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))