From 8b5da448fe36217c70bb659a390db8227cd68203 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 18:35:25 +0800 Subject: [PATCH 01/42] add PCA code --- PCA/PCA.py | 111 ++++++++++++++++++++++++++++++++++++++++++-------- PCA/data1.mat | Bin 0 -> 995 bytes 2 files changed, 94 insertions(+), 17 deletions(-) create mode 100644 PCA/data1.mat diff --git a/PCA/PCA.py b/PCA/PCA.py index 35aa82d..0f01f70 100644 --- a/PCA/PCA.py +++ b/PCA/PCA.py @@ -4,37 +4,76 @@ import numpy as np from matplotlib import pyplot as plt from scipy import io as spio +from sklearn.decomposition import pca ''' -主成分分析运行方法 +主成分分析_2维数据降维1维演示函数 ''' -def PCA(): +def PCA_2D(): data_2d = spio.loadmat("data.mat") X = data_2d['X'] m = X.shape[0] - plt = plot_data_2d(X) # 显示二维的数据 + plt = plot_data_2d(X,'bo') # 显示二维的数据 plt.show() X_copy = X.copy() X_norm,mu,sigma = featureNormalize(X_copy) # 归一化数据 - plot_data_2d(X_norm) # 显示归一化后的数据 + #plot_data_2d(X_norm) # 显示归一化后的数据 + #plt.show() - Sigma = np.dot(np.transpose(X_norm),X_norm)/m - U,S,V = np.linalg.svd(Sigma) + Sigma = np.dot(np.transpose(X_norm),X_norm)/m # 求Sigma + U,S,V = np.linalg.svd(Sigma) # 求Sigma的奇异值分解 - plt = plot_data_2d(X_norm) - plt.plot(mu.reshape(-1,1),mu.reshape(-1,1)+S[0]*(U[:,0].reshape(-1,1)),'k-') + plt = plot_data_2d(X,'bo') # 显示原本数据 + drawline(plt, mu, mu+S[0]*(U[:,0]), 'r-') # 线,为投影的方向 + + plt.axis('square') plt.show() - K = 1 - Z = projectData(X_norm,U,K) - print Z[0] - + K = 1 # 定义降维多少维(本来是2维的,这里降维1维) + '''投影之后数据(降维之后)''' + Z = projectData(X_norm,U,K) # 投影 + '''恢复数据''' + X_rec = recoverData(Z,U,K) # 恢复 + '''作图-----原数据与恢复的数据''' + plt = plot_data_2d(X_norm,'bo') + plot_data_2d(X_rec,'ro') + for i in range(X_norm.shape[0]): + drawline(plt, X_norm[i,:], X_rec[i,:], '--k') + plt.axis('square') + plt.show() +'''主成分分析_PCA图像数据降维''' +def PCA_faceImage(): + print (u'加载图像数据.....') + data_image = spio.loadmat('data_faces.mat') + X = data_image['X'] + display_imageData(X[0:100,:]) + m = X.shape[0] # 数据条数 + + print (u'运行PCA....') + X_norm,mu,sigma = featureNormalize(X) # 归一化 + + Sigma = np.dot(np.transpose(X_norm),X_norm)/m # 求Sigma + U,S,V = np.linalg.svd(Sigma) # 奇异值分解 + display_imageData(np.transpose(U[:,0:36])) # 显示U的数据 + + print (u'对face数据降维.....') + K = 100 # 降维100维(原先是32*32=1024维的) + Z = projectData(X_norm, U, K) + print (u'投影之后Z向量的大小:%d %d' %Z.shape) + + print (u'显示降维之后的数据......') + X_rec = recoverData(Z, U, K) # 恢复数据 + display_imageData(X_rec[0:100,:]) + + + + # 可视化二维数据 -def plot_data_2d(X): - plt.plot(X[:,0],X[:,1],'bo') +def plot_data_2d(X,marker): + plt.plot(X[:,0],X[:,1],marker) return plt # 归一化数据 @@ -55,10 +94,48 @@ def featureNormalize(X): def projectData(X_norm,U,K): Z = np.zeros((X_norm.shape[0],K)) - U_reduce = U[:,0:K] - Z = np.dot(X_norm,U_reduce) + U_reduce = U[:,0:K] # 取前K个 + Z = np.dot(X_norm,U_reduce) return Z +# 画一条线 +def drawline(plt,p1,p2,line_type): + plt.plot(np.array([p1[0],p2[0]]),np.array([p1[1],p2[1]]),line_type) + + +# 恢复数据 +def recoverData(Z,U,K): + X_rec = np.zeros((Z.shape[0],U.shape[0])) + U_recude = U[:,0:K] + X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) + return X_rec + +# 显示图片 +def display_imageData(imgData): + sum = 0 + ''' + 显示100个数(若是一个一个绘制将会非常慢,可以将要画的图片整理好,放到一个矩阵中,显示这个矩阵即可) + - 初始化一个二维数组 + - 将每行的数据调整成图像的矩阵,放进二维数组 + - 显示即可 + ''' + m,n = imgData.shape + width = np.int32(np.round(np.sqrt(n))) + height = np.int32(n/width); + rows_count = np.int32(np.floor(np.sqrt(m))) + cols_count = np.int32(np.ceil(m/rows_count)) + pad = 1 + display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad))) + for i in range(rows_count): + for j in range(cols_count): + max_val = np.max(np.abs(imgData[sum,:])) + display_array[pad+i*(height+pad):pad+i*(height+pad)+height,pad+j*(width+pad):pad+j*(width+pad)+width] = imgData[sum,:].reshape(height,width,order="F")/max_val # order=F指定以列优先,在matlab中是这样的,python中需要指定,默认以行 + sum += 1 + + plt.imshow(display_array,cmap='gray') #显示灰度图像 + plt.axis('off') + plt.show() if __name__ == 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+- 如下图所示,所有数据点可以投影到一条直线,是**投影距离的平方和**(投影误差)最小 +![enter description here][41] +- 注意数据需要`归一化`处理 +- 思路是找`1`个`向量u`,所有数据投影到上面使投影距离最小 +- 那么`nD-->kD`就是找`k`个向量![$${u^{(1)}},{u^{(2)}} \ldots {u^{(k)}}$$](http://latex.codecogs.com/gif.latex?%24%24%7Bu%5E%7B%281%29%7D%7D%2C%7Bu%5E%7B%282%29%7D%7D%20%5Cldots%20%7Bu%5E%7B%28k%29%7D%7D%24%24),所有数据投影到上面使投影误差最小 + - eg:3D-->2D,2个向量![$${u^{(1)}},{u^{(2)}}$$](http://latex.codecogs.com/gif.latex?%24%24%7Bu%5E%7B%281%29%7D%7D%2C%7Bu%5E%7B%282%29%7D%7D%24%24)就代表一个平面了,所有点投影到这个平面的投影误差最小即可 + +### 3、主成分分析PCA与线性回归的区别 +- 线性回归是找`x`与`y`的关系,然后用于预测`y` +- `PCA`是找一个投影面,最小化data到这个投影面的投影误差 + +### 4、PCA降维过程 +- 数据预处理(均值归一化) + - 公式:![$${\rm{x}}_j^{(i)} = {{{\rm{x}}_j^{(i)} - {u_j}} \over {{s_j}}}$$](http://latex.codecogs.com/gif.latex?%24%24%7B%5Crm%7Bx%7D%7D_j%5E%7B%28i%29%7D%20%3D%20%7B%7B%7B%5Crm%7Bx%7D%7D_j%5E%7B%28i%29%7D%20-%20%7Bu_j%7D%7D%20%5Cover%20%7B%7Bs_j%7D%7D%7D%24%24) + - 就是减去对应feature的均值,然后除以对应特征的标准差(也可以是最大值-最小值) + - 实现代码: + ``` + # 归一化数据 + def featureNormalize(X): + '''(每一个数据-当前列的均值)/当前列的标准差''' + n = X.shape[1] + mu = np.zeros((1,n)); + sigma = np.zeros((1,n)) + + mu = np.mean(X,axis=0) + sigma = np.std(X,axis=0) + for i in range(n): + X[:,i] = (X[:,i]-mu[i])/sigma[i] + return X,mu,sigma + ``` +- 计算`协方差矩阵Σ`(Covariance Matrix):![$$\Sigma = {1 \over m}\sum\limits_{i = 1}^n {{x^{(i)}}{{({x^{(i)}})}^T}} $$](http://latex.codecogs.com/gif.latex?%24%24%5CSigma%20%3D%20%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5En%20%7B%7Bx%5E%7B%28i%29%7D%7D%7B%7B%28%7Bx%5E%7B%28i%29%7D%7D%29%7D%5ET%7D%7D%20%24%24) + - 注意这里的`Σ`和求和符号不同 + - 协方差矩阵`对称正定`(不理解正定的看看线代) + - 大小为`nxn`,`n`为`feature`的维度 + - 实现代码: + ``` + Sigma = np.dot(np.transpose(X_norm),X_norm)/m # 求Sigma + ``` +- 计算`Σ`的特征值和特征向量 + - 可以是用`svd`奇异值分解函数:`U,S,V = svd(Σ)` + - 返回的是与`Σ`同样大小的对角阵`S`(由`Σ`的特征值组成)[**注意**:`matlab`中函数返回的是对角阵,在`python`中返回的是一个向量,节省空间] + - 还有两个**酉矩阵**U和V,且![$$\Sigma = US{V^T}$$](http://latex.codecogs.com/gif.latex?%24%24%5CSigma%20%3D%20US%7BV%5ET%7D%24%24) + - ![enter description here][42] + - **注意**:`svd`函数求出的`S`是按特征值降序排列的,若不是使用`svd`,需要按**特征值**大小重新排列`U` +- 降维 + - 选取`U`中的前`K`列(假设要降为`K`维) + - ![enter description here][43] + - `Z`就是对应降维之后的数据 + - 实现代码: + ``` + # 映射数据 + def projectData(X_norm,U,K): + Z = np.zeros((X_norm.shape[0],K)) + + U_reduce = U[:,0:K] # 取前K个 + Z = np.dot(X_norm,U_reduce) + return Z + ``` +- 过程总结: + - `Sigma = X'*X/m` + - `U,S,V = svd(Sigma)` + - `Ureduce = U[:,0:k]` + - `Z = Ureduce'*x` + +### 5、数据恢复 + - 因为:![$${Z^{(i)}} = U_{reduce}^T*{X^{(i)}}$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BZ%5E%7B%28i%29%7D%7D%20%3D%20U_%7Breduce%7D%5ET*%7BX%5E%7B%28i%29%7D%7D%24%24) + - 所以:![$${X_{approx}} = {(U_{reduce}^T)^{ - 1}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5ET%29%5E%7B%20-%201%7D%7DZ%24%24) (注意这里是X的近似值) + - 又因为`Ureduce`为正定矩阵,【正定矩阵满足:![$$A{A^T} = {A^T}A = E$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24A%7BA%5ET%7D%20%3D%20%7BA%5ET%7DA%20%3D%20E%24%24),所以:![$${A^{ - 1}} = {A^T}$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BA%5E%7B%20-%201%7D%7D%20%3D%20%7BA%5ET%7D%24%24)】,所以这里: + - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) + - 实现代码: + ``` + # 恢复数据 + def recoverData(Z,U,K): + X_rec = np.zeros((Z.shape[0],U.shape[0])) + U_recude = U[:,0:K] + X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) + return X_rec + ``` + +### 6、主成分个数的选择(即要降的维度) +- 如何选择 + - **投影误差**(project error):![$${1 \over m}\sum\limits_{i = 1}^m {||{x^{(i)}} - x_{approx}^{(i)}|{|^2}} $$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7C%7C%7Bx%5E%7B%28i%29%7D%7D%20-%20x_%7Bapprox%7D%5E%7B%28i%29%7D%7C%7B%7C%5E2%7D%7D%20%24%24) + - **总变差**(total variation):![$${1 \over m}\sum\limits_{i = 1}^m {||{x^{(i)}}|{|^2}} $$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7C%7C%7Bx%5E%7B%28i%29%7D%7D%7C%7B%7C%5E2%7D%7D%20%24%24) + - 若**误差率**(error ratio):![$${{{1 \over m}\sum\limits_{i = 1}^m {||{x^{(i)}} - x_{approx}^{(i)}|{|^2}} } \over {{1 \over m}\sum\limits_{i = 1}^m {||{x^{(i)}}|{|^2}} }} \le 0.01$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7B%7B%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7C%7C%7Bx%5E%7B%28i%29%7D%7D%20-%20x_%7Bapprox%7D%5E%7B%28i%29%7D%7C%7B%7C%5E2%7D%7D%20%7D%20%5Cover%20%7B%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7C%7C%7Bx%5E%7B%28i%29%7D%7D%7C%7B%7C%5E2%7D%7D%20%7D%7D%20%5Cle%200.01%24%24),则称`99%`保留差异性 + - 误差率一般取`1%,5%,10%`等 +- 如何实现 + - 若是一个个试的话代价太大 + - 之前`U,S,V = svd(Sigma)`,我们得到了`S`,这里误差率error ratio: + ![$$error{\kern 1pt} \;ratio = 1 - {{\sum\limits_{i = 1}^k {{S_{ii}}} } \over {\sum\limits_{i = 1}^n {{S_{ii}}} }} \le threshold$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24error%7B%5Ckern%201pt%7D%20%5C%3Bratio%20%3D%201%20-%20%7B%7B%5Csum%5Climits_%7Bi%20%3D%201%7D%5Ek%20%7B%7BS_%7Bii%7D%7D%7D%20%7D%20%5Cover%20%7B%5Csum%5Climits_%7Bi%20%3D%201%7D%5En%20%7B%7BS_%7Bii%7D%7D%7D%20%7D%7D%20%5Cle%20threshold%24%24) + - 可以一点点增加`K`尝试。 + +### 7、运行结果 +- 2维数据降为1维 + - 要投影的方向 +![enter description here][44] + - 2D降为1D及对应关系 +![enter description here][45] +- 人脸数据降维 + - 原始数据 + ![enter description here][46] + - 可视化部分`U`矩阵信息 + ![enter description here][47] + - 恢复数据 + ![enter description here][48] [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" @@ -912,4 +1023,12 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): [37]: ./images/K-Means_07.png "K-Means_07.png" [38]: ./images/K-Means_04.png "K-Means_04.png" [39]: ./images/K-Means_05.png "K-Means_05.png" - [40]: ./images/K-Means_06.png "K-Means_06.png" \ No newline at end of file + [40]: ./images/K-Means_06.png "K-Means_06.png" + [41]: ./images/PCA_01.png "PCA_01.png" + [42]: ./images/PCA_02.png "PCA_02.png" + [43]: ./images/PCA_03.png "PCA_03.png" + [44]: ./images/PCA_04.png "PCA_04.png" + [45]: ./images/PCA_05.png "PCA_05.png" + [46]: ./images/PCA_06.png "PCA_06.png" + [47]: ./images/PCA_07.png "PCA_07.png" + [48]: ./images/PCA_08.png "PCA_08.png" \ No newline at end of file From 75d6f370bbb3e8b5130f9ef2edc924da32bc99e1 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 21:51:30 +0800 Subject: [PATCH 03/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/readme.md b/readme.md index 5b12b37..b54b5fa 100644 --- a/readme.md +++ b/readme.md @@ -969,7 +969,11 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): ![$$error{\kern 1pt} \;ratio = 1 - {{\sum\limits_{i = 1}^k {{S_{ii}}} } \over {\sum\limits_{i = 1}^n {{S_{ii}}} }} \le threshold$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24error%7B%5Ckern%201pt%7D%20%5C%3Bratio%20%3D%201%20-%20%7B%7B%5Csum%5Climits_%7Bi%20%3D%201%7D%5Ek%20%7B%7BS_%7Bii%7D%7D%7D%20%7D%20%5Cover%20%7B%5Csum%5Climits_%7Bi%20%3D%201%7D%5En%20%7B%7BS_%7Bii%7D%7D%7D%20%7D%7D%20%5Cle%20threshold%24%24) - 可以一点点增加`K`尝试。 -### 7、运行结果 +### 7、使用建议 +- 不要使用PCA去解决过拟合问题`Overfitting`,还是使用正则化的方法(如果保留了很高的差异性还是可以的) +- 只有在原数据上有好的结果,但是运行很慢,才考虑使用PCA + +### 8、运行结果 - 2维数据降为1维 - 要投影的方向 ![enter description here][44] From e1b7fcd3cfbfe2d5742759277af2194e9e8971cb Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 21:52:11 +0800 Subject: [PATCH 04/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 1 + 1 file changed, 1 insertion(+) diff --git a/readme.md b/readme.md index b54b5fa..7891466 100644 --- a/readme.md +++ b/readme.md @@ -872,6 +872,7 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): ## 六、PCA主成分分析(降维) - [全部代码](/PCA/PCA.py) + ### 1、用处 - 数据压缩(Data Compression),使程序运行更快 - 可视化数据,例如`3D-->2D`等 From 0d17bd908ddddbb85f5be768cd2949f092d8efb5 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 21:54:25 +0800 Subject: [PATCH 05/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/readme.md b/readme.md index 7891466..e7ec552 100644 --- a/readme.md +++ b/readme.md @@ -948,7 +948,7 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - 所以:![$${X_{approx}} = {(U_{reduce}^T)^{ - 1}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5ET%29%5E%7B%20-%201%7D%7DZ%24%24) (注意这里是X的近似值) - 又因为`Ureduce`为正定矩阵,【正定矩阵满足:![$$A{A^T} = {A^T}A = E$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24A%7BA%5ET%7D%20%3D%20%7BA%5ET%7DA%20%3D%20E%24%24),所以:![$${A^{ - 1}} = {A^T}$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BA%5E%7B%20-%201%7D%7D%20%3D%20%7BA%5ET%7D%24%24)】,所以这里: - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - - 实现代码: + - 实现代码: ``` # 恢复数据 def recoverData(Z,U,K): From d3e367e553ad6eca03dc8211a46124e914770abe Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 21:56:30 +0800 Subject: [PATCH 06/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/readme.md b/readme.md index e7ec552..d51dab9 100644 --- a/readme.md +++ b/readme.md @@ -948,9 +948,9 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - 所以:![$${X_{approx}} = {(U_{reduce}^T)^{ - 1}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5ET%29%5E%7B%20-%201%7D%7DZ%24%24) (注意这里是X的近似值) - 又因为`Ureduce`为正定矩阵,【正定矩阵满足:![$$A{A^T} = {A^T}A = E$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24A%7BA%5ET%7D%20%3D%20%7BA%5ET%7DA%20%3D%20E%24%24),所以:![$${A^{ - 1}} = {A^T}$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BA%5E%7B%20-%201%7D%7D%20%3D%20%7BA%5ET%7D%24%24)】,所以这里: - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - - 实现代码: + - 实现代码: ``` - # 恢复数据 + # 恢复数据 def recoverData(Z,U,K): X_rec = np.zeros((Z.shape[0],U.shape[0])) U_recude = U[:,0:K] From d31823c07689bca362ba2b7f70169a76994dcf19 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 21:59:47 +0800 Subject: [PATCH 07/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/readme.md b/readme.md index d51dab9..993ef0c 100644 --- a/readme.md +++ b/readme.md @@ -950,12 +950,12 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - 实现代码: ``` - # 恢复数据 - def recoverData(Z,U,K): - X_rec = np.zeros((Z.shape[0],U.shape[0])) - U_recude = U[:,0:K] - X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) - return X_rec + # 恢复数据 +def recoverData(Z,U,K): + X_rec = np.zeros((Z.shape[0],U.shape[0])) + U_recude = U[:,0:K] + X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) + return X_rec ``` ### 6、主成分个数的选择(即要降的维度) From 324542bb626b56002754a1cbae582fd738f77f48 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 22:03:43 +0800 Subject: [PATCH 08/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/readme.md b/readme.md index 993ef0c..fa2cb0a 100644 --- a/readme.md +++ b/readme.md @@ -950,12 +950,13 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - 实现代码: ``` - # 恢复数据 -def recoverData(Z,U,K): - X_rec = np.zeros((Z.shape[0],U.shape[0])) - U_recude = U[:,0:K] - X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) - return X_rec + # 映射数据 + def projectData(X_norm,U,K): + Z = np.zeros((X_norm.shape[0],K)) + + U_reduce = U[:,0:K] # 取前K个 + Z = np.dot(X_norm,U_reduce) + return Z ``` ### 6、主成分个数的选择(即要降的维度) From b0944805d16b2906384488924457668aa62e1d7a Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 22:04:30 +0800 Subject: [PATCH 09/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 13 ++++++------- 1 file changed, 6 insertions(+), 7 deletions(-) diff --git a/readme.md b/readme.md index fa2cb0a..7891466 100644 --- a/readme.md +++ b/readme.md @@ -950,13 +950,12 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - 实现代码: ``` - # 映射数据 - def projectData(X_norm,U,K): - Z = np.zeros((X_norm.shape[0],K)) - - U_reduce = U[:,0:K] # 取前K个 - Z = np.dot(X_norm,U_reduce) - return Z + # 恢复数据 + def recoverData(Z,U,K): + X_rec = np.zeros((Z.shape[0],U.shape[0])) + U_recude = U[:,0:K] + X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) + return X_rec ``` ### 6、主成分个数的选择(即要降的维度) From 09781cd0f1f73d515aa4c6a19d0aaa8e35b1830b Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 22:07:12 +0800 Subject: [PATCH 10/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/readme.md b/readme.md index 7891466..d117035 100644 --- a/readme.md +++ b/readme.md @@ -950,7 +950,7 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - 实现代码: ``` - # 恢复数据 + # 恢复数据 def recoverData(Z,U,K): X_rec = np.zeros((Z.shape[0],U.shape[0])) U_recude = U[:,0:K] From 6860053c9858f74ecab7721b28ba6ac442b2fdf6 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 21 Dec 2016 22:14:38 +0800 Subject: [PATCH 11/42] =?UTF-8?q?:memo:=20PCA=E4=B8=BB=E6=88=90=E5=88=86?= =?UTF-8?q?=E5=88=86=E6=9E=90=EF=BC=8C=E6=95=B0=E6=8D=AE=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- PCA/PCA.py | 1 + readme.md | 4 ++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/PCA/PCA.py b/PCA/PCA.py index 0f01f70..92179ad 100644 --- a/PCA/PCA.py +++ b/PCA/PCA.py @@ -102,6 +102,7 @@ def projectData(X_norm,U,K): def drawline(plt,p1,p2,line_type): plt.plot(np.array([p1[0],p2[0]]),np.array([p1[1],p2[1]]),line_type) + # 恢复数据 def recoverData(Z,U,K): diff --git a/readme.md b/readme.md index d117035..4cf7982 100644 --- a/readme.md +++ b/readme.md @@ -949,14 +949,14 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - 又因为`Ureduce`为正定矩阵,【正定矩阵满足:![$$A{A^T} = {A^T}A = E$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24A%7BA%5ET%7D%20%3D%20%7BA%5ET%7DA%20%3D%20E%24%24),所以:![$${A^{ - 1}} = {A^T}$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BA%5E%7B%20-%201%7D%7D%20%3D%20%7BA%5ET%7D%24%24)】,所以这里: - ![$${X_{approx}} = {(U_{reduce}^{ - 1})^{ - 1}}Z = {U_{reduce}}Z$$](http://latex.codecogs.com/gif.latex?%5Cfn_cm%20%24%24%7BX_%7Bapprox%7D%7D%20%3D%20%7B%28U_%7Breduce%7D%5E%7B%20-%201%7D%29%5E%7B%20-%201%7D%7DZ%20%3D%20%7BU_%7Breduce%7D%7DZ%24%24) - 实现代码: - ``` +``` # 恢复数据 def recoverData(Z,U,K): X_rec = np.zeros((Z.shape[0],U.shape[0])) U_recude = U[:,0:K] X_rec = np.dot(Z,np.transpose(U_recude)) # 还原数据(近似) return X_rec - ``` +``` ### 6、主成分个数的选择(即要降的维度) - 如何选择 From 2a2326322e614785f83d1db2376072448221c654 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Thu, 22 Dec 2016 16:41:06 +0800 Subject: [PATCH 12/42] =?UTF-8?q?:memo:=20=E4=BD=BF=E7=94=A8scikit-learn?= =?UTF-8?q?=20=E4=B8=AD=E7=9A=84PCA=E5=AE=9E=E7=8E=B0=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- AnomalyDetection/AnomalyDetection.py | 3 + AnomalyDetection/data1.mat | Bin 0 -> 9501 bytes AnomalyDetection/data2.mat | Bin 0 -> 93481 bytes PCA/PCA_scikit-learn.py | 103 +++++++++++++++++++++++++++ formula/PCA.wmf | Bin 1810 -> 28284 bytes readme.md | 43 +++++++++++ 6 files changed, 149 insertions(+) create mode 100644 AnomalyDetection/AnomalyDetection.py create mode 100644 AnomalyDetection/data1.mat create mode 100644 AnomalyDetection/data2.mat create mode 100644 PCA/PCA_scikit-learn.py diff --git a/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py new file mode 100644 index 0000000..21a25cb --- /dev/null +++ b/AnomalyDetection/AnomalyDetection.py @@ -0,0 +1,3 @@ +#-*- coding: utf-8 -*- +# Author: Bob +# Date: 2016.12.22 diff --git 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plt = plot_data_2d(X,'bo') + plt.axis('square') + plt.title('original data') + plt.show() + '''归一化数据并作图''' + scaler = StandardScaler() + scaler.fit(X) + x_train = scaler.transform(X) + + plot_data_2d(x_train, 'bo') + plt.axis('square') + plt.title('scaler data') + plt.show() + + '''拟合数据''' + K=1 # 要降的维度 + model = pca.PCA(n_components=K).fit(x_train) # 拟合数据,n_components定义要降的维度 + Z = model.transform(x_train) # transform就会执行降维操作 + + '''数据恢复并作图''' + Ureduce = model.components_ # 得到降维用的Ureduce + x_rec = np.dot(Z,Ureduce) # 数据恢复 + + plot_data_2d(x_rec,'bo') + plt.plot() + plt.axis('square') + plt.title('recover data') + plt.show() + +def PCA_face_example(): + '''加载数据并显示''' + image_data = spio.loadmat('data_faces.mat') + X = image_data['X'] + display_imageData(X[0:100,:]) # 显示100个最初图像 + + '''归一化数据''' + scaler = StandardScaler() + scaler.fit(X) + x_train = scaler.transform(X) + + '''拟合模型''' + K=100 + model = pca.PCA(n_components=K).fit(x_train) + Z = model.transform(x_train) + Ureduce = model.components_ + + display_imageData(Ureduce[0:36,:]) # 可视化部分U数据 + x_rec = np.dot(Z,Ureduce) + + display_imageData(x_rec[0:100,:]) # 显示恢复的数据 + + + + +# 可视化二维数据 +def plot_data_2d(X,marker): + plt.plot(X[:,0],X[:,1],marker) + return plt + +# 显示图片 +def display_imageData(imgData): + sum = 0 + ''' + 显示100个数(若是一个一个绘制将会非常慢,可以将要画的图片整理好,放到一个矩阵中,显示这个矩阵即可) + - 初始化一个二维数组 + - 将每行的数据调整成图像的矩阵,放进二维数组 + - 显示即可 + ''' + m,n = imgData.shape + width = np.int32(np.round(np.sqrt(n))) + height = np.int32(n/width); + rows_count = np.int32(np.floor(np.sqrt(m))) + cols_count = np.int32(np.ceil(m/rows_count)) + pad = 1 + display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad))) + for i in range(rows_count): + for j in range(cols_count): + max_val = np.max(np.abs(imgData[sum,:])) + display_array[pad+i*(height+pad):pad+i*(height+pad)+height,pad+j*(width+pad):pad+j*(width+pad)+width] = imgData[sum,:].reshape(height,width,order="F")/max_val # order=F指定以列优先,在matlab中是这样的,python中需要指定,默认以行 + 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fd_6T(1i@8rKJKjO#7K(Ca-3^KDm)yWU{A>B*^eDSPYl*273Gu zP_G&rKSLFxV?jZ&ubZ%2`- diff --git a/readme.md b/readme.md index 4cf7982..35665e7 100644 --- a/readme.md +++ b/readme.md @@ -988,6 +988,49 @@ def runKMeans(X,initial_centroids,max_iters,plot_process): - 恢复数据 ![enter description here][48] +### 9、[使用scikit-learn库中的PCA实现降维](/PCA/PCA.py_scikit-learn.py) +- 导入需要的包: +``` +#-*- coding: utf-8 -*- +# Author:bob +# Date:2016.12.22 +import numpy as np +from matplotlib import pyplot as plt +from scipy import io as spio +from sklearn.decomposition import pca +from sklearn.preprocessing import StandardScaler +``` +- 归一化数据 +``` + '''归一化数据并作图''' + scaler = StandardScaler() + scaler.fit(X) + x_train = scaler.transform(X) +``` +- 使用PCA模型拟合数据,并降维 +``` + '''拟合数据''' + K=1 # 要降的维度 + model = pca.PCA(n_components=K).fit(x_train) # 拟合数据,n_components定义要降的维度 + Z = model.transform(x_train) # transform就会执行降维操作 +``` + - `n_components`对应要将的维度 + +- 数据恢复 +``` + '''数据恢复并作图''' + Ureduce = model.components_ # 得到降维用的Ureduce + x_rec = np.dot(Z,Ureduce) # 数据恢复 +``` + - `model.components_`会得到降维使用的`U`矩阵 + + +--------------------------------------------------------------- + + +### 七、异常检测 Anomaly Detection + + [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" [2]: ./images/LogisticRegression_01.png "LogisticRegression_01.png" From ce045fdf71ee9094565bd999e0be195ad067efb1 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Thu, 22 Dec 2016 16:44:54 +0800 Subject: [PATCH 13/42] =?UTF-8?q?:memo:=20=E4=BD=BF=E7=94=A8scikit-learn?= =?UTF-8?q?=20=E4=B8=AD=E7=9A=84PCA=E5=AE=9E=E7=8E=B0=E9=99=8D=E7=BB=B4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/readme.md b/readme.md index 35665e7..65c8bb8 100644 --- a/readme.md +++ b/readme.md @@ -1008,21 +1008,22 @@ from sklearn.preprocessing import StandardScaler x_train = scaler.transform(X) ``` - 使用PCA模型拟合数据,并降维 + - `n_components`对应要将的维度 ``` '''拟合数据''' K=1 # 要降的维度 model = pca.PCA(n_components=K).fit(x_train) # 拟合数据,n_components定义要降的维度 Z = model.transform(x_train) # transform就会执行降维操作 ``` - - `n_components`对应要将的维度 - 数据恢复 + - `model.components_`会得到降维使用的`U`矩阵 ``` '''数据恢复并作图''' Ureduce = model.components_ # 得到降维用的Ureduce x_rec = np.dot(Z,Ureduce) # 数据恢复 ``` - - `model.components_`会得到降维使用的`U`矩阵 + --------------------------------------------------------------- From 9f46fc7f3c58f03e6d0f964d61a50e992b132175 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Sun, 25 Dec 2016 18:52:33 +0800 Subject: [PATCH 14/42] :: coding --- AnomalyDetection/AnomalyDetection.py | 58 ++++++++++++++++++++++++++++ PCA/PCA.py | 2 +- 2 files changed, 59 insertions(+), 1 deletion(-) diff --git a/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py index 21a25cb..73dbf02 100644 --- a/AnomalyDetection/AnomalyDetection.py +++ b/AnomalyDetection/AnomalyDetection.py @@ -1,3 +1,61 @@ #-*- coding: utf-8 -*- # Author: Bob # Date: 2016.12.22 +import numpy as np +from matplotlib import pyplot as plt +from scipy import io as spio + +'''异常检测主运行程序''' +def anomalyDetection_example(): + '''加载并显示数据''' + data = spio.loadmat('data1.mat') + X = data['X'] + plt = display_2d_data(X, 'bx') + plt.title("origin data") + plt.show() + + mu,sigma2 = estimateGaussian(X) + print mu,sigma2 + p = multivariateGaussian(X,mu,sigma2) + print p + + visualizeFit(X,mu,sigma2) + + + +# 显示二维数据 +def display_2d_data(X,marker): + plt.plot(X[:,0],X[:,1],marker) + plt.axis('square') + return plt + +# 参数估计函数(就是求均值和方差) +def estimateGaussian(X): + m,n = X.shape + mu = np.zeros((n,1)) + sigma2 = np.zeros((n,1)) + + mu = np.mean(X, axis=0) # axis=0表示列,每列的均值 + sigma2 = np.var(X,axis=0) # 求每列的方差 + return mu,sigma2 + +# 多元高斯分布函数 +def multivariateGaussian(X,mu,Sigma2): + k = len(mu) + if (Sigma2.shape[0]>1): + Sigma2 = np.diag(Sigma2) + + X = X-mu + argu = (2*np.pi)**(-k/2)*np.linalg.det(Sigma2)**(-0.5) + p = argu*np.exp(-0.5*np.sum(np.dot(X,np.linalg.inv(Sigma2))*X,axis=1)) # axis表示每行 + return p + +# 可视化边界 +def visualizeFit(X,mu,sigma2): + X1,X2 = np.meshgrid(0,0.5,35) + Z = multivariateGaussian(np.vstack((X1,X2)), mu, Sigma2) + + +if __name__ == '__main__': + anomalyDetection_example() + \ No newline at end of file diff --git a/PCA/PCA.py b/PCA/PCA.py index 92179ad..2301ade 100644 --- a/PCA/PCA.py +++ b/PCA/PCA.py @@ -83,7 +83,7 @@ def featureNormalize(X): mu = np.zeros((1,n)); sigma = np.zeros((1,n)) - mu = np.mean(X,axis=0) + mu = np.mean(X,axis=0) # axis=0表示列 sigma = np.std(X,axis=0) for i in range(n): X[:,i] = (X[:,i]-mu[i])/sigma[i] From 3bc2172d05b03caa1809cd20411223964f378710 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 14:37:05 +0800 Subject: [PATCH 15/42] =?UTF-8?q?add=20code=20anomaly=20detection=E5=BC=82?= =?UTF-8?q?=E5=B8=B8=E6=A3=80=E6=B5=8B=E4=BB=A3=E7=A0=81?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- AnomalyDetection/AnomalyDetection.py | 61 ++++++++++++++++++++++++---- 1 file changed, 53 insertions(+), 8 deletions(-) diff --git a/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py index 73dbf02..cbe293b 100644 --- a/AnomalyDetection/AnomalyDetection.py +++ b/AnomalyDetection/AnomalyDetection.py @@ -13,13 +13,25 @@ def anomalyDetection_example(): plt = display_2d_data(X, 'bx') plt.title("origin data") plt.show() + '''多元高斯分布函数,并可视化拟合的边界''' + mu,sigma2 = estimateGaussian(X) # 参数估计(求均值和方差) + #print mu,sigma2 + p = multivariateGaussian(X,mu,sigma2) # 多元高斯分布函数 + #print p + visualizeFit(X,mu,sigma2) # 显示图像 - mu,sigma2 = estimateGaussian(X) - print mu,sigma2 - p = multivariateGaussian(X,mu,sigma2) - print p + '''选择异常点(在交叉验证CV上训练得到最好的epsilon)''' + Xval = data['Xval'] + yval = data['yval'] + pval = multivariateGaussian(Xval, mu, sigma2) # 计算CV上的概率密度值 + epsilon,F1 = selectThreshold(yval,pval) # 选择最优的epsilon临界值 + print u'在CV上得到的最好的epsilon是:%e'%epsilon + print u'对应的F1Score值为:%f'%F1 + outliers = np.where(p1): Sigma2 = np.diag(Sigma2) - + '''多元高斯分布函数''' X = X-mu argu = (2*np.pi)**(-k/2)*np.linalg.det(Sigma2)**(-0.5) p = argu*np.exp(-0.5*np.sum(np.dot(X,np.linalg.inv(Sigma2))*X,axis=1)) # axis表示每行 @@ -52,8 +64,41 @@ def multivariateGaussian(X,mu,Sigma2): # 可视化边界 def visualizeFit(X,mu,sigma2): - X1,X2 = np.meshgrid(0,0.5,35) - Z = multivariateGaussian(np.vstack((X1,X2)), mu, Sigma2) + x = np.arange(0, 36, 0.5) # 0-36,步长0.5 + y = np.arange(0, 36, 0.5) + X1,X2 = np.meshgrid(x,y) # 要画等高线,所以meshgird + Z = multivariateGaussian(np.hstack((X1.reshape(-1,1),X2.reshape(-1,1))), mu, sigma2) # 计算对应的高斯分布函数 + Z = Z.reshape(X1.shape) # 调整形状 + plt.plot(X[:,0],X[:,1],'bx') + + if np.sum(np.isinf(Z).astype(float)) == 0: # 如果计算的为无穷,就不用画了 + # plt.contourf(X1,X2,Z,10.**np.arange(-20, 0, 3),linewidth=.5) + CS = plt.contour(X1,X2,Z,10.**np.arange(-20, 0, 3),color='black',linewidth=.5) # 画等高线,Z的值在10.**np.arange(-20, 0, 3) + #plt.clabel(CS) + + plt.show() + +# 选择最优的epsilon,即:使F1Score最大 +def selectThreshold(yval,pval): + '''初始化所需变量''' + bestEpsilon = 0. + bestF1 = 0. + F1 = 0. + step = (np.max(pval)-np.min(pval))/1000 + '''计算''' + for epsilon in np.arange(np.min(pval),np.max(pval),step): + cvPrecision = pval bestF1: # 修改最优的F1 Score + bestF1 = F1 + bestEpsilon = epsilon + return bestEpsilon,bestF1 + if __name__ == '__main__': From efc8d31c9cdce0ae75309ed4280d42fbabc91415 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 14:57:18 +0800 Subject: [PATCH 16/42] :memo: add code anomaly detection readme --- readme.md | 17 +++++++++++++++-- 1 file changed, 15 insertions(+), 2 deletions(-) diff --git a/readme.md b/readme.md index 65c8bb8..69fd32f 100644 --- a/readme.md +++ b/readme.md @@ -1029,8 +1029,21 @@ from sklearn.preprocessing import StandardScaler --------------------------------------------------------------- -### 七、异常检测 Anomaly Detection - +## 七、异常检测 Anomaly Detection +- [全部代码](/AnomalyDetection/AnomalyDetection.py) + +### 1、异常检测流程 +- ![$${x^{(i)}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7Bx%5E%7B%28i%29%7D%7D%24%24)对应feature +- 建立模型model:`P(x)` +- 检查若是:`P(x)<ε`,则认为是异常,其中`ε`为我们要求的概率的临界值`threshold` + +### 2、高斯分布(正态分布)`Gaussian distribution` +- 分布函数:![$$p(x) = {1 \over {\sqrt {2\pi } \sigma }}{e^{ - {{{{(x - u)}^2}} \over {2{\sigma ^2}}}}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24p%28x%29%20%3D%20%7B1%20%5Cover%20%7B%5Csqrt%20%7B2%5Cpi%20%7D%20%5Csigma%20%7D%7D%7Be%5E%7B%20-%20%7B%7B%7B%7B%28x%20-%20u%29%7D%5E2%7D%7D%20%5Cover%20%7B2%7B%5Csigma%20%5E2%7D%7D%7D%7D%7D%24%24) + - 其中,`u`为数据的**均值**,`σ`为数据的**标准差** + - `σ`越**小**,对应的图像越**尖** +- 参数估计(`parameter estimation`) + - ![$$u = {1 \over m}\sum\limits_{i = 1}^m {{x^{(i)}}} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24u%20%3D%20%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7Bx%5E%7B%28i%29%7D%7D%7D%20%24%24) + - ![$${\sigma ^2} = {1 \over m}\sum\limits_{i = 1}^m {{{({x^{(i)}} - u)}^2}} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7B%5Csigma%20%5E2%7D%20%3D%20%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7B%7B%28%7Bx%5E%7B%28i%29%7D%7D%20-%20u%29%7D%5E2%7D%7D%20%24%24) [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" From 6c6288944e70986d3932420b457b67250d678cec Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 15:22:05 +0800 Subject: [PATCH 17/42] :memo: add anomaly detection readme --- readme.md | 17 +++++++++++------ 1 file changed, 11 insertions(+), 6 deletions(-) diff --git a/readme.md b/readme.md index 69fd32f..7cce84c 100644 --- a/readme.md +++ b/readme.md @@ -1032,12 +1032,7 @@ from sklearn.preprocessing import StandardScaler ## 七、异常检测 Anomaly Detection - [全部代码](/AnomalyDetection/AnomalyDetection.py) -### 1、异常检测流程 -- ![$${x^{(i)}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7Bx%5E%7B%28i%29%7D%7D%24%24)对应feature -- 建立模型model:`P(x)` -- 检查若是:`P(x)<ε`,则认为是异常,其中`ε`为我们要求的概率的临界值`threshold` - -### 2、高斯分布(正态分布)`Gaussian distribution` +### 1、高斯分布(正态分布)`Gaussian distribution` - 分布函数:![$$p(x) = {1 \over {\sqrt {2\pi } \sigma }}{e^{ - {{{{(x - u)}^2}} \over {2{\sigma ^2}}}}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24p%28x%29%20%3D%20%7B1%20%5Cover%20%7B%5Csqrt%20%7B2%5Cpi%20%7D%20%5Csigma%20%7D%7D%7Be%5E%7B%20-%20%7B%7B%7B%7B%28x%20-%20u%29%7D%5E2%7D%7D%20%5Cover%20%7B2%7B%5Csigma%20%5E2%7D%7D%7D%7D%7D%24%24) - 其中,`u`为数据的**均值**,`σ`为数据的**标准差** - `σ`越**小**,对应的图像越**尖** @@ -1045,6 +1040,16 @@ from sklearn.preprocessing import StandardScaler - ![$$u = {1 \over m}\sum\limits_{i = 1}^m {{x^{(i)}}} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24u%20%3D%20%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7Bx%5E%7B%28i%29%7D%7D%7D%20%24%24) - ![$${\sigma ^2} = {1 \over m}\sum\limits_{i = 1}^m {{{({x^{(i)}} - u)}^2}} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7B%5Csigma%20%5E2%7D%20%3D%20%7B1%20%5Cover%20m%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%7B%7B%28%7Bx%5E%7B%28i%29%7D%7D%20-%20u%29%7D%5E2%7D%7D%20%24%24) +### 2、异常检测算法 +- 例子 + - 训练集:![$$\{ {x^{(1)}},{x^{(2)}}, \cdots {x^{(m)}}\} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%5C%7B%20%7Bx%5E%7B%281%29%7D%7D%2C%7Bx%5E%7B%282%29%7D%7D%2C%20%5Ccdots%20%7Bx%5E%7B%28m%29%7D%7D%5C%7D%20%24%24),其中![$$x \in {R^n}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24x%20%5Cin%20%7BR%5En%7D%24%24) + - 假设![$${x_1},{x_2} \cdots {x_n}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7Bx_1%7D%2C%7Bx_2%7D%20%5Ccdots%20%7Bx_n%7D%24%24)相互独立,建立model模型:![$$p(x) = p({x_1};{u_1},\sigma _1^2)p({x_2};{u_2},\sigma _2^2) \cdots p({x_n};{u_n},\sigma _n^2) = \prod\limits_{j = 1}^n {p({x_j};{u_j},\sigma _j^2)} $$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24p%28x%29%20%3D%20p%28%7Bx_1%7D%3B%7Bu_1%7D%2C%5Csigma%20_1%5E2%29p%28%7Bx_2%7D%3B%7Bu_2%7D%2C%5Csigma%20_2%5E2%29%20%5Ccdots%20p%28%7Bx_n%7D%3B%7Bu_n%7D%2C%5Csigma%20_n%5E2%29%20%3D%20%5Cprod%5Climits_%7Bj%20%3D%201%7D%5En%20%7Bp%28%7Bx_j%7D%3B%7Bu_j%7D%2C%5Csigma%20_j%5E2%29%7D%20%24%24) +- 过程 + - 选择具有代表异常的`feature`:xi + - 参数估计:![$${u_1},{u_2}, \cdots ,{u_n};\sigma _1^2,\sigma _2^2 \cdots ,\sigma _n^2$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7Bu_1%7D%2C%7Bu_2%7D%2C%20%5Ccdots%20%2C%7Bu_n%7D%3B%5Csigma%20_1%5E2%2C%5Csigma%20_2%5E2%20%5Ccdots%20%2C%5Csigma%20_n%5E2%24%24) + - 计算`p(x)`,若是`P(x)<ε`则认为异常,其中`ε`为我们要求的概率的临界值`threshold` + + [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" [2]: ./images/LogisticRegression_01.png "LogisticRegression_01.png" From d6e6f300872213dec4aeeeec962b6bd883d621ad Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 15:40:07 +0800 Subject: [PATCH 18/42] :memo: add anomaly detection readme --- readme.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/readme.md b/readme.md index 7cce84c..1a417bc 100644 --- a/readme.md +++ b/readme.md @@ -1048,6 +1048,14 @@ from sklearn.preprocessing import StandardScaler - 选择具有代表异常的`feature`:xi - 参数估计:![$${u_1},{u_2}, \cdots ,{u_n};\sigma _1^2,\sigma _2^2 \cdots ,\sigma _n^2$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7Bu_1%7D%2C%7Bu_2%7D%2C%20%5Ccdots%20%2C%7Bu_n%7D%3B%5Csigma%20_1%5E2%2C%5Csigma%20_2%5E2%20%5Ccdots%20%2C%5Csigma%20_n%5E2%24%24) - 计算`p(x)`,若是`P(x)<ε`则认为异常,其中`ε`为我们要求的概率的临界值`threshold` +- 这里只是**单元高斯分布**,假设了`feature`之间是独立的,下面会讲到**多元高斯分布**,会自动捕捉到`feature`之间的关系 + +### 3、评价`p(x)`的好坏,以及`ε`的选取 +- 因为数据可能是非常**偏斜**的(就是`y=1`的个数非常少,(`y=1`表示异常)),所以可以使用`Precision/Recall`,计算`F1Score`(在**CV交叉验证集**上),公式: +![$${F_1}Score = 2{{PR} \over {P + R}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7BF_1%7DScore%20%3D%202%7B%7BPR%7D%20%5Cover%20%7BP%20+%20R%7D%7D%24%24) +- `ε`的选取 + - 尝试多个`ε`值,使`F1Score`的值高 + From 65325808e9278d53284071638b8f87a2755d9902 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 16:15:07 +0800 Subject: [PATCH 19/42] :memo: add anomaly detection readme --- images/AnomalyDetection.png | Bin 0 -> 7492 bytes readme.md | 18 +++++++++++++----- 2 files changed, 13 insertions(+), 5 deletions(-) create mode 100644 images/AnomalyDetection.png diff --git a/images/AnomalyDetection.png b/images/AnomalyDetection.png new file mode 100644 index 0000000000000000000000000000000000000000..7ffe9e734d2ea322f96f5ca7a94fb2d82f01590a GIT binary patch literal 7492 zcmeHMc~sNaw#F*uiUqV5kV#UhA~Gp+n9^7f5m1>$2&e=Q2=f%?D=C5^lOTvp6%a%q zXp|{|L_r}y0U1IFkRT#M5+KSHrjYjwR!i?%Z@snNy6=zsR{zM#Npj9U`<&n2-~PUx zTNlrp2nk9G^6~KrnVvPW;^W(OA9%U{;~U_cu~$;wz}v1ME0fcF=x%8`@L`V!)B?)K 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因为数据可能是非常**偏斜**的(就是`y=1`的个数非常少,(`y=1`表示异常)),所以可以使用`Precision/Recall`,计算`F1Score`(在**CV交叉验证集**上) + - 例如:预测癌症,假设模型可以得到`99%`能够预测正确,`1%`的错误率,但是实际癌症的概率很小,只有`0.5%`,那么我们始终预测没有癌症y=0反而可以得到更小的错误率。使用`error rate`来评估就不科学了。 + - 如下图记录: + ![enter description here][49] + - ![$$\Pr ecision = {{TP} \over {TP + FP}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%5CPr%20ecision%20%3D%20%7B%7BTP%7D%20%5Cover%20%7BTP%20+%20FP%7D%7D%24%24) ,即:**正确预测正样本/所有预测正样本** + - ![$${\mathop{\rm Re}\nolimits} {\rm{call}} = {{TP} \over {TP + FN}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7B%5Cmathop%7B%5Crm%20Re%7D%5Cnolimits%7D%20%7B%5Crm%7Bcall%7D%7D%20%3D%20%7B%7BTP%7D%20%5Cover%20%7BTP%20+%20FN%7D%7D%24%24) ,即:**正确预测正样本/真实值为正样本** + - 总是让`y=1`(较少的类),计算`Precision`和`Recall` + - ![$${F_1}Score = 2{{PR} \over {P + R}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%7BF_1%7DScore%20%3D%202%7B%7BPR%7D%20%5Cover%20%7BP%20+%20R%7D%7D%24%24) + - 还是以癌症预测为例,假设预测都是no-cancer,TN=199,FN=1,TP=0,FP=0,所以:Precision=0/0,Recall=0/1=0,尽管accuracy=199/200=99.5%,但是不可信。 + - `ε`的选取 - 尝试多个`ε`值,使`F1Score`的值高 - - [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" [2]: ./images/LogisticRegression_01.png "LogisticRegression_01.png" [3]: ./images/LogisticRegression_02.png "LogisticRegression_02.png" @@ -1106,4 +1113,5 @@ from sklearn.preprocessing import StandardScaler [45]: ./images/PCA_05.png "PCA_05.png" [46]: ./images/PCA_06.png "PCA_06.png" [47]: ./images/PCA_07.png "PCA_07.png" - [48]: ./images/PCA_08.png "PCA_08.png" \ No newline at end of file + [48]: ./images/PCA_08.png "PCA_08.png" + [49]: ./images/AnomalyDetection.png "AnomalyDetection.png" \ No newline at end of file From 1ed157a26ce7d351535ba2e432920565b9ac36f9 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 17:42:23 +0800 Subject: [PATCH 20/42] :memo: add anomaly detection readme --- ...yDetection.png => AnomalyDetection_01.png} | Bin images/AnomalyDetection_02.png | Bin 0 -> 18669 bytes images/AnomalyDetection_03.png | Bin 0 -> 18823 bytes images/AnomalyDetection_04.png | Bin 0 -> 9615 bytes images/AnomalyDetection_05.png | Bin 0 -> 4425 bytes images/AnomalyDetection_06.png | Bin 0 -> 4525 bytes images/AnomalyDetection_07.png | Bin 0 -> 6410 bytes readme.md | 70 +++++++++++++++++- 8 files changed, 69 insertions(+), 1 deletion(-) rename images/{AnomalyDetection.png => AnomalyDetection_01.png} (100%) create mode 100644 images/AnomalyDetection_02.png create mode 100644 images/AnomalyDetection_03.png create mode 100644 images/AnomalyDetection_04.png create mode 100644 images/AnomalyDetection_05.png create mode 100644 images/AnomalyDetection_06.png create mode 100644 images/AnomalyDetection_07.png diff --git a/images/AnomalyDetection.png b/images/AnomalyDetection_01.png similarity index 100% rename from images/AnomalyDetection.png rename to images/AnomalyDetection_01.png diff --git a/images/AnomalyDetection_02.png 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如下图,红色的点为异常点,其他的都是正常点(比如CPU和memory的变化) + ![enter description here][50] + - x1对应的高斯分布如下: + ![enter description here][51] + - x2对应的高斯分布如下: + ![enter description here][52] + - 可以看出对应的p(x1)和p(x2)的值变化并不大,就不会认为异常 + - 因为我们认为feature之间是相互独立的,所以如上图是以**正圆**的方式扩展 +- 多元高斯分布 + - ![$$x \in {R^n}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24x%20%5Cin%20%7BR%5En%7D%24%24),并不是建立`p(x1),p(x2)...p(xn)`,而是统一建立`p(x)` + - 其中参数:![$$\mu \in {R^n},\Sigma \in {R^{n \times {\rm{n}}}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24%5Cmu%20%5Cin%20%7BR%5En%7D%2C%5CSigma%20%5Cin%20%7BR%5E%7Bn%20%5Ctimes%20%7B%5Crm%7Bn%7D%7D%7D%7D%24%24),`Σ`为**协方差矩阵** + - ![$$p(x) = {1 \over {{{(2\pi )}^{{n \over 2}}}|\Sigma {|^{{1 \over 2}}}}}{e^{ - {1 \over 2}{{(x - u)}^T}{\Sigma ^{ - 1}}(x - u)}}$$](http://latex.codecogs.com/png.latex?%5Cfn_cm%20%24%24p%28x%29%20%3D%20%7B1%20%5Cover%20%7B%7B%7B%282%5Cpi%20%29%7D%5E%7B%7Bn%20%5Cover%202%7D%7D%7D%7C%5CSigma%20%7B%7C%5E%7B%7B1%20%5Cover%202%7D%7D%7D%7D%7D%7Be%5E%7B%20-%20%7B1%20%5Cover%202%7D%7B%7B%28x%20-%20u%29%7D%5ET%7D%7B%5CSigma%20%5E%7B%20-%201%7D%7D%28x%20-%20u%29%7D%7D%24%24) + - 同样,`|Σ|`越小,`p(x)`越尖 + - 例如: + ![enter description here][53], + 表示x1,x2**正相关**,即x1越大,x2也就越大 + ![enter description here][54] + 若: + ![enter description here][55], + 表示x1,x2**负相关** [1]: ./images/LinearRegression_01.png "LinearRegression_01.png" @@ -1114,4 +1176,10 @@ from sklearn.preprocessing import StandardScaler [46]: ./images/PCA_06.png "PCA_06.png" [47]: ./images/PCA_07.png "PCA_07.png" [48]: ./images/PCA_08.png "PCA_08.png" - [49]: ./images/AnomalyDetection.png "AnomalyDetection.png" \ No newline at end of file + [49]: ./images/AnomalyDetection_01.png "AnomalyDetection_01.png" + [50]: ./images/AnomalyDetection_04.png "AnomalyDetection_04.png" + [51]: ./images/AnomalyDetection_02.png "AnomalyDetection_02.png" + [52]: ./images/AnomalyDetection_03.png "AnomalyDetection_03.png" + [53]: ./images/AnomalyDetection_05.png "AnomalyDetection_05.png" + [54]: ./images/AnomalyDetection_07.png "AnomalyDetection_07.png" + [55]: ./images/AnomalyDetection_06.png "AnomalyDetection_06.png" \ No newline at end of file From 43d423290f8183320d3abd4106c1a600daa4e54a Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 17:43:59 +0800 Subject: [PATCH 21/42] :memo: add anomaly detection readme --- readme.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/readme.md b/readme.md index a80d237..7734c06 100644 --- a/readme.md +++ b/readme.md @@ -1121,10 +1121,10 @@ def selectThreshold(yval,pval): - 同样,`|Σ|`越小,`p(x)`越尖 - 例如: ![enter description here][53], - 表示x1,x2**正相关**,即x1越大,x2也就越大 - ![enter description here][54] + 表示x1,x2**正相关**,即x1越大,x2也就越大,如下图,也就可以将红色的异常点检查出了 + ![enter description here][54] 若: - ![enter description here][55], + ![enter description here][55], 表示x1,x2**负相关** From 941421f27c451d233de98775c8abdd9a6786b075 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Wed, 28 Dec 2016 17:53:34 +0800 Subject: [PATCH 22/42] :memo: add anomaly detection readme --- images/AnomalyDetection_08.png | Bin 0 -> 24047 bytes images/AnomalyDetection_09.png | Bin 0 -> 61147 bytes images/AnomalyDetection_10.png | Bin 0 -> 23750 bytes readme.md | 38 ++++++++++++++++++++++++++++++++- 4 files changed, 37 insertions(+), 1 deletion(-) create mode 100644 images/AnomalyDetection_08.png create mode 100644 images/AnomalyDetection_09.png create mode 100644 images/AnomalyDetection_10.png diff --git a/images/AnomalyDetection_08.png b/images/AnomalyDetection_08.png new file mode 100644 index 0000000000000000000000000000000000000000..d8a5fcc1012dabd7306630fc1c7adce82a0f03e3 GIT binary patch literal 24047 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[七、异常检测 Anomaly Detection](#七-异常检测-anomaly-detection) + * [1、高斯分布(正态分布)](#1-高斯分布正态分布) + * [2、异常检测算法](#2-异常检测算法) + * [3、评价的好坏,以及的选取](#3-评价的好坏以及的选取) + * [4、选择使用什么样的feature(单元高斯分布)](#4-选择使用什么样的feature单元高斯分布) + * [5、多元高斯分布](#5-多元高斯分布) + * [6、单元和多元高斯分布特点](#6-单元和多元高斯分布特点) + * [7、程序运行结果](#7-程序运行结果) + ## 一、[线性回归](/LinearRegression) - [全部代码](/LinearRegression/LinearRegression.py) @@ -1218,4 +1284,4 @@ def multivariateGaussian(X,mu,Sigma2): [55]: ./images/AnomalyDetection_06.png "AnomalyDetection_06.png" [56]: ./images/AnomalyDetection_08.png "AnomalyDetection_08.png" [57]: ./images/AnomalyDetection_09.png "AnomalyDetection_09.png" - [58]: ./images/AnomalyDetection_10.png "AnomalyDetection_10.png" \ No newline at end of file + [58]: ./images/AnomalyDetection_10.png "AnomalyDetection_10.png" From ad7375afd47b0dfd7f544a4b269dcc1fda921686 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Sat, 8 Apr 2017 23:05:58 +0800 Subject: [PATCH 26/42] =?UTF-8?q?:memo:=20=E6=B7=BB=E5=8A=A0=E7=9B=AE?= =?UTF-8?q?=E5=BD=95=E6=A0=91?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/readme.md b/readme.md index 84bedfd..ea6171e 100644 --- a/readme.md +++ b/readme.md @@ -1,6 +1,6 @@ 机器学习算法Python实现 ========= - +## 目录 * [机器学习算法Python实现](#机器学习算法python实现) * [一、线性回归](#一-线性回归) * [1、代价函数](#1-代价函数) From 3a5c22f2b9c4ff8d33a499b10a24b4b18e9921d3 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Tue, 11 Apr 2017 21:15:53 +0800 Subject: [PATCH 27/42] =?UTF-8?q?:tada:=20=E4=BF=AE=E5=A4=8D=E7=A5=9E?= =?UTF-8?q?=E7=BB=8F=E7=BD=91=E7=BB=9C=E5=9C=A8Pyhton3.5=E4=B8=AD=E5=8F=AF?= =?UTF-8?q?=E8=A7=86=E5=8C=96=E5=9B=BE=E7=89=87=E5=92=8C=E6=9D=83=E9=87=8D?= =?UTF-8?q?=E5=87=BD=E6=95=B0=E9=97=AE=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- NeuralNetwok/NeuralNetwork.py | 12 +- NeuralNetwok/predict.csv | 1212 ++++++++++++++++----------------- 2 files changed, 614 insertions(+), 610 deletions(-) diff --git a/NeuralNetwok/NeuralNetwork.py b/NeuralNetwok/NeuralNetwork.py index 7434c31..923a85b 100644 --- a/NeuralNetwok/NeuralNetwork.py +++ b/NeuralNetwok/NeuralNetwork.py @@ -44,8 +44,8 @@ def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer): #np.savetxt("testTheta.csv",initial_nn_params,delimiter=",") start = time.time() result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda)) - print u'执行时间:',time.time()-start - print result + print (u'执行时间:',time.time()-start) + print (result) '''可视化 Theta1''' length = result.shape[0] Theta1 = result[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1) @@ -54,7 +54,7 @@ def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer): display_data(Theta2[:,1:length]) '''预测''' p = predict(Theta1,Theta2,X) - print u"预测准确度为:%f%%"%np.mean(np.float64(p == y.reshape(-1,1))*100) + print (u"预测准确度为:%f%%"%np.mean(np.float64(p == y.reshape(-1,1))*100)) res = np.hstack((p,y.reshape(-1,1))) np.savetxt("predict.csv", res, delimiter=',') @@ -81,8 +81,12 @@ def display_data(imgData): display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad))) for i in range(rows_count): for j in range(cols_count): + if sum >= m: #超过了行数,退出当前循环 + break; display_array[pad+i*(height+pad):pad+i*(height+pad)+height,pad+j*(width+pad):pad+j*(width+pad)+width] = imgData[sum,:].reshape(height,width,order="F") # order=F指定以列优先,在matlab中是这样的,python中需要指定,默认以行 sum += 1 + if sum >= m: #超过了行数,退出当前循环 + break; plt.imshow(display_array,cmap='gray') #显示灰度图像 plt.axis('off') @@ -219,7 +223,7 @@ def checkGradient(Lambda = 0): step[i]=0 # 显示两列比较 res = np.hstack((num_grad.reshape(-1,1),grad.reshape(-1,1))) - print res + print (res) # 初始化调试的theta权重 def debugInitializeWeights(fan_in,fan_out): diff 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+3.000000000000000000e+00,9.000000000000000000e+00 From 63f6c1075b2cccf28f3ddc5bcbc575aee1ba0b6d Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Sun, 25 Jun 2017 10:30:04 +0800 Subject: [PATCH 28/42] Create LICENSE --- LICENSE | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) create mode 100644 LICENSE diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..351fe7e --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2017 lawlite + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. From 7fc56845e7ef008e5a28233d455f98fc82a77d18 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Sun, 25 Jun 2017 10:57:05 +0800 Subject: [PATCH 29/42] :memo: add MIT license --- NeuralNetwok/predict.csv | 1474 +++++++++++++++++++------------------- readme.md | 4 + 2 files changed, 741 insertions(+), 737 deletions(-) diff --git a/NeuralNetwok/predict.csv b/NeuralNetwok/predict.csv index f952bb4..42610e0 100644 --- a/NeuralNetwok/predict.csv +++ b/NeuralNetwok/predict.csv @@ -1,6 +1,5 @@ 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 -5.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 @@ -24,7 +23,6 @@ 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 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license](https://img.shields.io/dub/l/vibe-d.svg)](https://github.com/lawlite19/MachineLearning_Python/blob/master/LICENSE) + + ## 目录 * [机器学习算法Python实现](#机器学习算法python实现) * [一、线性回归](#一-线性回归) From 01d568878e1f49d3d983e78039442ce72bb90862 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Fri, 8 Dec 2017 10:40:59 +0800 Subject: [PATCH 30/42] =?UTF-8?q?:memo:=20=E4=BF=AE=E6=94=B9=E7=A5=9E?= =?UTF-8?q?=E7=BB=8F=E7=BD=91=E7=BB=9C=E9=83=A8=E5=88=86bug?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- LinearRegression/LinearRegression.py | 4 +- NeuralNetwok/NeuralNetwork.py | 24 +- NeuralNetwok/predict.csv | 588 +++++++++++++-------------- readme.md | 2 +- 4 files changed, 312 insertions(+), 306 deletions(-) diff --git a/LinearRegression/LinearRegression.py b/LinearRegression/LinearRegression.py index 3c1ae46..cc3a229 100644 --- a/LinearRegression/LinearRegression.py +++ b/LinearRegression/LinearRegression.py @@ -96,8 +96,8 @@ def plotJ(J_history,num_iters): # 测试linearRegression函数 def testLinearRegression(): mu,sigma,theta = linearRegression(0.01,400) - print u"\n计算的theta值为:\n",theta - print u"\n预测结果为:%f"%predict(mu, sigma, theta) + #print u"\n计算的theta值为:\n",theta + #print u"\n预测结果为:%f"%predict(mu, sigma, theta) # 测试学习效果(预测) def predict(mu,sigma,theta): diff --git a/NeuralNetwok/NeuralNetwork.py b/NeuralNetwok/NeuralNetwork.py index 923a85b..f728212 100644 --- a/NeuralNetwok/NeuralNetwork.py +++ b/NeuralNetwok/NeuralNetwork.py @@ -43,7 +43,7 @@ def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer): initial_nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1))) #展开theta #np.savetxt("testTheta.csv",initial_nn_params,delimiter=",") start = time.time() - result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda)) + result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda), maxiter=100) print (u'执行时间:',time.time()-start) print (result) '''可视化 Theta1''' @@ -124,14 +124,16 @@ def nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,L h = sigmoid(z3) '''代价''' J = -(np.dot(np.transpose(class_y.reshape(-1,1)),np.log(h.reshape(-1,1)))+np.dot(np.transpose(1-class_y.reshape(-1,1)),np.log(1-h.reshape(-1,1)))-Lambda*term/2)/m - + #temp1 = (h.reshape(-1,1)-class_y.reshape(-1,1)) + #temp2 = (temp1**2).sum() + #J = 1/(2*m)*temp2 return np.ravel(J) # 梯度 def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda): length = nn_params.shape[0] - Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1) - Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1) + Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1).copy() # 这里使用copy函数,否则下面修改Theta的值,nn_params也会一起修改 + Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1).copy() m = X.shape[0] class_y = np.zeros((m,num_labels)) # 数据的y对应0-9,需要映射为0/1的关系 # 映射y @@ -146,9 +148,8 @@ def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambd Theta1_grad = np.zeros((Theta1.shape)) #第一层到第二层的权重 Theta2_grad = np.zeros((Theta2.shape)) #第二层到第三层的权重 - - Theta1[:,0] = 0; - Theta2[:,0] = 0; + + '''正向传播,每次需要补上一列1的偏置bias''' a1 = np.hstack((np.ones((m,1)),X)) z2 = np.dot(a1,np.transpose(Theta1)) @@ -157,15 +158,19 @@ def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambd z3 = np.dot(a2,np.transpose(Theta2)) h = sigmoid(z3) + '''反向传播,delta为误差,''' delta3 = np.zeros((m,num_labels)) delta2 = np.zeros((m,hidden_layer_size)) for i in range(m): - delta3[i,:] = h[i,:]-class_y[i,:] + #delta3[i,:] = (h[i,:]-class_y[i,:])*sigmoidGradient(z3[i,:]) # 均方误差的误差率 + delta3[i,:] = h[i,:]-class_y[i,:] # 交叉熵误差率 Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3[i,:].reshape(1,-1)),a2[i,:].reshape(1,-1)) delta2[i,:] = np.dot(delta3[i,:].reshape(1,-1),Theta2_x)*sigmoidGradient(z2[i,:]) Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2[i,:].reshape(1,-1)),a1[i,:].reshape(1,-1)) + Theta1[:,0] = 0 + Theta2[:,0] = 0 '''梯度''' grad = (np.vstack((Theta1_grad.reshape(-1,1),Theta2_grad.reshape(-1,1)))+Lambda*np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1))))/m return np.ravel(grad) @@ -223,6 +228,7 @@ def checkGradient(Lambda = 0): step[i]=0 # 显示两列比较 res = np.hstack((num_grad.reshape(-1,1),grad.reshape(-1,1))) + print("检查梯度的结果,第一列为数值法计算得到的,第二列为BP得到的:") print (res) # 初始化调试的theta权重 @@ -256,5 +262,5 @@ def predict(Theta1,Theta2,X): return p if __name__ == "__main__": - #checkGradient() + checkGradient() neuralNetwork(400, 25, 10) \ No newline at end of file diff --git a/NeuralNetwok/predict.csv b/NeuralNetwok/predict.csv index 42610e0..4368d95 100644 --- a/NeuralNetwok/predict.csv +++ b/NeuralNetwok/predict.csv @@ -99,7 +99,6 @@ 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 -5.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 @@ -107,10 +106,8 @@ 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 -5.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 -3.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 0.000000000000000000e+00,0.000000000000000000e+00 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-5.000000000000000000e+00,9.000000000000000000e+00 +9.000000000000000000e+00,9.000000000000000000e+00 9.000000000000000000e+00,9.000000000000000000e+00 9.000000000000000000e+00,9.000000000000000000e+00 diff --git a/readme.md b/readme.md index b9127d2..1a013c9 100644 --- a/readme.md +++ b/readme.md @@ -547,7 +547,7 @@ def nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,L - ![{\delta ^{(3)}} = {({\theta ^{(3)}})^T}{\delta ^{(4)}}.*{g^}({a^{(3)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Cdelta%20%5E%7B%283%29%7D%7D%20%3D%20%7B%28%7B%5Ctheta%20%5E%7B%283%29%7D%7D%29%5ET%7D%7B%5Cdelta%20%5E%7B%284%29%7D%7D.%2A%7Bg%5E%7D%28%7Ba%5E%7B%283%29%7D%7D%29) - ![{\delta ^{(2)}} = {({\theta ^{(2)}})^T}{\delta ^{(3)}}.*{g^}({a^{(2)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Cdelta%20%5E%7B%282%29%7D%7D%20%3D%20%7B%28%7B%5Ctheta%20%5E%7B%282%29%7D%7D%29%5ET%7D%7B%5Cdelta%20%5E%7B%283%29%7D%7D.%2A%7Bg%5E%7D%28%7Ba%5E%7B%282%29%7D%7D%29) - 没有![{\delta ^{(1)}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Cdelta%20%5E%7B%281%29%7D%7D),因为对于输入没有误差 -- 因为S型函数![{\text{g(z)}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctext%7Bg%28z%29%7D%7D)的倒数为:![{g^}(z){\text{ = g(z)(1 - g(z))}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28z%29%7B%5Ctext%7B%20%3D%20g%28z%29%281%20-%20g%28z%29%29%7D%7D),所以上面的![{g^}({a^{(3)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28%7Ba%5E%7B%283%29%7D%7D%29)和![{g^}({a^{(2)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28%7Ba%5E%7B%282%29%7D%7D%29)可以在前向传播中计算出来 +- 因为S型函数![{\text{g(z)}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctext%7Bg%28z%29%7D%7D)的导数为:![{g^}(z){\text{ = g(z)(1 - g(z))}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28z%29%7B%5Ctext%7B%20%3D%20g%28z%29%281%20-%20g%28z%29%29%7D%7D),所以上面的![{g^}({a^{(3)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28%7Ba%5E%7B%283%29%7D%7D%29)和![{g^}({a^{(2)}})](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bg%5E%7D%28%7Ba%5E%7B%282%29%7D%7D%29)可以在前向传播中计算出来 - 反向传播计算梯度的过程为: - ![\Delta _{ij}^{(l)} = 0](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5CDelta%20_%7Bij%7D%5E%7B%28l%29%7D%20%3D%200)(![\Delta ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5CDelta%20)是大写的![\delta ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cdelta%20)) From 7eac77f7446a0c69bfb1a8be7da405895409d131 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Fri, 8 Dec 2017 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nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,L # 梯度 def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda): length = nn_params.shape[0] - Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1) - Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1) + Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1).copy() # 这里使用copy函数,否则下面修改Theta的值,nn_params也会一起修改 + Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1).copy() m = X.shape[0] class_y = np.zeros((m,num_labels)) # 数据的y对应0-9,需要映射为0/1的关系 # 映射y @@ -581,9 +581,8 @@ def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambd Theta1_grad = np.zeros((Theta1.shape)) #第一层到第二层的权重 Theta2_grad = np.zeros((Theta2.shape)) #第二层到第三层的权重 - - Theta1[:,0] = 0; - Theta2[:,0] = 0; + + '''正向传播,每次需要补上一列1的偏置bias''' a1 = np.hstack((np.ones((m,1)),X)) z2 = np.dot(a1,np.transpose(Theta1)) @@ -592,15 +591,19 @@ def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambd z3 = np.dot(a2,np.transpose(Theta2)) h = sigmoid(z3) + '''反向传播,delta为误差,''' delta3 = np.zeros((m,num_labels)) delta2 = np.zeros((m,hidden_layer_size)) for i in range(m): - delta3[i,:] = h[i,:]-class_y[i,:] + #delta3[i,:] = (h[i,:]-class_y[i,:])*sigmoidGradient(z3[i,:]) # 均方误差的误差率 + delta3[i,:] = h[i,:]-class_y[i,:] # 交叉熵误差率 Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3[i,:].reshape(1,-1)),a2[i,:].reshape(1,-1)) delta2[i,:] = np.dot(delta3[i,:].reshape(1,-1),Theta2_x)*sigmoidGradient(z2[i,:]) Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2[i,:].reshape(1,-1)),a1[i,:].reshape(1,-1)) + Theta1[:,0] = 0 + Theta2[:,0] = 0 '''梯度''' grad = (np.vstack((Theta1_grad.reshape(-1,1),Theta2_grad.reshape(-1,1)))+Lambda*np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1))))/m return np.ravel(grad) From e7b815f4043e06b7162a8730ac391616eb920766 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Tue, 2 Jan 2018 11:21:08 +0800 Subject: [PATCH 32/42] =?UTF-8?q?:memo:=20svm=E5=8F=AF=E8=A7=86=E5=8C=96?= =?UTF-8?q?=E8=BE=B9=E7=95=8Cfix?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- SVM/SVM_scikit-learn.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/SVM/SVM_scikit-learn.py b/SVM/SVM_scikit-learn.py index 3cdbb6a..43ba3df 100644 --- a/SVM/SVM_scikit-learn.py +++ b/SVM/SVM_scikit-learn.py @@ -46,7 +46,7 @@ def plot_decisionBoundary(X,y,model,class_='linear'): if class_=='linear': w = model.coef_ b = model.intercept_ - xp = np.linspace(np.min(X[:,0]),np.max(X[:,1]),100) + xp = np.linspace(np.min(X[:,0]),np.max(X[:,0]),100) yp = -(w[0,0]*xp+b)/w[0,1] plt.plot(xp,yp,'b-',linewidth=2.0) plt.show() From 0fe8d2e80db49ef529b3f3b9a1cdbda7cff7460f Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Thu, 4 Jan 2018 18:54:06 +0800 Subject: [PATCH 33/42] :memo: fix an error of NN --- NeuralNetwok/NeuralNetwork.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/NeuralNetwok/NeuralNetwork.py b/NeuralNetwok/NeuralNetwork.py index f728212..7929ad7 100644 --- a/NeuralNetwok/NeuralNetwork.py +++ b/NeuralNetwok/NeuralNetwork.py @@ -205,7 +205,7 @@ def checkGradient(Lambda = 0): initial_Theta1 = debugInitializeWeights(input_layer_size,hidden_layer_size); initial_Theta2 = debugInitializeWeights(hidden_layer_size,num_labels) X = debugInitializeWeights(input_layer_size-1,m) - y = 1+np.transpose(np.mod(np.arange(1,m+1), num_labels))# 初始化y + y = np.transpose(np.mod(np.arange(1,m+1), num_labels))# 初始化y y = y.reshape(-1,1) nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1))) #展开theta From 202ff3b0c04203fb9e74856d597f0318dbc825bc Mon Sep 17 00:00:00 2001 From: cclauss Date: Thu, 4 Jan 2018 12:22:59 +0100 Subject: [PATCH 34/42] Modernize Python 2 code to get ready for Python 3 --- AnomalyDetection/AnomalyDetection.py | 5 +-- K-Means/K-Menas.py | 15 +++++---- LinearRegression/LinearRegression.py | 7 ++-- .../LinearRegression_scikit-learn.py | 9 ++--- LogisticRegression/LogisticRegression.py | 5 +-- .../LogisticRegression_OneVsAll.py | 3 +- ...ogisticRegression_OneVsAll_scikit-learn.py | 3 +- .../LogisticRegression_scikit-learn.py | 33 +++++++++---------- 8 files changed, 43 insertions(+), 37 deletions(-) diff --git a/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py index 31bfa48..13f74a7 100644 --- a/AnomalyDetection/AnomalyDetection.py +++ b/AnomalyDetection/AnomalyDetection.py @@ -1,6 +1,7 @@ #-*- coding: utf-8 -*- # Author: Bob # Date: 2016.12.22 +from __future__ import print_function import numpy as np from matplotlib import pyplot as plt from scipy import io as spio @@ -25,8 +26,8 @@ def anomalyDetection_example(): yval = data['yval'] # y=1代表异常 pval = multivariateGaussian(Xval, mu, sigma2) # 计算CV上的概率密度值 epsilon,F1 = selectThreshold(yval,pval) # 选择最优的epsilon临界值 - print u'在CV上得到的最好的epsilon是:%e'%epsilon - print u'对应的F1Score值为:%f'%F1 + print(u'在CV上得到的最好的epsilon是:%e'%epsilon) + print(u'对应的F1Score值为:%f'%F1) outliers = np.where(p Date: Thu, 4 Jan 2018 12:33:24 +0100 Subject: [PATCH 35/42] # -*- coding: utf-8 -*- --- .../LogisticRegression_scikit-learn.py | 18 ++++++++++-------- 1 file changed, 10 insertions(+), 8 deletions(-) diff --git a/LogisticRegression/LogisticRegression_scikit-learn.py b/LogisticRegression/LogisticRegression_scikit-learn.py index d7f4a89..200abbb 100644 --- a/LogisticRegression/LogisticRegression_scikit-learn.py +++ b/LogisticRegression/LogisticRegression_scikit-learn.py @@ -1,3 +1,5 @@ +# -*- coding: utf-8 -*- + from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler from sklearn.cross_validation import train_test_split @@ -8,32 +10,32 @@ def logisticRegression(): X = data[:,0:-1] y = data[:,-1] - # ����Ϊѵ�����Ͳ��Լ� + # 划分为训练集和测试集 x_train,x_test,y_train,y_test = train_test_split(X,y,test_size=0.2) - # ��һ�� + # 归一化 scaler = StandardScaler() scaler.fit(x_train) x_train = scaler.fit_transform(x_train) x_test = scaler.fit_transform(x_test) - #�߼��ع� + # 逻辑回归 model = LogisticRegression() model.fit(x_train,y_train) - # Ԥ�� + # 预测 predict = model.predict(x_test) right = sum(predict == y_test) - predict = np.hstack((predict.reshape(-1,1),y_test.reshape(-1,1))) # ��Ԥ��ֵ����ʵֵ����һ�飬�ù۲� + predict = np.hstack((predict.reshape(-1,1),y_test.reshape(-1,1))) # 将预测值和真实值放在一块,好观察 print(predict) - print('���Լ�׼ȷ�ʣ�%f%%'%(right*100.0/predict.shape[0])) #�����ڲ��Լ��ϵ�׼ȷ�� + print('测试集准确率:%f%%'%(right*100.0/predict.shape[0])) # 计算在测试集上的准确度 -# ����txt��csv�ļ� +# 加载txt和csv文件 def loadtxtAndcsv_data(fileName,split,dataType): return np.loadtxt(fileName,delimiter=split,dtype=dataType) -# ����npy�ļ� +# 加载npy文件 def loadnpy_data(fileName): return np.load(fileName) From d8bd5f1f1ad4170336332205519daca9b52d2ac4 Mon Sep 17 00:00:00 2001 From: lawlite19 <849451478@qq.com> Date: Mon, 12 Mar 2018 11:23:20 +0800 Subject: [PATCH 36/42] =?UTF-8?q?:bug:=20fix=E5=BC=82=E5=B8=B8=E6=A3=80?= =?UTF-8?q?=E6=B5=8BF1Score=E8=AE=A1=E7=AE=97?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- AnomalyDetection/AnomalyDetection.py | 16 ++++++++-------- readme.md | 6 +++--- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py index 31bfa48..642b452 100644 --- a/AnomalyDetection/AnomalyDetection.py +++ b/AnomalyDetection/AnomalyDetection.py @@ -15,9 +15,9 @@ def anomalyDetection_example(): plt.show() '''多元高斯分布函数,并可视化拟合的边界''' mu,sigma2 = estimateGaussian(X) # 参数估计(求均值和方差) - #print mu,sigma2 + #print (mu,sigma2) p = multivariateGaussian(X,mu,sigma2) # 多元高斯分布函数 - #print p + #print (p) visualizeFit(X,mu,sigma2) # 显示图像 '''选择异常点(在交叉验证CV上训练得到最好的epsilon)''' @@ -25,8 +25,8 @@ def anomalyDetection_example(): yval = data['yval'] # y=1代表异常 pval = multivariateGaussian(Xval, mu, sigma2) # 计算CV上的概率密度值 epsilon,F1 = selectThreshold(yval,pval) # 选择最优的epsilon临界值 - print u'在CV上得到的最好的epsilon是:%e'%epsilon - print u'对应的F1Score值为:%f'%F1 + print (u'在CV上得到的最好的epsilon是:%e'%epsilon) + print (u'对应的F1Score值为:%f'%F1) outliers = np.where(p Date: Wed, 16 May 2018 09:53:34 +0800 Subject: [PATCH 37/42] =?UTF-8?q?fix=20=E6=A2=AF=E5=BA=A6=E4=B8=8B?= =?UTF-8?q?=E9=99=8D=E5=85=AC=E5=BC=8F?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/readme.md b/readme.md index f0ffee1..a982f17 100644 --- a/readme.md +++ b/readme.md @@ -105,7 +105,7 @@ def computerCost(X,y,theta): - 假设函数`f(x)` - 泰勒展开:`f(x+△x)=f(x)+f'(x)*△x+o(△x)` - 令:`△x=-α*f'(x)` ,即负梯度方向乘以一个很小的步长`α` - - 将`△x`代入泰勒展开式中:`f(x+x)=f(x)-α*[f'(x)]²+o(△x)` + - 将`△x`代入泰勒展开式中:`f(x+△x)=f(x)-α*[f'(x)]²+o(△x)` - 可以看出,`α`是取得很小的正数,`[f'(x)]²`也是正数,所以可以得出:`f(x+△x)<=f(x)` - 所以沿着**负梯度**放下,函数在减小,多维情况一样。 - 实现代码 From eb27bf95cfc2e82e83f255870a8f2e8717416aec Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Sat, 29 Sep 2018 00:34:27 +0800 Subject: [PATCH 38/42] :memo: some updates --- .../LogisticRegression_scikit-learn.py | 3 +- SVM/SVM_scikit-learn.py | 84 +++++++++---------- 2 files changed, 43 insertions(+), 44 deletions(-) diff --git a/LogisticRegression/LogisticRegression_scikit-learn.py b/LogisticRegression/LogisticRegression_scikit-learn.py index 200abbb..2630453 100644 --- a/LogisticRegression/LogisticRegression_scikit-learn.py +++ b/LogisticRegression/LogisticRegression_scikit-learn.py @@ -2,7 +2,8 @@ from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler -from sklearn.cross_validation import train_test_split +# from sklearn.cross_validation import train_test_split # 0.18版本之后废弃 +from sklearn.model_selection import train_test_split import numpy as np def logisticRegression(): diff --git a/SVM/SVM_scikit-learn.py b/SVM/SVM_scikit-learn.py index 43ba3df..5b81c7c 100644 --- a/SVM/SVM_scikit-learn.py +++ b/SVM/SVM_scikit-learn.py @@ -1,71 +1,69 @@ +#-*- coding: utf-8 -*- import numpy as np from scipy import io as spio from matplotlib import pyplot as plt from sklearn import svm + def SVM(): - '''data1Է''' + '''data1——线性分类''' data1 = spio.loadmat('data1.mat') X = data1['X'] y = data1['y'] y = np.ravel(y) - plot_data(X,y) - - model = svm.SVC(C=1.0,kernel='linear').fit(X,y) # ָ˺ΪԺ˺ - plot_decisionBoundary(X, y, model) # ߽߱ - '''data2Է''' + plot_data(X, y) + + model = svm.SVC(C=1.0, kernel='linear').fit(X, y) # 指定核函数为线性核函数 + plot_decisionBoundary(X, y, model) # 画决策边界 + '''data2——非线性分类''' data2 = spio.loadmat('data2.mat') X = data2['X'] y = data2['y'] y = np.ravel(y) - plt = plot_data(X,y) + plt = plot_data(X, y) plt.show() - - model = svm.SVC(gamma=100).fit(X,y) # gammaΪ˺ϵֵԽϵԽ - plot_decisionBoundary(X, y, model,class_='notLinear') # ߽߱ - - - -# ͼ -def plot_data(X,y): - plt.figure(figsize=(10,8)) - pos = np.where(y==1) # ҵy=1λ - neg = np.where(y==0) # ҵy=0λ - p1, = plt.plot(np.ravel(X[pos,0]),np.ravel(X[pos,1]),'ro',markersize=8) - p2, = plt.plot(np.ravel(X[neg,0]),np.ravel(X[neg,1]),'g^',markersize=8) + + model = svm.SVC(gamma=100).fit(X, y) # gamma为核函数的系数,值越大拟合的越好 + plot_decisionBoundary(X, y, model, class_='notLinear') # 画决策边界 + + +# 作图 +def plot_data(X, y): + plt.figure(figsize=(10, 8)) + pos = np.where(y == 1) # 找到y=1的位置 + neg = np.where(y == 0) # 找到y=0的位置 + p1, = plt.plot(np.ravel(X[pos, 0]), np.ravel(X[pos, 1]), 'ro', markersize=8) + p2, = plt.plot(np.ravel(X[neg, 0]), np.ravel(X[neg, 1]), 'g^', markersize=8) plt.xlabel("X1") plt.ylabel("X2") - plt.legend([p1,p2],["y==1","y==0"]) + plt.legend([p1, p2], ["y==1", "y==0"]) return plt - -# ߽߱ -def plot_decisionBoundary(X,y,model,class_='linear'): + + +# 画决策边界 +def plot_decisionBoundary(X, y, model, class_='linear'): plt = plot_data(X, y) - - # Ա߽ - if class_=='linear': + + # 线性边界 + if class_ == 'linear': w = model.coef_ b = model.intercept_ - xp = np.linspace(np.min(X[:,0]),np.max(X[:,0]),100) - yp = -(w[0,0]*xp+b)/w[0,1] - plt.plot(xp,yp,'b-',linewidth=2.0) + xp = np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100) + yp = -(w[0, 0] * xp + b) / w[0, 1] + plt.plot(xp, yp, 'b-', linewidth=2.0) plt.show() - else: # Ա߽ - x_1 = np.transpose(np.linspace(np.min(X[:,0]),np.max(X[:,0]),100).reshape(1,-1)) - x_2 = np.transpose(np.linspace(np.min(X[:,1]),np.max(X[:,1]),100).reshape(1,-1)) - X1,X2 = np.meshgrid(x_1,x_2) + else: # 非线性边界 + x_1 = np.transpose(np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100).reshape(1, -1)) + x_2 = np.transpose(np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 100).reshape(1, -1)) + X1, X2 = np.meshgrid(x_1, x_2) vals = np.zeros(X1.shape) for i in range(X1.shape[1]): - this_X = np.hstack((X1[:,i].reshape(-1,1),X2[:,i].reshape(-1,1))) - vals[:,i] = model.predict(this_X) - - plt.contour(X1,X2,vals,[0,1],color='blue') + this_X = np.hstack((X1[:, i].reshape(-1, 1), X2[:, i].reshape(-1, 1))) + vals[:, i] = model.predict(this_X) + + plt.contour(X1, X2, vals, [0, 1], color='blue') plt.show() - if __name__ == "__main__": - SVM() - - - \ No newline at end of file + SVM() \ No newline at end of file From 4f71b0cd8ada920a78a07b20b502b4e3e16d245e Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Sat, 29 Sep 2018 10:04:46 +0800 Subject: [PATCH 39/42] fix logisticRegression_scikit-learn.py --- .gitignore | 2 ++ LogisticRegression/LogisticRegression_scikit-learn.py | 2 +- readme.md | 1 - 3 files changed, 3 insertions(+), 2 deletions(-) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..ae945fa --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +.idea/ +venv/ diff --git a/LogisticRegression/LogisticRegression_scikit-learn.py b/LogisticRegression/LogisticRegression_scikit-learn.py index 2630453..37905cf 100644 --- a/LogisticRegression/LogisticRegression_scikit-learn.py +++ b/LogisticRegression/LogisticRegression_scikit-learn.py @@ -16,7 +16,7 @@ def logisticRegression(): # 归一化 scaler = StandardScaler() - scaler.fit(x_train) + # scaler.fit(x_train) x_train = scaler.fit_transform(x_train) x_test = scaler.fit_transform(x_test) diff --git a/readme.md b/readme.md index a982f17..5a29ac6 100644 --- a/readme.md +++ b/readme.md @@ -313,7 +313,6 @@ import numpy as np ``` # 归一化 scaler = StandardScaler() - scaler.fit(x_train) x_train = scaler.fit_transform(x_train) x_test = scaler.fit_transform(x_test) ``` From 5aeddce19286640becfcded59faf589453eba89e Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Wed, 7 Nov 2018 15:56:47 +0800 Subject: [PATCH 40/42] :memo: fix catalog of readme --- readme.md | 127 +++++++++++++++++++++++++++--------------------------- 1 file changed, 63 insertions(+), 64 deletions(-) diff --git a/readme.md b/readme.md index 5a29ac6..421901b 100644 --- a/readme.md +++ b/readme.md @@ -3,73 +3,72 @@ [![MIT license](https://img.shields.io/dub/l/vibe-d.svg)](https://github.com/lawlite19/MachineLearning_Python/blob/master/LICENSE) - ## 目录 * [机器学习算法Python实现](#机器学习算法python实现) - * [一、线性回归](#一-线性回归) - * [1、代价函数](#1-代价函数) - * [2、梯度下降算法](#2-梯度下降算法) - * [3、均值归一化](#3-均值归一化) - * [4、最终运行结果](#4-最终运行结果) - * [5、使用scikit-learn库中的线性模型实现](#5-使用scikit-learn库中的线性模型实现) - * [二、逻辑回归](#二-逻辑回归) - * [1、代价函数](#1-代价函数) - * [2、梯度](#2-梯度) - * [3、正则化](#3-正则化) - * [4、S型函数(即)](#4-s型函数即) - * [5、映射为多项式](#5-映射为多项式) - * [6、使用的优化方法](#6-使用的优化方法) - * [7、运行结果](#7-运行结果) - * [8、使用scikit-learn库中的逻辑回归模型实现](#8-使用scikit-learn库中的逻辑回归模型实现) + * [一、线性回归](#一线性回归) + * [1、代价函数](#1代价函数) + * [2、梯度下降算法](#2梯度下降算法) + * [3、均值归一化](#3均值归一化) + * [4、最终运行结果](#4最终运行结果) + * [5、使用scikit-learn库中的线性模型实现](#5使用scikit-learn库中的线性模型实现) + * [二、逻辑回归](#二逻辑回归) + * [1、代价函数](#1代价函数) + * [2、梯度](#2梯度) + * [3、正则化](#3正则化) + * [4、S型函数(即)](#4s型函数即) + * [5、映射为多项式](#5映射为多项式) + * [6、使用的优化方法](#6使用的优化方法) + * [7、运行结果](#7运行结果) + * [8、使用scikit-learn库中的逻辑回归模型实现](#8使用scikit-learn库中的逻辑回归模型实现) * [逻辑回归_手写数字识别_OneVsAll](#逻辑回归_手写数字识别_onevsall) - * [1、随机显示100个数字](#1-随机显示100个数字) - * [2、OneVsAll](#2-onevsall) - * [3、手写数字识别](#3-手写数字识别) - * [4、预测](#4-预测) - * [5、运行结果](#5-运行结果) - * [6、使用scikit-learn库中的逻辑回归模型实现](#6-使用scikit-learn库中的逻辑回归模型实现) - * [三、BP神经网络](#三-bp神经网络) - * [1、神经网络model](#1-神经网络model) - * [2、代价函数](#2-代价函数) - * [3、正则化](#3-正则化) - * [4、反向传播BP](#4-反向传播bp) - * [5、BP可以求梯度的原因](#5-bp可以求梯度的原因) - * [6、梯度检查](#6-梯度检查) - * [7、权重的随机初始化](#7-权重的随机初始化) - * [8、预测](#8-预测) - * [9、输出结果](#9-输出结果) - * [四、SVM支持向量机](#四-svm支持向量机) - * [1、代价函数](#1-代价函数) - * [2、Large Margin](#2-large-margin) - * [3、SVM Kernel(核函数)](#3-svm-kernel核函数) - * [4、使用中的模型代码](#4-使用中的模型代码) - * [5、运行结果](#5-运行结果) - * [五、K-Means聚类算法](#五-k-means聚类算法) - * [1、聚类过程](#1-聚类过程) - * [2、目标函数](#2-目标函数) - * [3、聚类中心的选择](#3-聚类中心的选择) - * [4、聚类个数K的选择](#4-聚类个数k的选择) - * [5、应用——图片压缩](#5-应用图片压缩) - * [6、使用scikit-learn库中的线性模型实现聚类](#6-使用scikit-learn库中的线性模型实现聚类) - * [7、运行结果](#7-运行结果) - * [六、PCA主成分分析(降维)](#六-pca主成分分析降维) - * [1、用处](#1-用处) - * [2、2D-->1D,nD-->kD](#2-2d-1dnd-kd) - * [3、主成分分析PCA与线性回归的区别](#3-主成分分析pca与线性回归的区别) - * [4、PCA降维过程](#4-pca降维过程) - * [5、数据恢复](#5-数据恢复) - * [6、主成分个数的选择(即要降的维度)](#6-主成分个数的选择即要降的维度) - * [7、使用建议](#7-使用建议) - * [8、运行结果](#8-运行结果) - * [9、使用scikit-learn库中的PCA实现降维](#9-使用scikit-learn库中的pca实现降维) - * [七、异常检测 Anomaly Detection](#七-异常检测-anomaly-detection) - * [1、高斯分布(正态分布)](#1-高斯分布正态分布) - * [2、异常检测算法](#2-异常检测算法) - * [3、评价的好坏,以及的选取](#3-评价的好坏以及的选取) - * [4、选择使用什么样的feature(单元高斯分布)](#4-选择使用什么样的feature单元高斯分布) - * [5、多元高斯分布](#5-多元高斯分布) - * [6、单元和多元高斯分布特点](#6-单元和多元高斯分布特点) - * [7、程序运行结果](#7-程序运行结果) + * [1、随机显示100个数字](#1随机显示100个数字) + * [2、OneVsAll](#2onevsall) + * [3、手写数字识别](#3手写数字识别) + * [4、预测](#4预测) + * [5、运行结果](#5运行结果) + * [6、使用scikit-learn库中的逻辑回归模型实现](#6使用scikit-learn库中的逻辑回归模型实现) + * [三、BP神经网络](#三bp神经网络) + * [1、神经网络model](#1神经网络model) + * [2、代价函数](#2代价函数) + * [3、正则化](#3正则化) + * [4、反向传播BP](#4反向传播bp) + * [5、BP可以求梯度的原因](#5bp可以求梯度的原因) + * [6、梯度检查](#6梯度检查) + * [7、权重的随机初始化](#7权重的随机初始化) + * [8、预测](#8预测) + * [9、输出结果](#9输出结果) + * [四、SVM支持向量机](#四svm支持向量机) + * [1、代价函数](#1代价函数) + * [2、Large Margin](#2large-margin) + * [3、SVM Kernel(核函数)](#3svm-kernel核函数) + * [4、使用中的模型代码](#4使用中的模型代码) + * [5、运行结果](#5运行结果) + * [五、K-Means聚类算法](#五k-means聚类算法) + * [1、聚类过程](#1聚类过程) + * [2、目标函数](#2目标函数) + * [3、聚类中心的选择](#3聚类中心的选择) + * [4、聚类个数K的选择](#4聚类个数k的选择) + * [5、应用——图片压缩](#5应用图片压缩) + * [6、使用scikit-learn库中的线性模型实现聚类](#6使用scikit-learn库中的线性模型实现聚类) + * [7、运行结果](#7运行结果) + * [六、PCA主成分分析(降维)](#六pca主成分分析降维) + * [1、用处](#1用处) + * [2、2D-->1D,nD-->kD](#22d-1dnd-kd) + * [3、主成分分析PCA与线性回归的区别](#3主成分分析pca与线性回归的区别) + * [4、PCA降维过程](#4pca降维过程) + * [5、数据恢复](#5数据恢复) + * [6、主成分个数的选择(即要降的维度)](#6主成分个数的选择即要降的维度) + * [7、使用建议](#7使用建议) + * [8、运行结果](#8运行结果) + * [9、使用scikit-learn库中的PCA实现降维](#9使用scikit-learn库中的pca实现降维) + * [七、异常检测 Anomaly Detection](#七异常检测-anomaly-detection) + * [1、高斯分布(正态分布)](#1高斯分布正态分布) + * [2、异常检测算法](#2异常检测算法) + * [3、评价的好坏,以及的选取](#3评价的好坏以及的选取) + * [4、选择使用什么样的feature(单元高斯分布)](#4选择使用什么样的feature单元高斯分布) + * [5、多元高斯分布](#5多元高斯分布) + * [6、单元和多元高斯分布特点](#6单元和多元高斯分布特点) + * [7、程序运行结果](#7程序运行结果) ## 一、[线性回归](/LinearRegression) - [全部代码](/LinearRegression/LinearRegression.py) From fc954f68d8b2d89ed4463308873ebce0d22ddaa2 Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Wed, 7 Nov 2018 16:01:44 +0800 Subject: [PATCH 41/42] :memo: fix catalog of readme --- readme.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/readme.md b/readme.md index 421901b..9624fc3 100644 --- a/readme.md +++ b/readme.md @@ -17,7 +17,7 @@ * [3、正则化](#3正则化) * [4、S型函数(即)](#4s型函数即) * [5、映射为多项式](#5映射为多项式) - * [6、使用的优化方法](#6使用的优化方法) + * [6、使用的优化方法](#6使用scipy的优化方法) * [7、运行结果](#7运行结果) * [8、使用scikit-learn库中的逻辑回归模型实现](#8使用scikit-learn库中的逻辑回归模型实现) * [逻辑回归_手写数字识别_OneVsAll](#逻辑回归_手写数字识别_onevsall) @@ -41,7 +41,7 @@ * [1、代价函数](#1代价函数) * [2、Large Margin](#2large-margin) * [3、SVM Kernel(核函数)](#3svm-kernel核函数) - * [4、使用中的模型代码](#4使用中的模型代码) + * [4、使用中的模型代码](#4使用scikit-learn中的svm模型代码) * [5、运行结果](#5运行结果) * [五、K-Means聚类算法](#五k-means聚类算法) * [1、聚类过程](#1聚类过程) @@ -53,7 +53,7 @@ * [7、运行结果](#7运行结果) * [六、PCA主成分分析(降维)](#六pca主成分分析降维) * [1、用处](#1用处) - * [2、2D-->1D,nD-->kD](#22d-1dnd-kd) + * [2、2D-->1D,nD-->kD](#22d--1dnd--kd) * [3、主成分分析PCA与线性回归的区别](#3主成分分析pca与线性回归的区别) * [4、PCA降维过程](#4pca降维过程) * [5、数据恢复](#5数据恢复) @@ -62,9 +62,9 @@ * [8、运行结果](#8运行结果) * [9、使用scikit-learn库中的PCA实现降维](#9使用scikit-learn库中的pca实现降维) * [七、异常检测 Anomaly Detection](#七异常检测-anomaly-detection) - * [1、高斯分布(正态分布)](#1高斯分布正态分布) + * [1、高斯分布(正态分布)](#1高斯分布正态分布gaussian-distribution) * [2、异常检测算法](#2异常检测算法) - * [3、评价的好坏,以及的选取](#3评价的好坏以及的选取) + * [3、评价的好坏,以及的选取](#3评价px的好坏以及ε的选取) * [4、选择使用什么样的feature(单元高斯分布)](#4选择使用什么样的feature单元高斯分布) * [5、多元高斯分布](#5多元高斯分布) * [6、单元和多元高斯分布特点](#6单元和多元高斯分布特点) From f8d02fd9fb2bb8268076cc7d30ae86c49988caf7 Mon Sep 17 00:00:00 2001 From: lawlite <849451478@qq.com> Date: Wed, 16 Dec 2020 15:49:22 +0800 Subject: [PATCH 42/42] Create FUNDING.yml --- .github/FUNDING.yml | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 .github/FUNDING.yml diff --git a/.github/FUNDING.yml b/.github/FUNDING.yml new file mode 100644 index 0000000..4b16f59 --- /dev/null +++ b/.github/FUNDING.yml @@ -0,0 +1,12 @@ +# These are supported funding model platforms + +github: # Replace with up to 4 GitHub Sponsors-enabled usernames e.g., [user1, user2] +patreon: # Replace with a single Patreon username +open_collective: # Replace with a single Open Collective username +ko_fi: # Replace with a single Ko-fi username +tidelift: # Replace with a single Tidelift platform-name/package-name e.g., npm/babel +community_bridge: # Replace with a single Community Bridge project-name e.g., cloud-foundry +liberapay: # Replace with a single Liberapay username +issuehunt: # Replace with a single IssueHunt username +otechie: # Replace with a single Otechie username +custom: # Replace with up to 4 custom sponsorship URLs e.g., ['link1', 'link2']

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