机器学习经典算法-logistic回归代码详解

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, 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.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, fte, numT, numIter):
  errors=[]
  for k in range(numT):
    error = colicTest(ftr, fte, 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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