --- assignment-1/submission/18340246016/source.py | 68 +++++++++++++++++-- 1 file changed, 61 insertions(+), 7 deletions(-) diff --git a/assignment-1/submission/18340246016/source.py b/assignment-1/submission/18340246016/source.py index ceb7e79..c43b0cc 100644 --- a/assignment-1/submission/18340246016/source.py +++ b/assignment-1/submission/18340246016/source.py @@ -1,6 +1,3 @@ -import numpy as np -import matplotlib.pyplot as plt - class KNN: def __init__(self): @@ -27,15 +24,14 @@ class KNN: mu = np.mean(train_data, axis=0) sigma = np.std(train_data, axis=0) train_data = (train_data - mu) / sigma - #train_data = train_data / np.sqrt(np.sum(train_data**2)) # 划分训练集/验证集 with rate =0.3 X_train, X_test, Y_train, Y_test = self.train_test_split(train_data,train_label,0.3) - # 对于不同的K[1-0.5*len(train)]，计算验证集到训练集的欧氏距离 + # 对于不同的K[1-20]，计算验证集到训练集的欧氏距离 best_k=0 k_candi=0; - for k in range(1,int(0.5*len(X_train))+1): + for k in range(1,20): true_couter=0 for test_counter in range(0,len(X_test)): @@ -67,6 +63,7 @@ class KNN: best_k = true_couter k_candi = k + # print(k_candi) self.k = k_candi self.train_data = train_data self.train_labels = train_label @@ -97,4 +94,61 @@ class KNN: test_label.append(result_list[np.argmax(result_list)]) return test_label - \ No newline at end of file + +def generate (amount_1,amount_2,amount_3): + + + mean = (2, 2) + cov = np.array([[1,0], [0, 1]]) + x = np.random.multivariate_normal(mean, cov, (amount_1,)) + + mean = (4, 6) + cov = np.array([[2, 0], [0, 2]]) + y = np.random.multivariate_normal(mean, cov, (amount_2,)) + + mean = (10, 10) + cov = np.array([[2,1],[1,3]]) + z = np.random.multivariate_normal(mean, cov, (amount_3,)) + + + data = np.concatenate([x,y,z]) + + label = np.concatenate([ + np.zeros((amount_1,),dtype=int), + np.ones((amount_2,),dtype=int), + np.ones((amount_3,),dtype=int)*2 + ]) + + return model.train_test_split(data,label,0.2) + + +def display(x,y): + type1_x = []; type1_y = [] + type2_x = []; type2_y = [] + type3_x = []; type3_y = [] + + plt.figure(figsize=(8,6)) + + for i in range(0,len(x)): + if(y[i]==0): + type1_x.append(x[i][0]) + type1_y.append(x[i][1]) + if(y[i]==1): + type2_x.append(x[i][0]) + type2_y.append(x[i][1]) + if(y[i]==2): + type3_x.append(x[i][0]) + type3_y.append(x[i][1]) + + fig = plt.figure(figsize = (10, 6)) + ax = fig.add_subplot(111) + + type1 = ax.scatter(type1_x, type1_y, s = 30, c = 'brown') + type2 = ax.scatter(type2_x, type2_y, s = 30, c = 'lime') + type3 = ax.scatter(type3_x, type3_y, s = 30, c = "darkviolet") + + + + ax.legend((type1, type2, type3), ("A", "B", "C"), loc = 0) + + plt.show() -- Gitee From 7c1648b7355ecf7f44b285f07427d8cef6e12476 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 1 Apr 2021 12:30:41 +0800 Subject: [PATCH 40/84] 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zHSR_G{d%W8$&vqji}kzjs3D-{R!euYN5if!5|uH9g_Z=Egz4t{cg27JvPgC#yi9LJ z4u0>uZ|!h}S6ng=GNgBtOU^h0^)W>GI?q~^!L4Np%)YZbC@BRG!|`EqKl&Qs@~B=F zz`p;X0kCDeA3l6xX)A)4AqE+}0Mo=JN0nEwJJ_eUQON8?bnZUv8O1wIc9cu&v{E z!v^np-mjk2V3$O;{2iHI%k6~Rd?~B)PsskbI8^Dj-BshVCHzdtFKH|6LBM@oQetQv z@nS#Pyn{G2)*{XJn8>x9d_^cjVZ!lU$YlT=2nR0`uUe(nyY;!?#b)8pd+Tnre9pXF zelyQAFi=UZeTBi*ypa6x|LXUGLFomXE?NH z{fPW`?(HoRQ{zA!H;&y+nAEJ=f6T7Ux*dq__3KKA@m{qcE`PPG)jv9XzhgPQ!GG*J z^2YT;aV~It7<7BD1-t~_jSp#UIm19=uzq>4>e0|1+A!)*_MPU>-0zh`%*2_D*6Gw( z#BQE+>;0F+NXT`*K@WN63=S;Y!p1T Date: Thu, 1 Apr 2021 12:33:33 +0800 Subject: [PATCH 42/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-1/submission/18340246016/.keep?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/18340246016/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-1/submission/18340246016/.keep diff --git a/assignment-1/submission/18340246016/.keep b/assignment-1/submission/18340246016/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From 795a640cda650617ac6fa0beffe0607878313908 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 29 Apr 2021 15:57:02 +0800 Subject: [PATCH 43/84] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20assignment-2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-2/.keep diff --git a/assignment-2/.keep b/assignment-2/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 3fc83e9476532947c88166d34f20120fd2beb061 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 29 Apr 2021 15:58:58 +0800 Subject: [PATCH 44/84] add assignment-2/numpy_fnn.py. --- assignment-2/numpy_fnn.py | 249 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 249 insertions(+) create mode 100644 assignment-2/numpy_fnn.py diff --git a/assignment-2/numpy_fnn.py b/assignment-2/numpy_fnn.py new file mode 100644 index 0000000..7f48bcd --- /dev/null +++ b/assignment-2/numpy_fnn.py @@ -0,0 +1,249 @@ +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) + w: shape(d, d') + """ + self.memory['x'] = x + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + x = self.memory['x'] + W = self.memory['W'] + + grad_W = np.matmul(x.T,grad_y) + grad_x = np.matmul(grad_y,W.T) + #################### + + 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 # + x = self.memory['x'] + + grad_x = np.where(x > 0, 1, 0) + + grad_x = grad_x * grad_y + + #################### + + 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 # + x = self.memory['x'] + + grad_x = (1/(x + self.epsilon)) + + grad_x = grad_x*grad_y + + + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + + out = np.array(x, copy="true") + + + result_list=[] + + for m in range(len(out)): + result_list.append(sum(np.exp(out[m]))) + + for m in range(len(out)): + for n in range(len(out[0])): + out[m][n]= np.exp(out[m][n]) / result_list[m] + + self.memory['x'] = x + + #################### + + return out + + + + def backward(self, grad_y): + + """ + grad_y: same shape as x + """ + + + + #################### + # code 5 # + + x = self.memory['x'] + softx = self.forward(x) + [n, m] = x.shape + out = [] + for i in range(n): + out.append([]) + for j in range(m): + out[i].append(0) + for k in range(m): + if j == k: + out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] + else: + out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] + grad_x = np.array(out) + + + + + #################### + + return grad_x + + +class NumpyLoss: + + def __init__(self): + self.target = None + + def get_loss(self, pred, target): + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self): + return -self.target / self.target.shape[0] + + +class NumpyModel: + 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)) + + # 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() + + # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） + 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 # + #x = torch.relu(torch.matmul(x, self.W1)) + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + 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 \ No newline at end of file -- Gitee From 605dfaf5e9b9de94eee7594e1a15855caebc6a45 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Thu, 29 Apr 2021 16:00:33 +0800 Subject: [PATCH 45/84] add assignment-2/numpy_mnist.py. --- assignment-2/numpy_mnist.py | 58 +++++++++++++++++++++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 assignment-2/numpy_mnist.py diff --git a/assignment-2/numpy_mnist.py b/assignment-2/numpy_mnist.py new file mode 100644 index 0000000..833e5aa --- /dev/null +++ b/assignment-2/numpy_mnist.py @@ -0,0 +1,58 @@ +import numpy as np +from numpy_fnn import NumpyModel, NumpyLoss +from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot + +def mini_batch(dataset, batch_size=128, numpy=False): + + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + res = [] + + + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res + + +def numpy_run(): + train_dataset, test_dataset = download_mnist() + + model = NumpyModel() + numpy_loss = NumpyLoss() + 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) + loss = numpy_loss.get_loss(y_pred, y) + + model.backward(numpy_loss.backward()) + 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) + + +if __name__ == "__main__": + numpy_run() \ No newline at end of file -- Gitee From 139a2e496eebaf4051ab3676600d4228161ef71a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:01:53 +0800 Subject: [PATCH 46/84] add assignment-2. --- assignment-2/readme.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-2/readme.md diff --git a/assignment-2/readme.md b/assignment-2/readme.md new file mode 100644 index 0000000..e69de29 -- Gitee From d951453c2bba3cf53ab9c487f308ce4d5e9cb43d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:15:41 +0800 Subject: [PATCH 47/84] rename assignment-2/readme.md to assignment-2/README.md. --- assignment-2/README.md | 25 +++++++++++++++++++++++++ assignment-2/readme.md | 0 2 files changed, 25 insertions(+) create mode 100644 assignment-2/README.md delete mode 100644 assignment-2/readme.md diff --git a/assignment-2/README.md b/assignment-2/README.md new file mode 100644 index 0000000..274c633 --- /dev/null +++ b/assignment-2/README.md @@ -0,0 +1,25 @@ +**1. Mini-batch 函数的实现** + +``` +def mini_batch(dataset, batch_size=128, numpy=False): + +# 仿照batch函数分离data与label + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + + res = [] + +# 以batch_size为单位，从[0,len(data)]分割mini-batch + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res +``` diff --git a/assignment-2/readme.md b/assignment-2/readme.md deleted file mode 100644 index e69de29..0000000 -- Gitee From e13104e97a34c3d66e9602020a90f47e2803d7a9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:23:28 +0800 Subject: [PATCH 48/84] update assignment-2/README.md. --- assignment-2/README.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/assignment-2/README.md b/assignment-2/README.md index 274c633..3a44836 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -23,3 +23,10 @@ def mini_batch(dataset, batch_size=128, numpy=False): return res ``` + + **2. 模型的训练和测试** + +| Epoch | Batch_size | +| ---------------- | ------ | +| 3 | 16 | +| 10 | 128 | -- Gitee From 680ebe33e6b18eff82e227d4a98ae34f9d62212d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:26:24 +0800 Subject: [PATCH 49/84] update assignment-2/README.md. --- assignment-2/README.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/assignment-2/README.md b/assignment-2/README.md index 3a44836..0fe8ee5 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -30,3 +30,12 @@ def mini_batch(dataset, batch_size=128, numpy=False): | ---------------- | ------ | | 3 | 16 | | 10 | 128 | + + +* Epoch = 3 Batch_size=128 * + +[0] Accuracy: 0.9373 +[1] Accuracy: 0.9583 +[2] Accuracy: 0.9683 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") \ No newline at end of file -- Gitee From 41cd8450b1cf1796252abdb3261cc93934b64f61 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:26:53 +0800 Subject: [PATCH 50/84] update assignment-2/README.md. --- assignment-2/README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index 0fe8ee5..cd9c6cf 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -32,10 +32,12 @@ def mini_batch(dataset, batch_size=128, numpy=False): | 10 | 128 | -* Epoch = 3 Batch_size=128 * +* Epoch = 3 Batch_size=128 [0] Accuracy: 0.9373 + [1] Accuracy: 0.9583 + [2] Accuracy: 0.9683 ![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") \ No newline at end of file -- Gitee From 8083ec87a9e58c3fb907d62403954677fde91bbe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:27:17 +0800 Subject: [PATCH 51/84] update assignment-2/README.md. --- assignment-2/README.md | 2 -- 1 file changed, 2 deletions(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index cd9c6cf..8fc9add 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -35,9 +35,7 @@ def mini_batch(dataset, batch_size=128, numpy=False): * Epoch = 3 Batch_size=128 [0] Accuracy: 0.9373 - [1] Accuracy: 0.9583 - [2] Accuracy: 0.9683 ![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") \ No newline at end of file -- Gitee From b38ba76f0f7c32a277dc7fb7441ee5c29b115fab Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:28:14 +0800 Subject: [PATCH 52/84] update assignment-2/README.md. --- assignment-2/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index 8fc9add..d440643 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -34,8 +34,8 @@ def mini_batch(dataset, batch_size=128, numpy=False): * Epoch = 3 Batch_size=128 -[0] Accuracy: 0.9373 -[1] Accuracy: 0.9583 -[2] Accuracy: 0.9683 +
[0] Accuracy: 0.9373 +
[1] Accuracy: 0.9583 +
[2] Accuracy: 0.9683 ![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") \ No newline at end of file -- Gitee From b39c0b86cc07885bf8566476d7fcee7a30e4a086 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 10:28:32 +0800 Subject: [PATCH 53/84] update assignment-2/README.md. --- assignment-2/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index d440643..4c7da37 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -34,7 +34,7 @@ def mini_batch(dataset, batch_size=128, numpy=False): * Epoch = 3 Batch_size=128 -
[0] Accuracy: 0.9373 +[0] Accuracy: 0.9373
[1] Accuracy: 0.9583
[2] Accuracy: 0.9683 -- Gitee From 800438d57751af2b14348f3685b3222d313c0b36 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:10:58 +0800 Subject: [PATCH 54/84] update assignment-2/README.md. --- assignment-2/README.md | 43 +++++++++++++++++++++++++++++++++++++++++- 1 file changed, 42 insertions(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index 4c7da37..b95f42e 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -38,4 +38,45 @@ def mini_batch(dataset, batch_size=128, numpy=False):
[1] Accuracy: 0.9583
[2] Accuracy: 0.9683 -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") \ No newline at end of file +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") + + + +* Epoch = 3 Batch_size=16 + +[0] Accuracy: 0.9640 +
[1] Accuracy: 0.9676 +
[2] Accuracy: 0.9707 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/103502_131ca59f_8823823.png "3-16.png") + +* Epoch = 10 Batch_size=16 + +[0] Accuracy: 0.9602 +
[1] Accuracy: 0.9657 +
[2] Accuracy: 0.9741 +
[3] Accuracy: 0.9747 +
[4] Accuracy: 0.9701 +
[5] Accuracy: 0.9731 +
[6] Accuracy: 0.9760 +
[7] Accuracy: 0.9763 +
[8] Accuracy: 0.9760 +
[9] Accuracy: 0.9780 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/105531_82cafce0_8823823.png "10-16.png") + + +* Epoch = 10 Batch_size=128 + +[0] Accuracy: 0.9389 +
[1] Accuracy: 0.9585 +
[2] Accuracy: 0.9679 +
[3] Accuracy: 0.9706 +
[4] Accuracy: 0.9746 +
[5] Accuracy: 0.9760 +
[6] Accuracy: 0.9769 +
[7] Accuracy: 0.9777 +
[8] Accuracy: 0.9781 +
[9] Accuracy: 0.9781 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") \ No newline at end of file -- Gitee From 54cf0081c52d2e22bff8236f8d6b53dca668aeb1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:34:14 +0800 Subject: [PATCH 55/84] update assignment-2/README.md. --- assignment-2/README.md | 59 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 59 insertions(+) diff --git a/assignment-2/README.md b/assignment-2/README.md index b95f42e..6d53862 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -26,6 +26,65 @@ def mini_batch(dataset, batch_size=128, numpy=False): **2. 模型的训练和测试** +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/113123_f204953a_8823823.png "processon.png") + +``` + # 前向传播过程 + def forward(self, x): + x = x.reshape(-1, 28 * 28) + + #################### + # code 6 # + + #x = torch.relu(torch.matmul(x, self.W1)) + # 模仿torch的relu(Matmul.(x,w1))操作，下同 + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + # 反向传播过程 + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + pass +``` + + + + + | Epoch | Batch_size | | ---------------- | ------ | | 3 | 16 | -- Gitee From d370041d49edc2d1cdc3cbf002d56681800b4723 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:35:12 +0800 Subject: [PATCH 56/84] update assignment-2/README.md. --- assignment-2/README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index 6d53862..4fdfff2 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -138,4 +138,8 @@ def mini_batch(dataset, batch_size=128, numpy=False):
[8] Accuracy: 0.9781
[9] Accuracy: 0.9781 -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") \ No newline at end of file +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") + + + +*探究发现* -- Gitee From 8fe4b7b70e26b55dc69d2052324383855689605c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:38:53 +0800 Subject: [PATCH 57/84] update assignment-2/README.md. --- assignment-2/README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/assignment-2/README.md b/assignment-2/README.md index 4fdfff2..d1d1917 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -143,3 +143,5 @@ def mini_batch(dataset, batch_size=128, numpy=False): *探究发现* +1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 +2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 \ No newline at end of file -- Gitee From 5240526a3b001b4f80dbf9fe573480a6f4e40e76 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:53:48 +0800 Subject: [PATCH 58/84] update assignment-2/README.md. --- assignment-2/README.md | 34 +++++++++++++++++++++++++++++++++- 1 file changed, 33 insertions(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index d1d1917..d5f6d85 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -144,4 +144,36 @@ def mini_batch(dataset, batch_size=128, numpy=False): *探究发现* 1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 -2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 \ No newline at end of file +2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 + + + **3.Momentum 优化函数下的对比试验** + + +``` + # 利用momentum优化下的optimize函数 + def optimize(self, learning_rate): + + # 初始化V值 + v1=0 + v2=0 + v3=0 + mu=0.9 + + # momentum下的更新算法 + v1 = mu * v1 - learning_rate * self.W1_grad + self.W1 = self.W1 + v1 + + v2 = mu * v2 - learning_rate * self.W2_grad + self.W2 = self.W2 + v2 + + v3 = mu * v3 - learning_rate * self.W3_grad + self.W3 = self.W3 + v3 + + + #self.W1 -= learning_rate * self.W1_grad + # self.W2 -= learning_rate * self.W2_grad + #self.W3 -= learning_rate * self.W3_grad +``` + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") \ No newline at end of file -- Gitee From 8be1d39f9827cfc85a501ab780070051982f2fbf Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Fri, 30 Apr 2021 11:59:36 +0800 Subject: [PATCH 59/84] update assignment-2/README.md. --- assignment-2/README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/assignment-2/README.md b/assignment-2/README.md index d5f6d85..827aa9f 100644 --- a/assignment-2/README.md +++ b/assignment-2/README.md @@ -176,4 +176,8 @@ def mini_batch(dataset, batch_size=128, numpy=False): #self.W3 -= learning_rate * self.W3_grad ``` -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") \ No newline at end of file +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") + +1. 在我们的测试数据下，momentum与梯度下降模型准确率差异不大 +2. momentum模型主要用来解决全局最优与局部最优之间的差异，但在本测试集下不存在全局与局部的差异 +3. 理论上来说，当 momentum 动量越大时，其转换为势能的能量也就越大，就越有可能摆脱局部凹域的束缚，进入全局凹域 \ No newline at end of file -- Gitee From 4cb244d6c1341f69f47a7e0dc2ab86ef2640174b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:17:46 +0800 Subject: [PATCH 60/84] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20submission?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-2/submission/.keep diff --git a/assignment-2/submission/.keep b/assignment-2/submission/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From f0366413984247ee36e0c7df3f78f3ac11b98ffb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:19:16 +0800 Subject: [PATCH 61/84] add assignment-2/submission/README.md. --- assignment-2/submission/README.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-2/submission/README.md diff --git a/assignment-2/submission/README.md b/assignment-2/submission/README.md new file mode 100644 index 0000000..e69de29 -- Gitee From 2ade6e8912a269748871af147816a198e279ea27 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:19:46 +0800 Subject: [PATCH 62/84] update assignment-2/submission/README.md. --- assignment-2/submission/README.md | 183 ++++++++++++++++++++++++++++++ 1 file changed, 183 insertions(+) diff --git a/assignment-2/submission/README.md b/assignment-2/submission/README.md index e69de29..827aa9f 100644 --- a/assignment-2/submission/README.md +++ b/assignment-2/submission/README.md @@ -0,0 +1,183 @@ +**1. Mini-batch 函数的实现** + +``` +def mini_batch(dataset, batch_size=128, numpy=False): + +# 仿照batch函数分离data与label + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + + res = [] + +# 以batch_size为单位，从[0,len(data)]分割mini-batch + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res +``` + + **2. 模型的训练和测试** + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/113123_f204953a_8823823.png "processon.png") + +``` + # 前向传播过程 + def forward(self, x): + x = x.reshape(-1, 28 * 28) + + #################### + # code 6 # + + #x = torch.relu(torch.matmul(x, self.W1)) + # 模仿torch的relu(Matmul.(x,w1))操作，下同 + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + # 反向传播过程 + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + pass +``` + + + + + +| Epoch | Batch_size | +| ---------------- | ------ | +| 3 | 16 | +| 10 | 128 | + + +* Epoch = 3 Batch_size=128 + +[0] Accuracy: 0.9373 +
[1] Accuracy: 0.9583 +
[2] Accuracy: 0.9683 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") + + + +* Epoch = 3 Batch_size=16 + +[0] Accuracy: 0.9640 +
[1] Accuracy: 0.9676 +
[2] Accuracy: 0.9707 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/103502_131ca59f_8823823.png "3-16.png") + +* Epoch = 10 Batch_size=16 + +[0] Accuracy: 0.9602 +
[1] Accuracy: 0.9657 +
[2] Accuracy: 0.9741 +
[3] Accuracy: 0.9747 +
[4] Accuracy: 0.9701 +
[5] Accuracy: 0.9731 +
[6] Accuracy: 0.9760 +
[7] Accuracy: 0.9763 +
[8] Accuracy: 0.9760 +
[9] Accuracy: 0.9780 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/105531_82cafce0_8823823.png "10-16.png") + + +* Epoch = 10 Batch_size=128 + +[0] Accuracy: 0.9389 +
[1] Accuracy: 0.9585 +
[2] Accuracy: 0.9679 +
[3] Accuracy: 0.9706 +
[4] Accuracy: 0.9746 +
[5] Accuracy: 0.9760 +
[6] Accuracy: 0.9769 +
[7] Accuracy: 0.9777 +
[8] Accuracy: 0.9781 +
[9] Accuracy: 0.9781 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") + + + +*探究发现* +1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 +2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 + + + **3.Momentum 优化函数下的对比试验** + + +``` + # 利用momentum优化下的optimize函数 + def optimize(self, learning_rate): + + # 初始化V值 + v1=0 + v2=0 + v3=0 + mu=0.9 + + # momentum下的更新算法 + v1 = mu * v1 - learning_rate * self.W1_grad + self.W1 = self.W1 + v1 + + v2 = mu * v2 - learning_rate * self.W2_grad + self.W2 = self.W2 + v2 + + v3 = mu * v3 - learning_rate * self.W3_grad + self.W3 = self.W3 + v3 + + + #self.W1 -= learning_rate * self.W1_grad + # self.W2 -= learning_rate * self.W2_grad + #self.W3 -= learning_rate * self.W3_grad +``` + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") + +1. 在我们的测试数据下，momentum与梯度下降模型准确率差异不大 +2. momentum模型主要用来解决全局最优与局部最优之间的差异，但在本测试集下不存在全局与局部的差异 +3. 理论上来说，当 momentum 动量越大时，其转换为势能的能量也就越大，就越有可能摆脱局部凹域的束缚，进入全局凹域 \ No newline at end of file -- Gitee From d31fadb39e915756efe8f197a7b8b2d19d217d34 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:20:31 +0800 Subject: [PATCH 63/84] add assignment-2/submission. --- .../submission/assignment-2/numpy_fnn.py | 249 ++++++++++++++++++ 1 file changed, 249 insertions(+) create mode 100644 assignment-2/submission/assignment-2/numpy_fnn.py diff --git a/assignment-2/submission/assignment-2/numpy_fnn.py b/assignment-2/submission/assignment-2/numpy_fnn.py new file mode 100644 index 0000000..7f48bcd --- /dev/null +++ b/assignment-2/submission/assignment-2/numpy_fnn.py @@ -0,0 +1,249 @@ +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) + w: shape(d, d') + """ + self.memory['x'] = x + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + x = self.memory['x'] + W = self.memory['W'] + + grad_W = np.matmul(x.T,grad_y) + grad_x = np.matmul(grad_y,W.T) + #################### + + 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 # + x = self.memory['x'] + + grad_x = np.where(x > 0, 1, 0) + + grad_x = grad_x * grad_y + + #################### + + 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 # + x = self.memory['x'] + + grad_x = (1/(x + self.epsilon)) + + grad_x = grad_x*grad_y + + + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + + out = np.array(x, copy="true") + + + result_list=[] + + for m in range(len(out)): + result_list.append(sum(np.exp(out[m]))) + + for m in range(len(out)): + for n in range(len(out[0])): + out[m][n]= np.exp(out[m][n]) / result_list[m] + + self.memory['x'] = x + + #################### + + return out + + + + def backward(self, grad_y): + + """ + grad_y: same shape as x + """ + + + + #################### + # code 5 # + + x = self.memory['x'] + softx = self.forward(x) + [n, m] = x.shape + out = [] + for i in range(n): + out.append([]) + for j in range(m): + out[i].append(0) + for k in range(m): + if j == k: + out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] + else: + out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] + grad_x = np.array(out) + + + + + #################### + + return grad_x + + +class NumpyLoss: + + def __init__(self): + self.target = None + + def get_loss(self, pred, target): + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self): + return -self.target / self.target.shape[0] + + +class NumpyModel: + 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)) + + # 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() + + # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） + 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 # + #x = torch.relu(torch.matmul(x, self.W1)) + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + 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 \ No newline at end of file -- Gitee From 6e49ac116d333d1a7927f79719dc2ae9e9aeb98e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:21:01 +0800 Subject: [PATCH 64/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/assignment-2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../submission/assignment-2/numpy_fnn.py | 249 ------------------ 1 file changed, 249 deletions(-) delete mode 100644 assignment-2/submission/assignment-2/numpy_fnn.py diff --git a/assignment-2/submission/assignment-2/numpy_fnn.py b/assignment-2/submission/assignment-2/numpy_fnn.py deleted file mode 100644 index 7f48bcd..0000000 --- a/assignment-2/submission/assignment-2/numpy_fnn.py +++ /dev/null @@ -1,249 +0,0 @@ -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) - w: shape(d, d') - """ - self.memory['x'] = x - self.memory['W'] = W - h = np.matmul(x, W) - return h - - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ - - #################### - # code 1 # - x = self.memory['x'] - W = self.memory['W'] - - grad_W = np.matmul(x.T,grad_y) - grad_x = np.matmul(grad_y,W.T) - #################### - - 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 # - x = self.memory['x'] - - grad_x = np.where(x > 0, 1, 0) - - grad_x = grad_x * grad_y - - #################### - - 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 # - x = self.memory['x'] - - grad_x = (1/(x + self.epsilon)) - - grad_x = grad_x*grad_y - - - #################### - - return grad_x - - -class Softmax(NumpyOp): - """ - softmax over last dimension - """ - - def forward(self, x): - """ - x: shape(N, c) - """ - - #################### - # code 4 # - - out = np.array(x, copy="true") - - - result_list=[] - - for m in range(len(out)): - result_list.append(sum(np.exp(out[m]))) - - for m in range(len(out)): - for n in range(len(out[0])): - out[m][n]= np.exp(out[m][n]) / result_list[m] - - self.memory['x'] = x - - #################### - - return out - - - - def backward(self, grad_y): - - """ - grad_y: same shape as x - """ - - - - #################### - # code 5 # - - x = self.memory['x'] - softx = self.forward(x) - [n, m] = x.shape - out = [] - for i in range(n): - out.append([]) - for j in range(m): - out[i].append(0) - for k in range(m): - if j == k: - out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] - else: - out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] - grad_x = np.array(out) - - - - - #################### - - return grad_x - - -class NumpyLoss: - - def __init__(self): - self.target = None - - def get_loss(self, pred, target): - self.target = target - return (-pred * target).sum(axis=1).mean() - - def backward(self): - return -self.target / self.target.shape[0] - - -class NumpyModel: - 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)) - - # 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() - - # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） - 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 # - #x = torch.relu(torch.matmul(x, self.W1)) - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - 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 \ No newline at end of file -- Gitee From 121ab91d1cd072097be024e26ac8d956b4e905a4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:21:07 +0800 Subject: [PATCH 65/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/.keep?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-2/submission/.keep diff --git a/assignment-2/submission/.keep b/assignment-2/submission/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From 8ab7d290014888a75155928cc93dbb8857f6f4a5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:21:29 +0800 Subject: [PATCH 66/84] add assignment-2/submission/numpy_fnn.py. --- assignment-2/submission/numpy_fnn.py | 249 +++++++++++++++++++++++++++ 1 file changed, 249 insertions(+) create mode 100644 assignment-2/submission/numpy_fnn.py diff --git a/assignment-2/submission/numpy_fnn.py b/assignment-2/submission/numpy_fnn.py new file mode 100644 index 0000000..7f48bcd --- /dev/null +++ b/assignment-2/submission/numpy_fnn.py @@ -0,0 +1,249 @@ +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) + w: shape(d, d') + """ + self.memory['x'] = x + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + x = self.memory['x'] + W = self.memory['W'] + + grad_W = np.matmul(x.T,grad_y) + grad_x = np.matmul(grad_y,W.T) + #################### + + 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 # + x = self.memory['x'] + + grad_x = np.where(x > 0, 1, 0) + + grad_x = grad_x * grad_y + + #################### + + 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 # + x = self.memory['x'] + + grad_x = (1/(x + self.epsilon)) + + grad_x = grad_x*grad_y + + + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + + out = np.array(x, copy="true") + + + result_list=[] + + for m in range(len(out)): + result_list.append(sum(np.exp(out[m]))) + + for m in range(len(out)): + for n in range(len(out[0])): + out[m][n]= np.exp(out[m][n]) / result_list[m] + + self.memory['x'] = x + + #################### + + return out + + + + def backward(self, grad_y): + + """ + grad_y: same shape as x + """ + + + + #################### + # code 5 # + + x = self.memory['x'] + softx = self.forward(x) + [n, m] = x.shape + out = [] + for i in range(n): + out.append([]) + for j in range(m): + out[i].append(0) + for k in range(m): + if j == k: + out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] + else: + out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] + grad_x = np.array(out) + + + + + #################### + + return grad_x + + +class NumpyLoss: + + def __init__(self): + self.target = None + + def get_loss(self, pred, target): + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self): + return -self.target / self.target.shape[0] + + +class NumpyModel: + 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)) + + # 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() + + # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） + 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 # + #x = torch.relu(torch.matmul(x, self.W1)) + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + 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 \ No newline at end of file -- Gitee From cda6edb4f818cee09a27b21c5398b560ed89dbfa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:21:56 +0800 Subject: [PATCH 67/84] add assignment-2/submission/numpy_mnist.py. --- assignment-2/submission/numpy_mnist.py | 58 ++++++++++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 assignment-2/submission/numpy_mnist.py diff --git a/assignment-2/submission/numpy_mnist.py b/assignment-2/submission/numpy_mnist.py new file mode 100644 index 0000000..833e5aa --- /dev/null +++ b/assignment-2/submission/numpy_mnist.py @@ -0,0 +1,58 @@ +import numpy as np +from numpy_fnn import NumpyModel, NumpyLoss +from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot + +def mini_batch(dataset, batch_size=128, numpy=False): + + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + res = [] + + + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res + + +def numpy_run(): + train_dataset, test_dataset = download_mnist() + + model = NumpyModel() + numpy_loss = NumpyLoss() + 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) + loss = numpy_loss.get_loss(y_pred, y) + + model.backward(numpy_loss.backward()) + 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) + + +if __name__ == "__main__": + numpy_run() \ No newline at end of file -- Gitee From d61dc27d2ca729a94196a033a62e287ac2f75326 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:22:14 +0800 Subject: [PATCH 68/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/.keep?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-2/.keep diff --git a/assignment-2/.keep b/assignment-2/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From dae7f126db9b777f53fb38fab8ecfa74a039ca8d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:22:45 +0800 Subject: [PATCH 69/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/README.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/README.md | 183 ----------------------------------------- 1 file changed, 183 deletions(-) delete mode 100644 assignment-2/README.md diff --git a/assignment-2/README.md b/assignment-2/README.md deleted file mode 100644 index 827aa9f..0000000 --- a/assignment-2/README.md +++ /dev/null @@ -1,183 +0,0 @@ -**1. Mini-batch 函数的实现** - -``` -def mini_batch(dataset, batch_size=128, numpy=False): - -# 仿照batch函数分离data与label - data = [] - label = [] - for each in dataset: - data.append(np.array(each[0])) - label.append(each[1]) - - data = np.array(data) - label = np.array(label) - - - res = [] - -# 以batch_size为单位，从[0,len(data)]分割mini-batch - for start_idx in range(0, data.shape[0], batch_size): - end_idx = min(start_idx + batch_size, len(data)) - res.append((data[start_idx:end_idx],label[start_idx:end_idx])) - - return res -``` - - **2. 模型的训练和测试** - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/113123_f204953a_8823823.png "processon.png") - -``` - # 前向传播过程 - def forward(self, x): - x = x.reshape(-1, 28 * 28) - - #################### - # code 6 # - - #x = torch.relu(torch.matmul(x, self.W1)) - # 模仿torch的relu(Matmul.(x,w1))操作，下同 - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - # 反向传播过程 - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - pass -``` - - - - - -| Epoch | Batch_size | -| ---------------- | ------ | -| 3 | 16 | -| 10 | 128 | - - -* Epoch = 3 Batch_size=128 - -[0] Accuracy: 0.9373 -
[1] Accuracy: 0.9583 -
[2] Accuracy: 0.9683 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") - - - -* Epoch = 3 Batch_size=16 - -[0] Accuracy: 0.9640 -
[1] Accuracy: 0.9676 -
[2] Accuracy: 0.9707 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/103502_131ca59f_8823823.png "3-16.png") - -* Epoch = 10 Batch_size=16 - -[0] Accuracy: 0.9602 -
[1] Accuracy: 0.9657 -
[2] Accuracy: 0.9741 -
[3] Accuracy: 0.9747 -
[4] Accuracy: 0.9701 -
[5] Accuracy: 0.9731 -
[6] Accuracy: 0.9760 -
[7] Accuracy: 0.9763 -
[8] Accuracy: 0.9760 -
[9] Accuracy: 0.9780 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/105531_82cafce0_8823823.png "10-16.png") - - -* Epoch = 10 Batch_size=128 - -[0] Accuracy: 0.9389 -
[1] Accuracy: 0.9585 -
[2] Accuracy: 0.9679 -
[3] Accuracy: 0.9706 -
[4] Accuracy: 0.9746 -
[5] Accuracy: 0.9760 -
[6] Accuracy: 0.9769 -
[7] Accuracy: 0.9777 -
[8] Accuracy: 0.9781 -
[9] Accuracy: 0.9781 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") - - - -*探究发现* -1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 -2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 - - - **3.Momentum 优化函数下的对比试验** - - -``` - # 利用momentum优化下的optimize函数 - def optimize(self, learning_rate): - - # 初始化V值 - v1=0 - v2=0 - v3=0 - mu=0.9 - - # momentum下的更新算法 - v1 = mu * v1 - learning_rate * self.W1_grad - self.W1 = self.W1 + v1 - - v2 = mu * v2 - learning_rate * self.W2_grad - self.W2 = self.W2 + v2 - - v3 = mu * v3 - learning_rate * self.W3_grad - self.W3 = self.W3 + v3 - - - #self.W1 -= learning_rate * self.W1_grad - # self.W2 -= learning_rate * self.W2_grad - #self.W3 -= learning_rate * self.W3_grad -``` - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") - -1. 在我们的测试数据下，momentum与梯度下降模型准确率差异不大 -2. momentum模型主要用来解决全局最优与局部最优之间的差异，但在本测试集下不存在全局与局部的差异 -3. 理论上来说，当 momentum 动量越大时，其转换为势能的能量也就越大，就越有可能摆脱局部凹域的束缚，进入全局凹域 \ No newline at end of file -- Gitee From 9cb49c85bc07a789ad43b8a390cec684f2383dd6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:22:53 +0800 Subject: [PATCH 70/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/numpy=5Ffnn.py?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/numpy_fnn.py | 249 -------------------------------------- 1 file changed, 249 deletions(-) delete mode 100644 assignment-2/numpy_fnn.py diff --git a/assignment-2/numpy_fnn.py b/assignment-2/numpy_fnn.py deleted file mode 100644 index 7f48bcd..0000000 --- a/assignment-2/numpy_fnn.py +++ /dev/null @@ -1,249 +0,0 @@ -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) - w: shape(d, d') - """ - self.memory['x'] = x - self.memory['W'] = W - h = np.matmul(x, W) - return h - - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ - - #################### - # code 1 # - x = self.memory['x'] - W = self.memory['W'] - - grad_W = np.matmul(x.T,grad_y) - grad_x = np.matmul(grad_y,W.T) - #################### - - 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 # - x = self.memory['x'] - - grad_x = np.where(x > 0, 1, 0) - - grad_x = grad_x * grad_y - - #################### - - 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 # - x = self.memory['x'] - - grad_x = (1/(x + self.epsilon)) - - grad_x = grad_x*grad_y - - - #################### - - return grad_x - - -class Softmax(NumpyOp): - """ - softmax over last dimension - """ - - def forward(self, x): - """ - x: shape(N, c) - """ - - #################### - # code 4 # - - out = np.array(x, copy="true") - - - result_list=[] - - for m in range(len(out)): - result_list.append(sum(np.exp(out[m]))) - - for m in range(len(out)): - for n in range(len(out[0])): - out[m][n]= np.exp(out[m][n]) / result_list[m] - - self.memory['x'] = x - - #################### - - return out - - - - def backward(self, grad_y): - - """ - grad_y: same shape as x - """ - - - - #################### - # code 5 # - - x = self.memory['x'] - softx = self.forward(x) - [n, m] = x.shape - out = [] - for i in range(n): - out.append([]) - for j in range(m): - out[i].append(0) - for k in range(m): - if j == k: - out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] - else: - out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] - grad_x = np.array(out) - - - - - #################### - - return grad_x - - -class NumpyLoss: - - def __init__(self): - self.target = None - - def get_loss(self, pred, target): - self.target = target - return (-pred * target).sum(axis=1).mean() - - def backward(self): - return -self.target / self.target.shape[0] - - -class NumpyModel: - 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)) - - # 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() - - # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） - 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 # - #x = torch.relu(torch.matmul(x, self.W1)) - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - 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 \ No newline at end of file -- Gitee From acbf2200229d4e565447acbf88b4fd69ccd3cea7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:23:07 +0800 Subject: [PATCH 71/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/numpy=5Fmnist.py?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/numpy_mnist.py | 58 ------------------------------------- 1 file changed, 58 deletions(-) delete mode 100644 assignment-2/numpy_mnist.py diff --git a/assignment-2/numpy_mnist.py b/assignment-2/numpy_mnist.py deleted file mode 100644 index 833e5aa..0000000 --- a/assignment-2/numpy_mnist.py +++ /dev/null @@ -1,58 +0,0 @@ -import numpy as np -from numpy_fnn import NumpyModel, NumpyLoss -from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot - -def mini_batch(dataset, batch_size=128, numpy=False): - - data = [] - label = [] - for each in dataset: - data.append(np.array(each[0])) - label.append(each[1]) - - data = np.array(data) - label = np.array(label) - - res = [] - - - for start_idx in range(0, data.shape[0], batch_size): - end_idx = min(start_idx + batch_size, len(data)) - res.append((data[start_idx:end_idx],label[start_idx:end_idx])) - - return res - - -def numpy_run(): - train_dataset, test_dataset = download_mnist() - - model = NumpyModel() - numpy_loss = NumpyLoss() - 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) - loss = numpy_loss.get_loss(y_pred, y) - - model.backward(numpy_loss.backward()) - 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) - - -if __name__ == "__main__": - numpy_run() \ No newline at end of file -- Gitee From 4c08c606bcf6b4920e85efc4207735ffdb22f00e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:23:18 +0800 Subject: [PATCH 72/84] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2018340246016?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/18340246016/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-2/submission/18340246016/.keep diff --git a/assignment-2/submission/18340246016/.keep b/assignment-2/submission/18340246016/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From eba8f7486ce326563afca56f95914c6c4385490f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:25:00 +0800 Subject: [PATCH 73/84] add assignment-2/submission/18340246016/README.md. --- assignment-2/submission/18340246016/README.md | 183 ++++++++++++++++++ 1 file changed, 183 insertions(+) create mode 100644 assignment-2/submission/18340246016/README.md diff --git a/assignment-2/submission/18340246016/README.md b/assignment-2/submission/18340246016/README.md new file mode 100644 index 0000000..be11b1d --- /dev/null +++ b/assignment-2/submission/18340246016/README.md @@ -0,0 +1,183 @@ +**1. Mini-batch 函数的实现** + +``` +def mini_batch(dataset, batch_size=128, numpy=False): + +# 仿照batch函数分离data与label + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + + res = [] + +# 以batch_size为单位，从[0,len(data)]分割mini-batch + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res +``` + + **2. 模型的训练和测试** + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/113123_f204953a_8823823.png "processon.png") + +``` + # 前向传播过程 + def forward(self, x): + x = x.reshape(-1, 28 * 28) + + #################### + # code 6 # + + #x = torch.relu(torch.matmul(x, self.W1)) + # 模仿torch的relu(Matmul.(x,w1))操作，下同 + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + # 反向传播过程 + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + pass +``` + + + + + +| Epoch | Batch_size | +| ---------------- | ------ | +| 3 | 16 | +| 10 | 128 | + + +* Epoch = 3 Batch_size=128 + +[0] Accuracy: 0.9373 +
[1] Accuracy: 0.9583 +
[2] Accuracy: 0.9683 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") + + + +* Epoch = 3 Batch_size=16 + +[0] Accuracy: 0.9640 +
[1] Accuracy: 0.9676 +
[2] Accuracy: 0.9707 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/103502_131ca59f_8823823.png "3-16.png") + +* Epoch = 10 Batch_size=16 + +[0] Accuracy: 0.9602 +
[1] Accuracy: 0.9657 +
[2] Accuracy: 0.9741 +
[3] Accuracy: 0.9747 +
[4] Accuracy: 0.9701 +
[5] Accuracy: 0.9731 +
[6] Accuracy: 0.9760 +
[7] Accuracy: 0.9763 +
[8] Accuracy: 0.9760 +
[9] Accuracy: 0.9780 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/105531_82cafce0_8823823.png "10-16.png") + + +* Epoch = 10 Batch_size=128 + +[0] Accuracy: 0.9389 +
[1] Accuracy: 0.9585 +
[2] Accuracy: 0.9679 +
[3] Accuracy: 0.9706 +
[4] Accuracy: 0.9746 +
[5] Accuracy: 0.9760 +
[6] Accuracy: 0.9769 +
[7] Accuracy: 0.9777 +
[8] Accuracy: 0.9781 +
[9] Accuracy: 0.9781 + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") + + + +*探究发现* +1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 +2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 + + + **3.Momentum 优化函数下的对比试验** + + +``` + # 利用momentum优化下的optimize函数 + def optimize(self, learning_rate): + + # 初始化V值 + v1=0 + v2=0 + v3=0 + mu=0.9 + + # momentum下的更新算法 + v1 = mu * v1 - learning_rate * self.W1_grad + self.W1 = self.W1 + v1 + + v2 = mu * v2 - learning_rate * self.W2_grad + self.W2 = self.W2 + v2 + + v3 = mu * v3 - learning_rate * self.W3_grad + self.W3 = self.W3 + v3 + + + #self.W1 -= learning_rate * self.W1_grad + # self.W2 -= learning_rate * self.W2_grad + #self.W3 -= learning_rate * self.W3_grad +``` + +![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") + +1. 在我们的测试数据下，momentum与梯度下降模型准确率差异不大 +2. momentum模型主要用来解决全局最优与局部最优之间的差异，但在本测试集下不存在全局与局部的差异 +3. 理论上来说，当 momentum 动量越大时，其转换为势能的能量也就越大，就越有可能摆脱局部凹域的束缚，进入全局凹域 \ No newline at end of file -- Gitee From b302284b2cf17d7a85c049e032b02d3da57dad0e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:25:30 +0800 Subject: [PATCH 74/84] add assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py. --- .../assignment-2/submission/numpy_fnn.py | 249 ++++++++++++++++++ 1 file changed, 249 insertions(+) create mode 100644 assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py diff --git a/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py b/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py new file mode 100644 index 0000000..7f48bcd --- /dev/null +++ b/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py @@ -0,0 +1,249 @@ +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) + w: shape(d, d') + """ + self.memory['x'] = x + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + x = self.memory['x'] + W = self.memory['W'] + + grad_W = np.matmul(x.T,grad_y) + grad_x = np.matmul(grad_y,W.T) + #################### + + 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 # + x = self.memory['x'] + + grad_x = np.where(x > 0, 1, 0) + + grad_x = grad_x * grad_y + + #################### + + 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 # + x = self.memory['x'] + + grad_x = (1/(x + self.epsilon)) + + grad_x = grad_x*grad_y + + + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + + out = np.array(x, copy="true") + + + result_list=[] + + for m in range(len(out)): + result_list.append(sum(np.exp(out[m]))) + + for m in range(len(out)): + for n in range(len(out[0])): + out[m][n]= np.exp(out[m][n]) / result_list[m] + + self.memory['x'] = x + + #################### + + return out + + + + def backward(self, grad_y): + + """ + grad_y: same shape as x + """ + + + + #################### + # code 5 # + + x = self.memory['x'] + softx = self.forward(x) + [n, m] = x.shape + out = [] + for i in range(n): + out.append([]) + for j in range(m): + out[i].append(0) + for k in range(m): + if j == k: + out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] + else: + out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] + grad_x = np.array(out) + + + + + #################### + + return grad_x + + +class NumpyLoss: + + def __init__(self): + self.target = None + + def get_loss(self, pred, target): + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self): + return -self.target / self.target.shape[0] + + +class NumpyModel: + 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)) + + # 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() + + # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） + 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 # + #x = torch.relu(torch.matmul(x, self.W1)) + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + 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 \ No newline at end of file -- Gitee From 8a602e23c34830acabd2c7d4a661dbb143a7cf2d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:25:55 +0800 Subject: [PATCH 75/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/18340246016/assignment-2/submission?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../assignment-2/submission/numpy_fnn.py | 249 ------------------ 1 file changed, 249 deletions(-) delete mode 100644 assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py diff --git a/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py b/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py deleted file mode 100644 index 7f48bcd..0000000 --- a/assignment-2/submission/18340246016/assignment-2/submission/numpy_fnn.py +++ /dev/null @@ -1,249 +0,0 @@ -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) - w: shape(d, d') - """ - self.memory['x'] = x - self.memory['W'] = W - h = np.matmul(x, W) - return h - - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ - - #################### - # code 1 # - x = self.memory['x'] - W = self.memory['W'] - - grad_W = np.matmul(x.T,grad_y) - grad_x = np.matmul(grad_y,W.T) - #################### - - 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 # - x = self.memory['x'] - - grad_x = np.where(x > 0, 1, 0) - - grad_x = grad_x * grad_y - - #################### - - 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 # - x = self.memory['x'] - - grad_x = (1/(x + self.epsilon)) - - grad_x = grad_x*grad_y - - - #################### - - return grad_x - - -class Softmax(NumpyOp): - """ - softmax over last dimension - """ - - def forward(self, x): - """ - x: shape(N, c) - """ - - #################### - # code 4 # - - out = np.array(x, copy="true") - - - result_list=[] - - for m in range(len(out)): - result_list.append(sum(np.exp(out[m]))) - - for m in range(len(out)): - for n in range(len(out[0])): - out[m][n]= np.exp(out[m][n]) / result_list[m] - - self.memory['x'] = x - - #################### - - return out - - - - def backward(self, grad_y): - - """ - grad_y: same shape as x - """ - - - - #################### - # code 5 # - - x = self.memory['x'] - softx = self.forward(x) - [n, m] = x.shape - out = [] - for i in range(n): - out.append([]) - for j in range(m): - out[i].append(0) - for k in range(m): - if j == k: - out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] - else: - out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] - grad_x = np.array(out) - - - - - #################### - - return grad_x - - -class NumpyLoss: - - def __init__(self): - self.target = None - - def get_loss(self, pred, target): - self.target = target - return (-pred * target).sum(axis=1).mean() - - def backward(self): - return -self.target / self.target.shape[0] - - -class NumpyModel: - 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)) - - # 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() - - # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） - 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 # - #x = torch.relu(torch.matmul(x, self.W1)) - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - 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 \ No newline at end of file -- Gitee From 126872f63e45f7b5762f6902d8b9cd3496daaef9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:26:01 +0800 Subject: [PATCH 76/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/18340246016/.keep?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/18340246016/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-2/submission/18340246016/.keep diff --git a/assignment-2/submission/18340246016/.keep b/assignment-2/submission/18340246016/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From 264545a4b530857590fb9539428b57c50b6949a5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:26:18 +0800 Subject: [PATCH 77/84] add assignment-2/submission/18340246016/numpy_mnist.py. --- .../submission/18340246016/numpy_mnist.py | 58 +++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 assignment-2/submission/18340246016/numpy_mnist.py diff --git a/assignment-2/submission/18340246016/numpy_mnist.py b/assignment-2/submission/18340246016/numpy_mnist.py new file mode 100644 index 0000000..833e5aa --- /dev/null +++ b/assignment-2/submission/18340246016/numpy_mnist.py @@ -0,0 +1,58 @@ +import numpy as np +from numpy_fnn import NumpyModel, NumpyLoss +from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot + +def mini_batch(dataset, batch_size=128, numpy=False): + + data = [] + label = [] + for each in dataset: + data.append(np.array(each[0])) + label.append(each[1]) + + data = np.array(data) + label = np.array(label) + + res = [] + + + for start_idx in range(0, data.shape[0], batch_size): + end_idx = min(start_idx + batch_size, len(data)) + res.append((data[start_idx:end_idx],label[start_idx:end_idx])) + + return res + + +def numpy_run(): + train_dataset, test_dataset = download_mnist() + + model = NumpyModel() + numpy_loss = NumpyLoss() + 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) + loss = numpy_loss.get_loss(y_pred, y) + + model.backward(numpy_loss.backward()) + 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) + + +if __name__ == "__main__": + numpy_run() \ No newline at end of file -- Gitee From 0dbb52ed31d3b95a5918474aad2d9e3105bd1743 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:26:44 +0800 Subject: [PATCH 78/84] add assignment-2/submission/18340246016/numpy_fnn.py. --- .../submission/18340246016/numpy_fnn.py | 249 ++++++++++++++++++ 1 file changed, 249 insertions(+) create mode 100644 assignment-2/submission/18340246016/numpy_fnn.py diff --git a/assignment-2/submission/18340246016/numpy_fnn.py b/assignment-2/submission/18340246016/numpy_fnn.py new file mode 100644 index 0000000..7f48bcd --- /dev/null +++ b/assignment-2/submission/18340246016/numpy_fnn.py @@ -0,0 +1,249 @@ +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) + w: shape(d, d') + """ + self.memory['x'] = x + self.memory['W'] = W + h = np.matmul(x, W) + return h + + def backward(self, grad_y): + """ + grad_y: shape(N, d') + """ + + #################### + # code 1 # + x = self.memory['x'] + W = self.memory['W'] + + grad_W = np.matmul(x.T,grad_y) + grad_x = np.matmul(grad_y,W.T) + #################### + + 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 # + x = self.memory['x'] + + grad_x = np.where(x > 0, 1, 0) + + grad_x = grad_x * grad_y + + #################### + + 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 # + x = self.memory['x'] + + grad_x = (1/(x + self.epsilon)) + + grad_x = grad_x*grad_y + + + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + + out = np.array(x, copy="true") + + + result_list=[] + + for m in range(len(out)): + result_list.append(sum(np.exp(out[m]))) + + for m in range(len(out)): + for n in range(len(out[0])): + out[m][n]= np.exp(out[m][n]) / result_list[m] + + self.memory['x'] = x + + #################### + + return out + + + + def backward(self, grad_y): + + """ + grad_y: same shape as x + """ + + + + #################### + # code 5 # + + x = self.memory['x'] + softx = self.forward(x) + [n, m] = x.shape + out = [] + for i in range(n): + out.append([]) + for j in range(m): + out[i].append(0) + for k in range(m): + if j == k: + out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] + else: + out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] + grad_x = np.array(out) + + + + + #################### + + return grad_x + + +class NumpyLoss: + + def __init__(self): + self.target = None + + def get_loss(self, pred, target): + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self): + return -self.target / self.target.shape[0] + + +class NumpyModel: + 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)) + + # 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() + + # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） + 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 # + #x = torch.relu(torch.matmul(x, self.W1)) + x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) + + #x = torch.relu(torch.matmul(x, self.W2)) + x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) + + #x = torch.matmul(x, self.W3) + #x = torch.softmax(x, 1) + x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) + + #x = torch.log(x) + x = self.log.forward(x) + + #################### + + return x + + def backward(self, y): + + #################### + # code 7 # + + self.log_grad = self.log.backward(y) + + self.softmax_grad = self.softmax.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) + + + + #################### + + 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 \ No newline at end of file -- Gitee From ef4e29e453691647681aa3d4077982661733d508 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:26:55 +0800 Subject: [PATCH 79/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/README.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/README.md | 183 ------------------------------ 1 file changed, 183 deletions(-) delete mode 100644 assignment-2/submission/README.md diff --git a/assignment-2/submission/README.md b/assignment-2/submission/README.md deleted file mode 100644 index 827aa9f..0000000 --- a/assignment-2/submission/README.md +++ /dev/null @@ -1,183 +0,0 @@ -**1. Mini-batch 函数的实现** - -``` -def mini_batch(dataset, batch_size=128, numpy=False): - -# 仿照batch函数分离data与label - data = [] - label = [] - for each in dataset: - data.append(np.array(each[0])) - label.append(each[1]) - - data = np.array(data) - label = np.array(label) - - - res = [] - -# 以batch_size为单位，从[0,len(data)]分割mini-batch - for start_idx in range(0, data.shape[0], batch_size): - end_idx = min(start_idx + batch_size, len(data)) - res.append((data[start_idx:end_idx],label[start_idx:end_idx])) - - return res -``` - - **2. 模型的训练和测试** - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/113123_f204953a_8823823.png "processon.png") - -``` - # 前向传播过程 - def forward(self, x): - x = x.reshape(-1, 28 * 28) - - #################### - # code 6 # - - #x = torch.relu(torch.matmul(x, self.W1)) - # 模仿torch的relu(Matmul.(x,w1))操作，下同 - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - # 反向传播过程 - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - pass -``` - - - - - -| Epoch | Batch_size | -| ---------------- | ------ | -| 3 | 16 | -| 10 | 128 | - - -* Epoch = 3 Batch_size=128 - -[0] Accuracy: 0.9373 -
[1] Accuracy: 0.9583 -
[2] Accuracy: 0.9683 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/102618_2f8a1661_8823823.png "3-128.png") - - - -* Epoch = 3 Batch_size=16 - -[0] Accuracy: 0.9640 -
[1] Accuracy: 0.9676 -
[2] Accuracy: 0.9707 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/103502_131ca59f_8823823.png "3-16.png") - -* Epoch = 10 Batch_size=16 - -[0] Accuracy: 0.9602 -
[1] Accuracy: 0.9657 -
[2] Accuracy: 0.9741 -
[3] Accuracy: 0.9747 -
[4] Accuracy: 0.9701 -
[5] Accuracy: 0.9731 -
[6] Accuracy: 0.9760 -
[7] Accuracy: 0.9763 -
[8] Accuracy: 0.9760 -
[9] Accuracy: 0.9780 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/105531_82cafce0_8823823.png "10-16.png") - - -* Epoch = 10 Batch_size=128 - -[0] Accuracy: 0.9389 -
[1] Accuracy: 0.9585 -
[2] Accuracy: 0.9679 -
[3] Accuracy: 0.9706 -
[4] Accuracy: 0.9746 -
[5] Accuracy: 0.9760 -
[6] Accuracy: 0.9769 -
[7] Accuracy: 0.9777 -
[8] Accuracy: 0.9781 -
[9] Accuracy: 0.9781 - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/111052_ddb4ecda_8823823.png "10-128.png") - - - -*探究发现* -1. mini-batch size太小的情况下，模型的波动率非常高，并不是对batch_size越细分模型的准确率就越高 -2. 从epoch的数量上来看，epoch的数量与模型accuracy有正相关性 - - - **3.Momentum 优化函数下的对比试验** - - -``` - # 利用momentum优化下的optimize函数 - def optimize(self, learning_rate): - - # 初始化V值 - v1=0 - v2=0 - v3=0 - mu=0.9 - - # momentum下的更新算法 - v1 = mu * v1 - learning_rate * self.W1_grad - self.W1 = self.W1 + v1 - - v2 = mu * v2 - learning_rate * self.W2_grad - self.W2 = self.W2 + v2 - - v3 = mu * v3 - learning_rate * self.W3_grad - self.W3 = self.W3 + v3 - - - #self.W1 -= learning_rate * self.W1_grad - # self.W2 -= learning_rate * self.W2_grad - #self.W3 -= learning_rate * self.W3_grad -``` - -![输入图片说明](https://images.gitee.com/uploads/images/2021/0430/115301_1fa39f2b_8823823.png "屏幕截图.png") - -1. 在我们的测试数据下，momentum与梯度下降模型准确率差异不大 -2. momentum模型主要用来解决全局最优与局部最优之间的差异，但在本测试集下不存在全局与局部的差异 -3. 理论上来说，当 momentum 动量越大时，其转换为势能的能量也就越大，就越有可能摆脱局部凹域的束缚，进入全局凹域 \ No newline at end of file -- Gitee From 7c63abea7400a9d3414b647fec383c3acc354f59 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:27:01 +0800 Subject: [PATCH 80/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/numpy=5Ffnn.py?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/numpy_fnn.py | 249 --------------------------- 1 file changed, 249 deletions(-) delete mode 100644 assignment-2/submission/numpy_fnn.py diff --git a/assignment-2/submission/numpy_fnn.py b/assignment-2/submission/numpy_fnn.py deleted file mode 100644 index 7f48bcd..0000000 --- a/assignment-2/submission/numpy_fnn.py +++ /dev/null @@ -1,249 +0,0 @@ -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) - w: shape(d, d') - """ - self.memory['x'] = x - self.memory['W'] = W - h = np.matmul(x, W) - return h - - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ - - #################### - # code 1 # - x = self.memory['x'] - W = self.memory['W'] - - grad_W = np.matmul(x.T,grad_y) - grad_x = np.matmul(grad_y,W.T) - #################### - - 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 # - x = self.memory['x'] - - grad_x = np.where(x > 0, 1, 0) - - grad_x = grad_x * grad_y - - #################### - - 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 # - x = self.memory['x'] - - grad_x = (1/(x + self.epsilon)) - - grad_x = grad_x*grad_y - - - #################### - - return grad_x - - -class Softmax(NumpyOp): - """ - softmax over last dimension - """ - - def forward(self, x): - """ - x: shape(N, c) - """ - - #################### - # code 4 # - - out = np.array(x, copy="true") - - - result_list=[] - - for m in range(len(out)): - result_list.append(sum(np.exp(out[m]))) - - for m in range(len(out)): - for n in range(len(out[0])): - out[m][n]= np.exp(out[m][n]) / result_list[m] - - self.memory['x'] = x - - #################### - - return out - - - - def backward(self, grad_y): - - """ - grad_y: same shape as x - """ - - - - #################### - # code 5 # - - x = self.memory['x'] - softx = self.forward(x) - [n, m] = x.shape - out = [] - for i in range(n): - out.append([]) - for j in range(m): - out[i].append(0) - for k in range(m): - if j == k: - out[i][j] += (1 - softx[i][k]) * softx[i][k] * grad_y[i][k] - else: - out[i][j] += -softx[i][j] * softx[i][k] * grad_y[i][k] - grad_x = np.array(out) - - - - - #################### - - return grad_x - - -class NumpyLoss: - - def __init__(self): - self.target = None - - def get_loss(self, pred, target): - self.target = target - return (-pred * target).sum(axis=1).mean() - - def backward(self): - return -self.target / self.target.shape[0] - - -class NumpyModel: - 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)) - - # 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() - - # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导） - 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 # - #x = torch.relu(torch.matmul(x, self.W1)) - x = self.relu_1.forward(self.matmul_1.forward(x,self.W1)) - - #x = torch.relu(torch.matmul(x, self.W2)) - x = self.relu_2.forward(self.matmul_2.forward(x,self.W2)) - - #x = torch.matmul(x, self.W3) - #x = torch.softmax(x, 1) - x = self.softmax.forward(self.matmul_3.forward(x,self.W3)) - - #x = torch.log(x) - x = self.log.forward(x) - - #################### - - return x - - def backward(self, y): - - #################### - # code 7 # - - self.log_grad = self.log.backward(y) - - self.softmax_grad = self.softmax.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) - - - - #################### - - 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 \ No newline at end of file -- Gitee From 2bb30db8c563d399d70196dfa9484349a30248f6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:27:07 +0800 Subject: [PATCH 81/84] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-2/submission/numpy=5Fmnist.py?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/numpy_mnist.py | 58 -------------------------- 1 file changed, 58 deletions(-) delete mode 100644 assignment-2/submission/numpy_mnist.py diff --git a/assignment-2/submission/numpy_mnist.py b/assignment-2/submission/numpy_mnist.py deleted file mode 100644 index 833e5aa..0000000 --- a/assignment-2/submission/numpy_mnist.py +++ /dev/null @@ -1,58 +0,0 @@ -import numpy as np -from numpy_fnn import NumpyModel, NumpyLoss -from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot - -def mini_batch(dataset, batch_size=128, numpy=False): - - data = [] - label = [] - for each in dataset: - data.append(np.array(each[0])) - label.append(each[1]) - - data = np.array(data) - label = np.array(label) - - res = [] - - - for start_idx in range(0, data.shape[0], batch_size): - end_idx = min(start_idx + batch_size, len(data)) - res.append((data[start_idx:end_idx],label[start_idx:end_idx])) - - return res - - -def numpy_run(): - train_dataset, test_dataset = download_mnist() - - model = NumpyModel() - numpy_loss = NumpyLoss() - 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) - loss = numpy_loss.get_loss(y_pred, y) - - model.backward(numpy_loss.backward()) - 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) - - -if __name__ == "__main__": - numpy_run() \ No newline at end of file -- Gitee From 4cc5d1548a24d00aaae7731be6d7dbada0bdbe56 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E4=B8=81=E5=87=AF=E4=B9=90?= <8823823+y3sm1r@user.noreply.gitee.com> Date: Sun, 2 May 2021 09:27:37 +0800 Subject: [PATCH 82/84] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20img?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-2/submission/18340246016/img/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 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--git a/assignment-2/submission/18340246016/img/.keep b/assignment-2/submission/18340246016/img/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee