机器学习经典算法-logistic回归代码详解

概述一、算法简要我们希望有这么一种函数：接受输入然后预测出类别，这样用于分类。这里，用到了数学中的sigmoid函数，sigmoid函数的具体表达式和函数图象如下：

一、算法简要

我们希望有这么一种函数：接受输入然后预测出类别，这样用于分类。这里，用到了数学中的sigmoID函数，sigmoID函数的具体表达式和函数图象如下：

可以较为清楚的看到，当输入的x小于0时，函数值<0.5，将分类预测为0；当输入的x大于0时，函数值>0.5，将分类预测为1。

1.1 预测函数的表示

1.2参数的求解

二、代码实现

函数sigmoID计算相应的函数值；gradAscent实现的batch-梯度上升，意思就是在每次迭代中所有数据集都考虑到了；而stoGradAscent0中，则是将数据集中的示例都比那里了一遍，复杂度大大降低；stoGradAscent1则是对随机梯度上升的改进，具体变化是Alpha每次变化的频率是变化的，而且每次更新参数用到的示例都是随机选取的。

from numpy import * import matplotlib.pyplot as plt def loadDataSet():   dataMat = []   labelMat = []   fr = open('testSet.txt')   for line in fr.readlines():     lineArr = line.strip('\n').split('\t')     dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])     labelMat.append(int(lineArr[2]))   fr.close()   return dataMat,labelMat def sigmoID(inX):   return 1.0/(1+exp(-inX)) def gradAscent(dataMatIn,classLabels):   dataMatrix = mat(dataMatIn)   labelMat = mat(classLabels).transpose()   m,n=shape(dataMatrix)   Alpha = 0.001   maxCycles = 500   weights = ones((n,1))   errors=[]   for k in range(maxCycles):     h = sigmoID(dataMatrix*weights)     error = labelMat - h     errors.append(sum(error))     weights = weights + Alpha*dataMatrix.transpose()*error   return weights,errors def stoGradAscent0(dataMatIn,classLabels):   m,n=shape(dataMatIn)   Alpha = 0.01   weights = ones(n)   for i in range(m):     h = sigmoID(sum(dataMatIn[i]*weights))     error = classLabels[i] - h      weights = weights + Alpha*error*dataMatIn[i]   return weights def stoGradAscent1(dataMatrix,classLabels,numIter = 150):   m,n=shape(dataMatrix)   weights = ones(n)   for j in range(numIter):     dataIndex=range(m)     for i in range(m):       Alpha= 4/(1.0+j+i)+0.01       randindex = int(random.uniform(0,len(dataIndex)))       h = sigmoID(sum(dataMatrix[randindex]*weights))       error = classLabels[randindex]-h       weights=weights+Alpha*error*dataMatrix[randindex]       del(dataIndex[randindex])     return weights def plotError(errs):   k = len(errs)   x = range(1,k+1)   plt.plot(x,errs,'g--')   plt.show() def plotBestFit(wei):   weights = wei.getA()   dataMat,labelMat = loadDataSet()   dataArr = array(dataMat)   n = shape(dataArr)[0]   xcord1=[]   ycord1=[]   xcord2=[]   ycord2=[]   for i in range(n):      if int(labelMat[i])==1:       xcord1.append(dataArr[i,1])       ycord1.append(dataArr[i,2])     else:       xcord2.append(dataArr[i,1])       ycord2.append(dataArr[i,2])   fig = plt.figure()   ax = fig.add_subplot(111)   ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')   ax.scatter(xcord2,ycord2,c='green')   x = arange(-3.0,3.0,0.1)   y=(-weights[0]-weights[1]*x)/weights[2]   ax.plot(x,y)   plt.xlabel('x1')   plt.ylabel('x2')   plt.show() def classifyVector(inX,weights):   prob = sigmoID(sum(inX*weights))   if prob>0.5:     return 1.0   else:     return 0 def colicTest(ftr,fte,numIter):   frTrain = open(ftr)   frTest = open(fte)   trainingSet=[]   trainingLabels=[]   for line in frTrain.readlines():     currline = line.strip('\n').split('\t')     lineArr=[]     for i in range(21):       lineArr.append(float(currline[i]))     trainingSet.append(lineArr)     trainingLabels.append(float(currline[21]))   frTrain.close()   trainWeights = stoGradAscent1(array(trainingSet),trainingLabels,numIter)   errorCount = 0   numTestVec = 0.0   for line in frTest.readlines():     numTestVec += 1.0     currline = line.strip('\n').split('\t')     lineArr=[]     for i in range(21):       lineArr.append(float(currline[i]))     if int(classifyVector(array(lineArr),trainWeights))!=int(currline[21]):       errorCount += 1   frTest.close()   errorRate = (float(errorCount))/numTestVec   return errorRate def multiTest(ftr,numT,numIter):   errors=[]   for k in range(numT):     error = colicTest(ftr,numIter)     errors.append(error)   print "There "+str(len(errors))+" test with "+str(numIter)+" interations in all!"   for i in range(numT):     print "The "+str(i+1)+"th"+" testError is:"+str(errors[i])   print "Average testError: ",float(sum(errors))/len(errors) ''''' data,labels = loadDataSet() weights0 = stoGradAscent0(array(data),labels) weights,errors = gradAscent(data,labels) weights1= stoGradAscent1(array(data),labels,500) print weights plotBestFit(weights) print weights0 weights00 = [] for w in weights0:   weights00.append([w]) plotBestFit(mat(weights00)) print weights1 weights11=[] for w in weights1:   weights11.append([w]) plotBestFit(mat(weights11)) ''' multiTest(r"horseColicTraining.txt",r"horseColicTest.txt",10,500) 

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