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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来源：http://blog.csdn.net/moodytong/article/details/9731283