Python机器学习logistic回归代码解析

#coding:utf-8 from numpy import *import math def loadDataSet():  dataMat = []; labelMat = []  fr = open('testSet.txt')  for line in fr.readlines():    lineArr = line.strip().split()    dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])    labelMat.append(int(lineArr[2]))  return dataMat,labelMat def sigmoid(inX):  return longfloat(1.0/(1+exp(-inX))) #sigmoid函数公式 def gradAscent(dataMatIn, classLabels):  #dataMatIn 一个2维的数组；classLabels 类别标签  dataMatrix = mat(dataMatIn)       #转换为矩阵  labelMat = mat(classLabels).transpose() #得到矩阵的转置矩阵  m,n = shape(dataMatrix)  #读取矩阵的长度,二维矩阵，返回两个值  alpha = 0.001     #向目标移动的步长  maxCycles = 500    #迭代次数   weights = ones((n,1))  #ones()函数用以创建指定形状和类型的数组，默认情况下返回的类型是float64。但是，如果使用ones()函数时指定了数据类型，那么返回的就是该类型  for k in range(maxCycles):           h = sigmoid(dataMatrix*weights)   #matrix mult    error = (labelMat - h)       #vector subtraction    weights = weights + alpha * dataMatrix.transpose()* error #matrix mult  return weights def plotBestFit(weights):  import matplotlib as mpl  mpl.use('Agg')         #为了防止出现:RuntimeError: could not open display报错  import matplotlib.pyplot as plt  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() #figure: 控制dpi、边界颜色、图形大小、和子区( subplot)设置  ax = fig.add_subplot(111) # 参数111的意思是：将画布分割成1行1列，图像画在从左到右从上到下的第1块，  ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')  ax.scatter(xcord2, ycord2, s=30, 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.savefig('plotBestFit.png')  #因为我是腾讯云服务器,没有图形界面，所以我保存为图片。 #随机梯度上升算法def stocGradAscent0(dataMatrix, classLabels):  m,n = shape(dataMatrix)  alpha = 0.01  weights = ones(n)  #initialize to all ones  for i in range(m):    h = sigmoid(sum(dataMatrix[i]*weights))    error = classLabels[i] - h    weights = weights + alpha * error * dataMatrix[i] #回归系数的更新操作  return weights #改进的随机梯度上升算法def stocGradAscent1(dataMatrix, classLabels, numIter=150):  #较之前的增加了一个迭代次数作为第三个参数，默认值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)+0.0001        randIndex = int(random.uniform(0,len(dataIndex)))  #样本随机选择      h = sigmoid(sum(dataMatrix[randIndex]*weights))      error = classLabels[randIndex] - h      weights = weights + alpha * error * dataMatrix[randIndex] #回归系数的更新操作      del(dataIndex[randIndex])  return weights #以回归系数和特征向量作为输入计算对应的sigmoid值def classifyVector(inX, weights):  prob = sigmoid(sum(inX*weights))  if prob > 0.5: return 1.0        #如果sigmoid值大于0.5函数返回1，否则返回0  else: return 0.0 #打开测试集和训练集，并对数据进行格式化处理的函数def colicTest():  frTrain = open('horseColicTraining.txt'); frTest = open('horseColicTest.txt')  trainingSet = []; trainingLabels = []  for line in frTrain.readlines():    currLine = line.strip().split('/t')    lineArr =[]    for i in range(21):      lineArr.append(float(currLine[i]))    trainingSet.append(lineArr)    trainingLabels.append(float(currLine[21]))  trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 1000) #计算回归系数向量  errorCount = 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(array(lineArr), trainWeights))!= int(currLine[21]):      errorCount += 1  errorRate = (float(errorCount)/numTestVec)  print "the error rate of this test is: %f" % errorRate  return errorRate#调用函数colicTest()10次，并求结果的平均值def multiTest():  numTests = 10; errorSum=0.0  for k in range(numTests):    errorSum += colicTest()  print "after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests))