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)

总结

以上就是本文关于机器学习经典算法-logistic回归代码详解的全部内容，希望对大家有所帮助。感兴趣的朋友可以继续参阅本站：

python中实现k-means聚类算法详解

Python编程实现粒子群算法(PSO)详解

Python编程实现蚁群算法详解

如有不足之处，欢迎留言指出。感谢朋友们对本站的支持！