Full Code of lawlite19/MachineLearning_Python for AI

Repository: lawlite19/MachineLearning_Python
Branch: master
Commit: f8d02fd9fb2b
Files: 45
Total size: 11.3 MB

Directory structure:
gitextract_y2eizqsm/

├── .github/
│   └── FUNDING.yml
├── .gitignore
├── AnomalyDetection/
│   ├── AnomalyDetection.py
│   ├── data1.mat
│   └── data2.mat
├── K-Means/
│   ├── K-Means_scikit-learn.py
│   ├── K-Menas.py
│   ├── bird.mat
│   └── data.mat
├── LICENSE
├── LinearRegression/
│   ├── LinearRegression.py
│   ├── LinearRegression_scikit-learn.py
│   ├── data.csv
│   ├── data.npy
│   └── data.txt
├── LogisticRegression/
│   ├── LogisticRegression.py
│   ├── LogisticRegression_OneVsAll.py
│   ├── LogisticRegression_OneVsAll_scikit-learn.py
│   ├── LogisticRegression_scikit-learn.py
│   ├── class_y.csv
│   ├── data1.npy
│   ├── data1.txt
│   ├── data2.txt
│   ├── data_digits.mat
│   └── predict.csv
├── NeuralNetwok/
│   ├── NeuralNetwork.py
│   ├── data_digits.mat
│   └── predict.csv
├── PCA/
│   ├── PCA.py
│   ├── PCA_scikit-learn.py
│   ├── data.mat
│   └── data_faces.mat
├── SVM/
│   ├── SVM_scikit-learn.py
│   ├── data.txt
│   ├── data1.mat
│   ├── data2.mat
│   └── data3.mat
├── formula/
│   ├── AnomalyDetection.wmf
│   ├── K-Means.wmf
│   ├── LinearRegression_01.wmf
│   ├── LogisticRegression_01.wmf
│   ├── NeuralNetwork.wmf
│   ├── PCA.wmf
│   └── SVM.wmf
└── readme.md

================================================
FILE CONTENTS
================================================

================================================
FILE: .github/FUNDING.yml
================================================
# 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']


================================================
FILE: .gitignore
================================================
.idea/
venv/


================================================
FILE: AnomalyDetection/AnomalyDetection.py
================================================
#-*- 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

'''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()
    '''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
    
    '''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']   # 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)
    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')
    plt.show()
    
    
    
    
# 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)
    '''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
    return p
    
# 可视化边界
def visualizeFit(X,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<epsilon
        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
        if F1 > bestF1:  # 修改最优的F1 Score
            bestF1 = F1
            bestEpsilon = epsilon
    return bestEpsilon,bestF1
        


if __name__ == '__main__':
    anomalyDetection_example()
    

================================================
FILE: K-Means/K-Means_scikit-learn.py
================================================
#-*- coding: utf-8 -*-
import numpy as np
from scipy import io as spio
from matplotlib import pyplot as plt
from sklearn.cluster import KMeans


def kMenas():
    data = spio.loadmat("data.mat")
    X = data['X']   
    model = KMeans(n_clusters=3).fit(X) # n_clusters指定3类，拟合数据
    centroids = model.cluster_centers_  # 聚类中心
    
    plt.scatter(X[:,0], X[:,1])     # 原数据的散点图
    plt.plot(centroids[:,0],centroids[:,1],'r^',markersize=10)  # 聚类中心
    plt.show()

if __name__ == "__main__":
    kMenas()


================================================
FILE: K-Means/K-Menas.py
================================================
#-*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
from matplotlib import pyplot as plt
from matplotlib import colors
from scipy import io as spio
from scipy import misc      # 图片操作
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)    # 解决windows环境下画图汉字乱码问题



def KMeans():
    '''二维数据聚类过程演示'''
    print(u'聚类过程展示...\n')
    data = spio.loadmat("data.mat")
    X = data['X']
    K = 3   # 总类数
    initial_centroids = np.array([[3,3],[6,2],[8,5]])   # 初始化类中心
    max_iters = 10
    runKMeans(X,initial_centroids,max_iters,True)       # 执行K-Means聚类算法
    '''
    图片压缩
    '''
    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
    X = img_data.reshape(img_size[0]*img_size[1],3)    # 调整为N*3的矩阵，N是所有像素点个数
    
    K = 16
    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')
    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')
    plt.subplot(1,2,1)
    plt.imshow(img_data)
    plt.title(u"原先图片",fontproperties=font)
    plt.subplot(1,2,2)
    plt.imshow(X_recovered)
    plt.title(u"压缩图像",fontproperties=font)
    plt.show()
    print(u'运行结束！')
    
    
# 找到每条数据距离哪个类中心最近    
def findClosestCentroids(X,initial_centroids):
    m = X.shape[0]                  # 数据条数
    K = initial_centroids.shape[0]  # 类的总数
    dis = np.zeros((m,K))           # 存储计算每个点分别到K个类的距离
    idx = np.zeros((m,1))           # 要返回的每条数据属于哪个类
    
    '''计算每个点到每个类中心的距离'''
    for i in range(m):
        for j in range(K):
            dis[i,j] = np.dot((X[i,:]-initial_centroids[j,:]).reshape(1,-1),(X[i,:]-initial_centroids[j,:]).reshape(-1,1))
    
    '''返回dis每一行的最小值对应的列号，即为对应的类别
    - np.min(dis, axis=1)返回每一行的最小值
    - np.where(dis == np.min(dis, axis=1).reshape(-1,1)) 返回对应最小值的坐标
     - 注意：可能最小值对应的坐标有多个，where都会找出来，所以返回时返回前m个需要的即可（因为对于多个最小值，属于哪个类别都可以）
    '''  
    dummy,idx = np.where(dis == np.min(dis, axis=1).reshape(-1,1))
    return idx[0:dis.shape[0]]  # 注意截取一下
             

# 计算类中心
def computerCentroids(X,idx,K):
    n = X.shape[1]
    centroids = np.zeros((K,n))
    for i in range(K):
        centroids[i,:] = np.mean(X[np.ravel(idx==i),:], axis=0).reshape(1,-1)   # 索引要是一维的,axis=0为每一列，idx==i一次找出属于哪一类的，然后计算均值
    return centroids

# 聚类算法
def runKMeans(X,initial_centroids,max_iters,plot_process):
    m,n = X.shape                   # 数据条数和维度
    K = initial_centroids.shape[0]  # 类数
    centroids = initial_centroids   # 记录当前类中心
    previous_centroids = centroids  # 记录上一次类中心
    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))
        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
            previous_centroids = centroids  # 重置
        centroids = computerCentroids(X, idx, K)    # 重新计算类中心
    if plot_process:    # 显示最终的绘制结果
        plt.show()
    return centroids,idx    # 返回聚类中心和数据属于哪个类

# 画图，聚类中心的移动过程        
def plotProcessKMeans(X,centroids,previous_centroids):
    plt.scatter(X[:,0], X[:,1])     # 原数据的散点图
    plt.plot(previous_centroids[:,0],previous_centroids[:,1],'rx',markersize=10,linewidth=5.0)  # 上一次聚类中心
    plt.plot(centroids[:,0],centroids[:,1],'rx',markersize=10,linewidth=5.0)                    # 当前聚类中心
    for j in range(centroids.shape[0]): # 遍历每个类，画类中心的移动直线
        p1 = centroids[j,:]
        p2 = previous_centroids[j,:]
        plt.plot([p1[0],p2[0]],[p1[1],p2[1]],"->",linewidth=2.0)
    return plt


# 初始化类中心--随机取K个点作为聚类中心
def kMeansInitCentroids(X,K):
    m = X.shape[0]
    m_arr = np.arange(0,m)      # 生成0-m-1
    centroids = np.zeros((K,X.shape[1]))
    np.random.shuffle(m_arr)    # 打乱m_arr顺序    
    rand_indices = m_arr[:K]    # 取前K个
    centroids = X[rand_indices,:]
    return centroids

if __name__ == "__main__":
    KMeans()
    

================================================
FILE: LICENSE
================================================
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.


================================================
FILE: LinearRegression/LinearRegression.py
================================================
#-*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)    # 解决windows环境下画图汉字乱码问题


def linearRegression(alpha=0.01,num_iters=400):
    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                  
    y = data[:,-1]        # y对应最后一列  
    m = len(y)            # 总的数据条数
    col = data.shape[1]      # data的列数
    
    X,mu,sigma = featureNormaliza(X)    # 归一化
    plot_X1_X2(X)         # 画图看一下归一化效果
    
    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")
    
    theta = np.zeros((col,1))
    y = y.reshape(-1,1)   #将行向量转化为列
    theta,J_history = gradientDescent(X, y, theta, alpha, num_iters)
    
    plotJ(J_history, num_iters)
    
    return mu,sigma,theta   #返回均值mu,标准差sigma,和学习的结果theta
    
   
# 加载txt和csv文件
def loadtxtAndcsv_data(fileName,split,dataType):
    return np.loadtxt(fileName,delimiter=split,dtype=dataType)

# 加载npy文件
def loadnpy_data(fileName):
    return np.load(fileName)

# 归一化feature
def featureNormaliza(X):
    X_norm = np.array(X)            #将X转化为numpy数组对象，才可以进行矩阵的运算
    #定义所需变量
    mu = np.zeros((1,X.shape[1]))   
    sigma = np.zeros((1,X.shape[1]))
    
    mu = np.mean(X_norm,0)          # 求每一列的平均值（0指定为列，1代表行）
    sigma = np.std(X_norm,0)        # 求每一列的标准差
    for i in range(X.shape[1]):     # 遍历列
        X_norm[:,i] = (X_norm[:,i]-mu[i])/sigma[i]  # 归一化
    
    return X_norm,mu,sigma

# 画二维图
def plot_X1_X2(X):
    plt.scatter(X[:,0],X[:,1])
    plt.show()


# 梯度下降算法
def gradientDescent(X,y,theta,alpha,num_iters):
    m = len(y)      
    n = len(theta)
    
    temp = np.matrix(np.zeros((n,num_iters)))   # 暂存每次迭代计算的theta，转化为矩阵形式
    
    
    J_history = np.zeros((num_iters,1)) #记录每次迭代计算的代价值
    
    for i in range(num_iters):  # 遍历迭代次数    
        h = np.dot(X,theta)     # 计算内积，matrix可以直接乘
        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('.', end=' ')      
    return theta,J_history  

# 计算代价函数
def computerCost(X,y,theta):
    m = len(y)
    J = 0
    
    J = (np.transpose(X*theta-y))*(X*theta-y)/(2*m) #计算代价J
    return J

# 画每次迭代代价的变化图
def plotJ(J_history,num_iters):
    x = np.arange(1,num_iters+1)
    plt.plot(x,J_history)
    plt.xlabel(u"迭代次数",fontproperties=font) # 注意指定字体，要不然出现乱码问题
    plt.ylabel(u"代价值",fontproperties=font)
    plt.title(u"代价随迭代次数的变化",fontproperties=font)
    plt.show()

# 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)
    
# 测试学习效果（预测）
def predict(mu,sigma,theta):
    result = 0
    # 注意归一化
    predict = np.array([1650,3])
    norm_predict = (predict-mu)/sigma
    final_predict = np.hstack((np.ones((1)),norm_predict))
    
    result = np.dot(final_predict,theta)    # 预测结果
    return result
    
    
if __name__ == "__main__":
    testLinearRegression()

================================================
FILE: LinearRegression/LinearRegression_scikit-learn.py
================================================
#-*- 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")
    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  
        
    # 归一化操作
    scaler = StandardScaler()   
    scaler.fit(X)
    x_train = scaler.transform(X)
    x_test = scaler.transform(np.array([1650,3]))
    
    # 线性模型拟合
    model = linear_model.LinearRegression()
    model.fit(x_train, y)
    
    #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


# 加载txt和csv文件
def loadtxtAndcsv_data(fileName,split,dataType):
    return np.loadtxt(fileName,delimiter=split,dtype=dataType)

# 加载npy文件
def loadnpy_data(fileName):
    return np.load(fileName)




if __name__ == "__main__":
    linearRegression()

================================================
FILE: LinearRegression/data.csv
================================================
2104,3,399900
1600,3,329900
2400,3,369000
1416,2,232000
3000,4,539900
1985,4,299900
1534,3,314900
1427,3,198999
1380,3,212000
1494,3,242500
1940,4,239999
2000,3,347000
1890,3,329999
4478,5,699900
1268,3,259900
2300,4,449900
1320,2,299900
1236,3,199900
2609,4,499998
3031,4,599000
1767,3,252900
1888,2,255000
1604,3,242900
1962,4,259900
3890,3,573900
1100,3,249900
1458,3,464500
2526,3,469000
2200,3,475000
2637,3,299900
1839,2,349900
1000,1,169900
2040,4,314900
3137,3,579900
1811,4,285900
1437,3,249900
1239,3,229900
2132,4,345000
4215,4,549000
2162,4,287000
1664,2,368500
2238,3,329900
2567,4,314000
1200,3,299000
852,2,179900
1852,4,299900
1203,3,239500


================================================
FILE: LinearRegression/data.txt
================================================
2104,3,399900
1600,3,329900
2400,3,369000
1416,2,232000
3000,4,539900
1985,4,299900
1534,3,314900
1427,3,198999
1380,3,212000
1494,3,242500
1940,4,239999
2000,3,347000
1890,3,329999
4478,5,699900
1268,3,259900
2300,4,449900
1320,2,299900
1236,3,199900
2609,4,499998
3031,4,599000
1767,3,252900
1888,2,255000
1604,3,242900
1962,4,259900
3890,3,573900
1100,3,249900
1458,3,464500
2526,3,469000
2200,3,475000
2637,3,299900
1839,2,349900
1000,1,169900
2040,4,314900
3137,3,579900
1811,4,285900
1437,3,249900
1239,3,229900
2132,4,345000
4215,4,549000
2162,4,287000
1664,2,368500
2238,3,329900
2567,4,314000
1200,3,299000
852,2,179900
1852,4,299900
1203,3,239500


================================================
FILE: LogisticRegression/LogisticRegression.py
================================================
#-*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)    # 解决windows环境下画图汉字乱码问题


def LogisticRegression():
    data = loadtxtAndcsv_data("data2.txt", ",", np.float64) 
    X = data[:,0:-1]
    y = data[:,-1]
    
    plot_data(X,y)  # 作图
    
    X = mapFeature(X[:,0],X[:,1])           #映射为多项式
    initial_theta = np.zeros((X.shape[1],1))#初始化theta
    initial_lambda = 0.1                    #初始化正则化系数，一般取0.01,0.1,1.....
    
    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
    #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，
    - initial_theta表示初始化的值,
    - fprime指定costFunction的梯度
    - args是其余测参数，以元组的形式传入，最后会将最小化costFunction的theta返回 
    '''
    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   
    
    X = data[:,0:-1]
    y = data[:,-1]    
    plotDecisionBoundary(result,X,y)    #画决策边界  
    
    

# 加载txt和csv文件
def loadtxtAndcsv_data(fileName,split,dataType):
    return np.loadtxt(fileName,delimiter=split,dtype=dataType)

# 加载npy文件
def loadnpy_data(fileName):
    return np.load(fileName)

# 显示二维图形
def plot_data(X,y):
    pos = np.where(y==1)    #找到y==1的坐标位置
    neg = np.where(y==0)    #找到y==0的坐标位置
    #作图
    plt.figure(figsize=(15,12))
    plt.plot(X[pos,0],X[pos,1],'ro')        # red o
    plt.plot(X[neg,0],X[neg,1],'bo')        # blue o
    plt.title(u"两个类别散点图",fontproperties=font)
    plt.show()

# 映射为多项式 
def mapFeature(X1,X2):
    degree = 2;                     # 映射的最高次方
    out = np.ones((X1.shape[0],1))  # 映射后的结果数组（取代X）
    '''
    这里以degree=2为例，映射为1,x1,x2,x1^2,x1,x2,x2^2
    '''
    for i in np.arange(1,degree+1): 
        for j in range(i+1):
            temp = X1**(i-j)*(X2**j)    #矩阵直接乘相当于matlab中的点乘.*
            out = np.hstack((out, temp.reshape(-1,1)))
    return out

# 代价函数
def costFunction(initial_theta,X,y,inital_lambda):
    m = len(y)
    J = 0
    
    h = sigmoid(np.dot(X,initial_theta))    # 计算h(z)
    theta1 = initial_theta.copy()           # 因为正则化j=1从1开始，不包含0，所以复制一份，前theta(0)值为0 
    theta1[0] = 0   
    
    temp = np.dot(np.transpose(theta1),theta1)
    J = (-np.dot(np.transpose(y),np.log(h))-np.dot(np.transpose(1-y),np.log(1-h))+temp*inital_lambda/2)/m   # 正则化的代价方程
    return J

# 计算梯度
def gradient(initial_theta,X,y,inital_lambda):
    m = len(y)
    grad = np.zeros((initial_theta.shape[0]))
    
    h = sigmoid(np.dot(X,initial_theta))# 计算h(z)
    theta1 = initial_theta.copy()
    theta1[0] = 0

    grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
    return grad

# S型函数    
def sigmoid(z):
    h = np.zeros((len(z),1))    # 初始化，与z的长度一置
    
    h = 1.0/(1.0+np.exp(-z))
    return h


#画决策边界
def plotDecisionBoundary(theta,X,y):
    pos = np.where(y==1)    #找到y==1的坐标位置
    neg = np.where(y==0)    #找到y==0的坐标位置
    #作图
    plt.figure(figsize=(15,12))
    plt.plot(X[pos,0],X[pos,1],'ro')        # red o
    plt.plot(X[neg,0],X[neg,1],'bo')        # blue o
    plt.title(u"决策边界",fontproperties=font)
    
    #u = np.linspace(30,100,100)
    #v = np.linspace(30,100,100)
    
    u = np.linspace(-1,1.5,50)  #根据具体的数据，这里需要调整
    v = np.linspace(-1,1.5,50)
    
    z = np.zeros((len(u),len(v)))
    for i in range(len(u)):
        for j in range(len(v)):
            z[i,j] = np.dot(mapFeature(u[i].reshape(1,-1),v[j].reshape(1,-1)),theta)    # 计算对应的值，需要map
    
    z = np.transpose(z)
    plt.contour(u,v,z,[0,0.01],linewidth=2.0)   # 画等高线，范围在[0,0.01]，即近似为决策边界
    #plt.legend()
    plt.show()

# 预测
def predict(X,theta):
    m = X.shape[0]
    p = np.zeros((m,1))
    p = sigmoid(np.dot(X,theta))    # 预测的结果，是个概率值
    
    for i in range(m):
        if p[i] > 0.5:  #概率大于0.5预测为1，否则预测为0
            p[i] = 1
        else:
            p[i] = 0
    return p


# 测试逻辑回归函数
def testLogisticRegression():
    LogisticRegression()


if __name__ == "__main__":
    testLogisticRegression()
    



================================================
FILE: LogisticRegression/LogisticRegression_OneVsAll.py
================================================
#-*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
import scipy.io as spio
from scipy import optimize
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)    # 解决windows环境下画图汉字乱码问题


def logisticRegression_OneVsAll():
    data = loadmat_data("data_digits.mat") 
    X = data['X']   # 获取X数据，每一行对应一个数字20x20px
    y = data['y']
    m,n = X.shape
    num_labels = 10 # 数字个数，0-9
    
    ##　随机显示几行数据
    rand_indices = [t for t in [np.random.randint(x-x, m) for x in range(100)]]  # 生成100个0-m的随机数
    display_data(X[rand_indices,:])     # 显示100个数字
    
    Lambda = 0.1    # 正则化系数
    #y = y.reshape(-1,1)
    all_theta = oneVsAll(X, y, num_labels, Lambda)  # 计算所有的theta
    
    p = predict_oneVsAll(all_theta,X)               # 预测
    # 将预测结果和真实结果保存到文件中
    #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))
     
# 加载mat文件
def loadmat_data(fileName):
    return spio.loadmat(fileName)
    
# 显示100个数字
def display_data(imgData):
    sum = 0
    '''
    显示100个数（若是一个一个绘制将会非常慢，可以将要画的数字整理好，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
    '''
    pad = 1
    display_array = -np.ones((pad+10*(20+pad),pad+10*(20+pad)))
    for i in range(10):
        for j in range(10):
            display_array[pad+i*(20+pad):pad+i*(20+pad)+20,pad+j*(20+pad):pad+j*(20+pad)+20] = (imgData[sum,:].reshape(20,20,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
            
    plt.imshow(display_array,cmap='gray')   #显示灰度图像
    plt.axis('off')
    plt.show()

# 求每个分类的theta，最后返回所有的all_theta    
def oneVsAll(X,y,num_labels,Lambda):
    # 初始化变量
    m,n = X.shape
    all_theta = np.zeros((n+1,num_labels))  # 每一列对应相应分类的theta,共10列
    X = np.hstack((np.ones((m,1)),X))       # X前补上一列1的偏置bias
    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
    initial_theta = np.zeros((n+1,1))       # 初始化一个分类的theta
    
    # 映射y
    for i in range(num_labels):
        class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值
    
    #np.savetxt("class_y.csv", class_y[0:600,:], delimiter=',')    
    
    '''遍历每个分类，计算对应的theta值'''
    for i in range(num_labels):
        #optimize.fmin_cg
        result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,class_y[:,i],Lambda)) # 调用梯度下降的优化方法
        all_theta[:,i] = result.reshape(1,-1)   # 放入all_theta中
        
    all_theta = np.transpose(all_theta) 
    return all_theta

# 代价函数
def costFunction(initial_theta,X,y,inital_lambda):
    m = len(y)
    J = 0
    
    h = sigmoid(np.dot(X,initial_theta))    # 计算h(z)
    theta1 = initial_theta.copy()           # 因为正则化j=1从1开始，不包含0，所以复制一份，前theta(0)值为0 
    theta1[0] = 0   
    
    temp = np.dot(np.transpose(theta1),theta1)
    J = (-np.dot(np.transpose(y),np.log(h))-np.dot(np.transpose(1-y),np.log(1-h))+temp*inital_lambda/2)/m   # 正则化的代价方程
    return J

# 计算梯度
def gradient(initial_theta,X,y,inital_lambda):
    m = len(y)
    grad = np.zeros((initial_theta.shape[0]))
    
    h = sigmoid(np.dot(X,initial_theta))  # 计算h(z)
    theta1 = initial_theta.copy()
    theta1[0] = 0

    grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
    return grad   
    
# S型函数    
def sigmoid(z):
    h = np.zeros((len(z),1))    # 初始化，与z的长度一致
    
    h = 1.0/(1.0+np.exp(-z))
    return h

# 预测
def predict_oneVsAll(all_theta,X):
    m = X.shape[0]
    num_labels = all_theta.shape[0]
    p = np.zeros((m,1))
    X = np.hstack((np.ones((m,1)),X))   #在X最前面加一列1
    
    h = sigmoid(np.dot(X,np.transpose(all_theta)))  #预测

    '''
    返回h中每一行最大值所在的列号
    - np.max(h, axis=1)返回h中每一行的最大值（是某个数字的最大概率）
    - 最后where找到的最大概率所在的列号（列号即是对应的数字）
    '''
    p = np.array(np.where(h[0,:] == np.max(h, axis=1)[0]))  
    for i in np.arange(1, m):
        t = np.array(np.where(h[i,:] == np.max(h, axis=1)[i]))
        p = np.vstack((p,t))
    return p
        
        
if __name__ == "__main__":
    logisticRegression_OneVsAll()

================================================
FILE: LogisticRegression/LogisticRegression_OneVsAll_scikit-learn.py
================================================
#-*- coding: utf-8 -*-
from __future__ import print_function
from scipy import io as spio
import numpy as np
from sklearn import svm
from sklearn.linear_model import LogisticRegression



def logisticRegression_oneVsAll():
    data = loadmat_data("data_digits.mat") 
    X = data['X']   # 获取X数据，每一行对应一个数字20x20px
    y = data['y']   # 这里读取mat文件y的shape=(5000, 1)
    y = np.ravel(y) # 调用sklearn需要转化成一维的(5000,)
    
    model = LogisticRegression()
    model.fit(X, y) # 拟合
    
    predict = model.predict(X) #预测
    
    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):
    return spio.loadmat(fileName)

if __name__ == "__main__":
    logisticRegression_oneVsAll()

================================================
FILE: LogisticRegression/LogisticRegression_scikit-learn.py
================================================
# -*- coding: utf-8 -*-

from sklearn.linear_model import LogisticRegression
from sklearn.preprocessing import StandardScaler
# 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)
    X = data[:,0:-1]
    y = data[:,-1]

    # 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)

    # 归一化
    scaler = StandardScaler()
    # scaler.fit(x_train)
    x_train = scaler.fit_transform(x_train)
    x_test = scaler.fit_transform(x_test)

    # 逻辑回归
    model = LogisticRegression()
    model.fit(x_train,y_train)

    # 预测
    predict = model.predict(x_test)
    right = sum(predict == y_test)

    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)

# 加载npy文件
def loadnpy_data(fileName):
    return np.load(fileName)


if __name__ == "__main__":
    logisticRegression()


================================================
FILE: LogisticRegression/class_y.csv
================================================
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================================================
FILE: LogisticRegression/data1.txt
================================================
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FILE: LogisticRegression/data2.txt
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FILE: LogisticRegression/predict.csv
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