《机器学习实战》Logistic回归

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注释：Ng的视频有完整的推到步骤，不过理论和实践还是有很大差别的，代码实现还得完成

1.Logistic回归理论

　　http://www.cnblogs.com/wjy-lulu/p/7759515.html，Ng的推导很完美，看懂就可以了，没必要自己推导一遍，因为几天不用就忘记 了。

2.代码实现

　　2.1全局梯度上升

　　　　每次训练针对整体，依据整体去找最值。

　　　　好处：容易过滤局部极值，找到真正的全局极值。

　　　　坏处：整体数据太多，花费时间太久，而且新来的样本必须重新训练。

　　　　推倒公式：见博文刚开始的链接，Ng大神的全部推导及证明！

 def loadDataSet():
     dataMat  = []
     labelMat = []
     fr = open('testSet.txt')
     for line in fr.readlines():
         lineArr = line.strip().split()#分割空格
         #改变存储data:[[a,b],[c,d]]/
         #       labels:[1,0,0,1...]
         dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
         labelMat.append([int(lineArr[2])])
     return dataMat, labelMat
 def sigmoid(intX):
     return 1.0/(1.0+np.exp(-intX))
 #全局梯度上升法
 def gradAscent(dataMatIn,classLabels):
     dataMatrix = np.mat(dataMatIn)
     labelsMat = np.mat(classLabels)
     m, n = dataMatrix.shape
     alpha = 0.001
     maxCycle = 200
     weight = np.ones((n,1))#这里为了简单写,把b也当作一个w了
     for k in range(maxCycle):
         h = sigmoid(dataMatrix*weight)
         error = labelsMat - np.mat(h)
         weight = weight + alpha*dataMatrix.transpose()*error
     return weight

　　2.1简单分类可视化

　　　　利用matplotlib画出简单分类的决策边界

　　　　注意：这里plot转化为list之后绘制的，看网上说可以直接用matrix，但是我运行出错。

 def plotBestFit(weight):
     dataMat, labelMat = loadDataSet()
     dataArr = np.array(dataMat)#转化为数组
     n = dataArr.shape[0]
     xcode1=[];ycode1=[]
     xcode2=[];ycode2=[]
     for i in range(n):
         if int(labelMat[i][0])==1:
             xcode1.append(dataArr[i,1])
             ycode1.append(dataArr[i,2])
         else:
             xcode2.append(dataArr[i,1])
             ycode2.append(dataArr[i,2])
     fig = plt.figure("data_x_y")
     ax  = fig.add_subplot(111)
     ax.scatter(xcode1,ycode1,s=30,c='r',marker='s')
     ax.scatter(xcode2,ycode2,s=30,c='g')
     x = np.mat(np.arange(-3.0,3.0,0.1))
     y = (-weight[0]-weight[1]*x)/weight[2]
     ax.plot(x.tolist()[0],y.tolist()[0])
     plt.xlabel('X1')
     plt.ylabel('X2')
     plt.show()

　　2.3局部随机梯度上升法及改进

　　　　局部随机梯度：和全局相对，利用单个样本更新W，同时又是利用正太分布的规律去随机选择样本的次序。

　　　　好处：‘局部’训练效率高，而且新的样本可以直接添加不用重新训练，‘随机’解决了样本规律性的波动，树上有图解。

　　　　坏处：可能得到局部极值。

 #局部梯度上升法-老版本
 def stoGradAscent0(dataMatrix,classLabels):
     m,n = dataMatrix.shape
     alpha = 0.01
     weights = np.ones(n)#最好别写0,因为0的拟合速度很慢
     for i in range(m):
         h = sigmoid(sum(dataMatrix[i]*weights))
         error = classLabels - h
         weights = weights +alpha* error* dataMatrix[i]
     return weights
 #随机梯度上升法-新版本
 def stoGradAscent1(dataMatraix,classLabels,numIter=150):
     #alpha不断改变
     #选取的样本随机改变
     m,n = dataMatraix.shape
     weights = np.ones(n)
     for j in range(numIter):
         dataIndex = list(range(m))#样本
         for i in range(m):
             alpha = 4/(1.0+j+i) +0.01#随着迭代次数和样本的训练次数的增加而减小
             randIndex = int(np.random.uniform(0,len(dataIndex)))#随机样本下标
             h = sigmoid(sum(dataMatraix[randIndex]*weights))
             error = classLabels[randIndex] - h
             weights = weights +alpha*error*dataMatraix[randIndex]
             del(dataIndex[randIndex])#执行之后删除，避免重复执行
     return weights

　　2.4实际应用

　　　　和前面朴素贝叶斯都差不多，预处理数据-->>训练-->>测试

 分类函数
 def classifyVector(inX,weight):
     prob = sigmoid(sum(inX*weight))
     if prob>0.5: return 1.0
     return 0.0
 def colicTest():
     frTrain = open('horseColicTraining.txt')
     frtest  = open('horseColicTest.txt')
     trainingSet   = []
     trainingLabel = []
     for line in frTrain.readlines():
         currLine = line.strip().split('\t')
         lineArr = []
         #最后一个是标签
         for i in range(len(currLine)-1):
             lineArr.append(float(currLine[i]))
         trainingSet.append(lineArr)
         trainingLabel.append(float(currLine[-1]))
     #改进之后的随机梯度下降法--->>>局部算法=在线学习
     trainWeight = stoGradAscent1(np.array(trainingSet),trainingLabel,500)
     errorCount = 0.0
     numTestVec = 0.0
     for line in frtest.readlines():
         numTestVec += 1.0
         currLine =line.strip().split('\t')
         lineArr = []
         for i in range(21):
             lineArr.append(float(currLine[i]))
         if int(classifyVector(np.array(lineArr),trainWeight)) != int(currLine[21]):
             errorCount+=1
     errorRate = (1.0*errorCount)/(1.0*numTestVec)
     print('the error Rate is : ',errorRate,'\n')
     return errorRate
 def multiTest():
     numTest = 10;errorSum = 0.0
     for k in range(numTest):
         errorSum += colicTest()
     print('error Rate Average is : ',(errorSum/numTest))

　　2.5总程序

 import numpy as np
 import matplotlib.pyplot as plt

 def loadDataSet():
     dataMat  = []
     labelMat = []
     fr = open('testSet.txt')
     for line in fr.readlines():
         lineArr = line.strip().split()#分割空格
         #改变存储data:[[a,b],[c,d]]/
         #       labels:[1,0,0,1...]
         dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
         labelMat.append([int(lineArr[2])])
     return dataMat, labelMat
 def sigmoid(intX):
     return 1.0/(1.0+np.exp(-intX))
 #全局梯度上升法
 def gradAscent(dataMatIn,classLabels):
     dataMatrix = np.mat(dataMatIn)
     labelsMat = np.mat(classLabels)
     m, n = dataMatrix.shape
     alpha = 0.001
     maxCycle = 200
     weight = np.ones((n,1))#这里为了简单写,把b也当作一个w了
     for k in range(maxCycle):
         h = sigmoid(dataMatrix*weight)
         error = labelsMat - np.mat(h)
         weight = weight + alpha*dataMatrix.transpose()*error
     return weight

 def plotBestFit(weight):
     dataMat, labelMat = loadDataSet()
     dataArr = np.array(dataMat)#转化为数组
     n = dataArr.shape[0]
     xcode1=[];ycode1=[]
     xcode2=[];ycode2=[]
     for i in range(n):
         if int(labelMat[i][0])==1:
             xcode1.append(dataArr[i,1])
             ycode1.append(dataArr[i,2])
         else:
             xcode2.append(dataArr[i,1])
             ycode2.append(dataArr[i,2])
     fig = plt.figure("data_x_y")
     ax  = fig.add_subplot(111)
     ax.scatter(xcode1,ycode1,s=30,c='r',marker='s')
     ax.scatter(xcode2,ycode2,s=30,c='g')
     x = np.mat(np.arange(-3.0,3.0,0.1))
     y = (-weight[0]-weight[1]*x)/weight[2]
     ax.plot(x.tolist()[0],y.tolist()[0])
     plt.xlabel('X1')
     plt.ylabel('X2')
     plt.show()
 #局部梯度上升法-老版本
 def stoGradAscent0(dataMatrix,classLabels):
     m,n = dataMatrix.shape
     alpha = 0.01
     weights = np.ones(n)#最好别写0,因为0的拟合速度很慢
     for i in range(m):
         h = sigmoid(sum(dataMatrix[i]*weights))
         error = classLabels - h
         weights = weights +alpha* error* dataMatrix[i]
     return weights
 #随机梯度上升法-新版本
 def stoGradAscent1(dataMatraix,classLabels,numIter=150):
     #alpha不断改变
     #选取的样本随机改变
     m,n = dataMatraix.shape
     weights = np.ones(n)
     for j in range(numIter):
         dataIndex = list(range(m))#样本
         for i in range(m):
             alpha = 4/(1.0+j+i) +0.01#随着迭代次数和样本的训练次数的增加而减小
             randIndex = int(np.random.uniform(0,len(dataIndex)))#随机样本下标
             h = sigmoid(sum(dataMatraix[randIndex]*weights))
             error = classLabels[randIndex] - h
             weights = weights +alpha*error*dataMatraix[randIndex]
             del(dataIndex[randIndex])#执行之后删除，避免重复执行
     return weights
 #分类函数
 def classifyVector(inX,weight):
     prob = sigmoid(sum(inX*weight))
     if prob>0.5: return 1.0
     return 0.0
 def colicTest():
     frTrain = open('horseColicTraining.txt')
     frtest  = open('horseColicTest.txt')
     trainingSet   = []
     trainingLabel = []
     for line in frTrain.readlines():
         currLine = line.strip().split('\t')
         lineArr = []
         #最后一个是标签
         for i in range(len(currLine)-1):
             lineArr.append(float(currLine[i]))
         trainingSet.append(lineArr)
         trainingLabel.append(float(currLine[-1]))
     #改进之后的随机梯度下降法--->>>局部算法=在线学习
     trainWeight = stoGradAscent1(np.array(trainingSet),trainingLabel,500)
     errorCount = 0.0
     numTestVec = 0.0
     for line in frtest.readlines():
         numTestVec += 1.0
         currLine =line.strip().split('\t')
         lineArr = []
         for i in range(21):
             lineArr.append(float(currLine[i]))
         if int(classifyVector(np.array(lineArr),trainWeight)) != int(currLine[21]):
             errorCount+=1
     errorRate = (1.0*errorCount)/(1.0*numTestVec)
     print('the error Rate is : ',errorRate,'\n')
     return errorRate
 def multiTest():
     numTest = 10;errorSum = 0.0
     for k in range(numTest):
         errorSum += colicTest()
     print('error Rate Average is : ',(errorSum/numTest))