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']
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/AnomalyDetection/AnomalyDetection.py b/AnomalyDetection/AnomalyDetection.py
index cbe293b..d481dc2 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
@@ -15,18 +16,18 @@ 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）'''
     Xval = data['Xval']
-    yval = data['yval']
+    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<epsilon)  # 找到小于临界值的异常点，并作图
     plt.plot(X[outliers,0],X[outliers,1],'o',markeredgecolor='r',markerfacecolor='w',markersize=10.)
     plt = display_2d_data(X, 'bx')
@@ -72,7 +73,7 @@ def visualizeFit(X,mu,sigma2):
     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)
+        #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)
             
@@ -88,9 +89,9 @@ def selectThreshold(yval,pval):
     '''计算'''
     for epsilon in np.arange(np.min(pval),np.max(pval),step):
         cvPrecision = pval<epsilon
-        tp = np.sum((cvPrecision == 1) & (yval == 1)).astype(float)  # sum求和是int型的，需要转为float
-        fp = np.sum((cvPrecision == 1) & (yval == 0)).astype(float)
-        fn = np.sum((cvPrecision == 1) & (yval == 0)).astype(float)
+        tp = np.sum((cvPrecision == 1) & (yval == 1).ravel()).astype(float)  # sum求和是int型的，需要转为float
+        fp = np.sum((cvPrecision == 1) & (yval == 0).ravel()).astype(float)
+        fn = np.sum((cvPrecision == 0) & (yval == 1).ravel()).astype(float)
         precision = tp/(tp+fp)  # 精准度
         recision = tp/(tp+fn)   # 召回率
         F1 = (2*precision*recision)/(precision+recision)  # F1Score计算公式
diff --git a/K-Means/K-Menas.py b/K-Means/K-Menas.py
index 0042fae..5f6493d 100644
--- a/K-Means/K-Menas.py
+++ b/K-Means/K-Menas.py
@@ -1,4 +1,5 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 import numpy as np
 from matplotlib import pyplot as plt
 from matplotlib import colors
@@ -11,7 +12,7 @@
 
 def KMeans():
     '''二维数据聚类过程演示'''
-    print u'聚类过程展示...\n'
+    print(u'聚类过程展示...\n')
     data = spio.loadmat("data.mat")
     X = data['X']
     K = 3   # 总类数
@@ -21,7 +22,7 @@ def KMeans():
     '''
     图片压缩
     '''
-    print u'K-Means压缩图片\n'
+    print(u'K-Means压缩图片\n')
     img_data = misc.imread("bird.png")  # 读取图片像素数据
     img_data = img_data/255.0             # 像素值映射到0-1
     img_size = img_data.shape
@@ -31,13 +32,13 @@ def KMeans():
     max_iters = 5
     initial_centroids = kMeansInitCentroids(X,K)
     centroids,idx = runKMeans(X, initial_centroids, max_iters, False)
-    print u'\nK-Means运行结束\n'
-    print u'\n压缩图片...\n'
+    print(u'\nK-Means运行结束\n')
+    print(u'\n压缩图片...\n')
     idx = findClosestCentroids(X, centroids)
     X_recovered = centroids[idx,:]
     X_recovered = X_recovered.reshape(img_size[0],img_size[1],3)
     
-    print u'绘制图片...\n'
+    print(u'绘制图片...\n')
     plt.subplot(1,2,1)
     plt.imshow(img_data)
     plt.title(u"原先图片",fontproperties=font)
@@ -45,7 +46,7 @@ def KMeans():
     plt.imshow(X_recovered)
     plt.title(u"压缩图像",fontproperties=font)
     plt.show()
-    print u'运行结束！'
+    print(u'运行结束！')
     
     
 # 找到每条数据距离哪个类中心最近    
@@ -86,7 +87,7 @@ def runKMeans(X,initial_centroids,max_iters,plot_process):
     idx = np.zeros((m,1))           # 每条数据属于哪个类
     
     for i in range(max_iters):      # 迭代次数
-        print u'迭代计算次数：%d'%(i+1)
+        print(u'迭代计算次数：%d'%(i+1))
         idx = findClosestCentroids(X, centroids)
         if plot_process:    # 如果绘制图像
             plt = plotProcessKMeans(X,centroids,previous_centroids) # 画聚类中心的移动过程
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.
diff --git a/LinearRegression/LinearRegression.py b/LinearRegression/LinearRegression.py
index 3c1ae46..c84e966 100644
--- a/LinearRegression/LinearRegression.py
+++ b/LinearRegression/LinearRegression.py
@@ -1,4 +1,5 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 import numpy as np
 from matplotlib import pyplot as plt
 from matplotlib.font_manager import FontProperties
@@ -6,7 +7,7 @@
 
 
 def linearRegression(alpha=0.01,num_iters=400):
-    print u"加载数据...\n"
+    print(u"加载数据...\n")
     
     data = loadtxtAndcsv_data("data.txt",",",np.float64)  #读取数据
     X = data[:,0:-1]      # X对应0到倒数第2列                  
@@ -19,7 +20,7 @@ def linearRegression(alpha=0.01,num_iters=400):
     
     X = np.hstack((np.ones((m,1)),X))    # 在X前加一列1
     
-    print u"\n执行梯度下降算法....\n"
+    print(u"\n执行梯度下降算法....\n")
     
     theta = np.zeros((col,1))
     y = y.reshape(-1,1)   #将行向量转化为列
@@ -73,7 +74,7 @@ def gradientDescent(X,y,theta,alpha,num_iters):
         temp[:,i] = theta - ((alpha/m)*(np.dot(np.transpose(X),h-y)))   #梯度的计算
         theta = temp[:,i]
         J_history[i] = computerCost(X,y,theta)      #调用计算代价函数
-        print '.',      
+        print('.', end=' ')      
     return theta,J_history  
 
 # 计算代价函数
@@ -96,8 +97,8 @@ 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/LinearRegression/LinearRegression_scikit-learn.py b/LinearRegression/LinearRegression_scikit-learn.py
index 172a7af..8036d58 100644
--- a/LinearRegression/LinearRegression_scikit-learn.py
+++ b/LinearRegression/LinearRegression_scikit-learn.py
@@ -1,10 +1,11 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 import numpy as np
 from sklearn import linear_model
 from sklearn.preprocessing import StandardScaler    #引入归一化的包
 
 def linearRegression():
-    print u"加载数据...\n"
+    print(u"加载数据...\n")
     data = loadtxtAndcsv_data("data.txt",",",np.float64)  #读取数据
     X = np.array(data[:,0:-1],dtype=np.float64)      # X对应0到倒数第2列                  
     y = np.array(data[:,-1],dtype=np.float64)        # y对应最后一列  
@@ -21,9 +22,9 @@ def linearRegression():
     
     #预测结果
     result = model.predict(x_test)
-    print model.coef_       # Coefficient of the features 决策函数中的特征系数
-    print model.intercept_  # 又名bias偏置,若设置为False，则为0
-    print result            # 预测结果
+    print(model.coef_)       # Coefficient of the features 决策函数中的特征系数
+    print(model.intercept_)  # 又名bias偏置,若设置为False，则为0
+    print(result)            # 预测结果
 
 
 # 加载txt和csv文件
diff --git a/LogisticRegression/LogisticRegression.py b/LogisticRegression/LogisticRegression.py
index b203b33..83a7ac9 100644
--- a/LogisticRegression/LogisticRegression.py
+++ b/LogisticRegression/LogisticRegression.py
@@ -1,4 +1,5 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 import numpy as np
 import matplotlib.pyplot as plt
 from scipy import optimize
@@ -19,7 +20,7 @@ def LogisticRegression():
     
     J = costFunction(initial_theta,X,y,initial_lambda)  #计算一下给定初始化的theta和lambda求出的代价J
     
-    print J  #输出一下计算的值，应该为0.693147
+    print(J)  #输出一下计算的值，应该为0.693147
     #result = optimize.fmin(costFunction, initial_theta, args=(X,y,initial_lambda))    #直接使用最小化的方法，效果不好
     '''调用scipy中的优化算法fmin_bfgs（拟牛顿法Broyden-Fletcher-Goldfarb-Shanno）
     - costFunction是自己实现的一个求代价的函数，
@@ -29,7 +30,7 @@ def LogisticRegression():
     '''
     result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda))    
     p = predict(X, result)   #预测
-    print u'在训练集上的准确度为%f%%'%np.mean(np.float64(p==y)*100)   # 与真实值比较，p==y返回True，转化为float   
+    print(u'在训练集上的准确度为%f%%'%np.mean(np.float64(p==y)*100))   # 与真实值比较，p==y返回True，转化为float   
     
     X = data[:,0:-1]
     y = data[:,-1]    
diff --git a/LogisticRegression/LogisticRegression_OneVsAll.py b/LogisticRegression/LogisticRegression_OneVsAll.py
index 9a2e950..7a9173a 100644
--- a/LogisticRegression/LogisticRegression_OneVsAll.py
+++ b/LogisticRegression/LogisticRegression_OneVsAll.py
@@ -1,4 +1,5 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 import numpy as np
 import matplotlib.pyplot as plt
 import scipy.io as spio
@@ -27,7 +28,7 @@ def logisticRegression_OneVsAll():
     #res = np.hstack((p,y.reshape(-1,1)))
     #np.savetxt("predict.csv", res, delimiter=',')
     
-    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))
      
 # 加载mat文件
 def loadmat_data(fileName):
diff --git a/LogisticRegression/LogisticRegression_OneVsAll_scikit-learn.py b/LogisticRegression/LogisticRegression_OneVsAll_scikit-learn.py
index 5d9374b..b304c08 100644
--- a/LogisticRegression/LogisticRegression_OneVsAll_scikit-learn.py
+++ b/LogisticRegression/LogisticRegression_OneVsAll_scikit-learn.py
@@ -1,4 +1,5 @@
 #-*- coding: utf-8 -*-
+from __future__ import print_function
 from scipy import io as spio
 import numpy as np
 from sklearn import svm
@@ -17,7 +18,7 @@ def logisticRegression_oneVsAll():
     
     predict = model.predict(X) #预测
     
-    print u"预测准确度为：%f%%"%np.mean(np.float64(predict == y)*100)
+    print(u"预测准确度为：%f%%"%np.mean(np.float64(predict == y)*100))
 
 # 加载mat文件
 def loadmat_data(fileName):
diff --git a/LogisticRegression/LogisticRegression_scikit-learn.py b/LogisticRegression/LogisticRegression_scikit-learn.py
index 469c941..37905cf 100644
--- a/LogisticRegression/LogisticRegression_scikit-learn.py
+++ b/LogisticRegression/LogisticRegression_scikit-learn.py
@@ -1,43 +1,45 @@
+# -*- coding: utf-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():
-    data = loadtxtAndcsv_data("data1.txt", ",", np.float64) 
+    data = loadtxtAndcsv_data("data1.txt", ",", np.float64)
     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)
+    # 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�
-    print predict
-    print ('���Լ�׼ȷ�ʣ�%f%%'%(right*100.0/predict.shape[0]))          #�����ڲ��Լ��ϵ�׼ȷ��
 
-# ����txt��csv�ļ�
+    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('测试集准确率：%f%%'%(right*100.0/predict.shape[0]))          # 计算在测试集上的准确度
+
+# 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)
 
 
-
 if __name__ == "__main__":
-    logisticRegression()
\ No newline at end of file
+    logisticRegression()
diff --git a/NeuralNetwok/NeuralNetwork.py b/NeuralNetwok/NeuralNetwork.py
index 7434c31..7929ad7 100644
--- a/NeuralNetwok/NeuralNetwork.py
+++ b/NeuralNetwok/NeuralNetwork.py
@@ -43,9 +43,9 @@ 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))
-    print u'执行时间：',time.time()-start
-    print result
+    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'''
     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')
@@ -120,14 +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
@@ -142,9 +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))
@@ -153,15 +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)
@@ -196,7 +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 
@@ -219,7 +228,8 @@ 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("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
 def debugInitializeWeights(fan_in,fan_out):
@@ -252,5 +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 4d1087c..4368d95 100644
--- a/NeuralNetwok/predict.csv
+++ b/NeuralNetwok/predict.csv
@@ -24,7 +24,6 @@
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@@ -69,7 +68,6 @@
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@@ -87,7 +85,6 @@
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@@ -96,10 +93,8 @@
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@@ -110,7 +105,6 @@
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@@ -129,9 +123,7 @@
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@@ -140,7 +132,7 @@
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@@ -178,7 +170,6 @@
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@@ -205,7 +196,6 @@
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@@ -242,7 +232,6 @@
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@@ -263,7 +252,6 @@
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@@ -273,7 +261,6 @@
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@@ -314,7 +301,6 @@
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@@ -327,7 +313,6 @@
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@@ -339,7 +324,6 @@
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@@ -390,7 +371,6 @@
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@@ -406,7 +386,6 @@
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@@ -459,7 +438,6 @@
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@@ -486,7 +464,29 @@
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@@ -503,7 +503,7 @@
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diff --git a/SVM/SVM_scikit-learn.py b/SVM/SVM_scikit-learn.py
index 3cdbb6a..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():
-    '''data1�������Է���'''
+    '''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) # ָ���˺���Ϊ���Ժ˺���
-    plot_decisionBoundary(X, y, model)  # �����߽߱�
-    '''data2���������Է���'''
+    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�˺�����ϵ����ֵԽ����ϵ�Խ��
-    plot_decisionBoundary(X, y, model,class_='notLinear')   # �����߽߱�
-    
-    
-    
-# ��ͼ
-def plot_data(X,y):
-    plt.figure(figsize=(10,8))
-    pos = np.where(y==1)    # �ҵ�y=1��λ��
-    neg = np.where(y==0)    # �ҵ�y=0��λ��
-    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[:,1]),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
diff --git a/images/NeuralNetwork_05.png b/images/NeuralNetwork_05.png
index 72c4df3..241d2a0 100644
Binary files a/images/NeuralNetwork_05.png and b/images/NeuralNetwork_05.png differ
diff --git a/readme.md b/readme.md
index aee619e..9624fc3 100644
--- a/readme.md
+++ b/readme.md
@@ -1,6 +1,75 @@
 机器学习算法Python实现
 =========
 
+[![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）](#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)
+		* [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)
+		* [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)
+		* [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)
 
@@ -35,7 +104,7 @@ 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
@@ -243,7 +312,6 @@ 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)
 ```
@@ -477,7 +545,7 @@ 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)）
@@ -495,8 +563,8 @@ def 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
@@ -511,9 +579,8 @@ 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))
@@ -522,15 +589,19 @@ 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)
@@ -1088,9 +1159,9 @@ def selectThreshold(yval,pval):
     '''计算'''
     for epsilon in np.arange(np.min(pval),np.max(pval),step):
         cvPrecision = pval<epsilon
-        tp = np.sum((cvPrecision == 1) & (yval == 1)).astype(float)  # sum求和是int型的，需要转为float
-        fp = np.sum((cvPrecision == 1) & (yval == 0)).astype(float)
-        fn = np.sum((cvPrecision == 1) & (yval == 0)).astype(float)
+        tp = np.sum((cvPrecision == 1) & (yval == 1).ravel()).astype(float)  # sum求和是int型的，需要转为float
+        fp = np.sum((cvPrecision == 1) & (yval == 0).ravel()).astype(float)
+        fn = np.sum((cvPrecision == 0) & (yval == 1).ravel()).astype(float)
         precision = tp/(tp+fp)  # 精准度
         recision = tp/(tp+fn)   # 召回率
         F1 = (2*precision*recision)/(precision+recision)  # F1Score计算公式
@@ -1218,4 +1289,4 @@ 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"