python机器学习实战4：Logistic回归

1.Logistic回归简介

先给出本次实战的代码和数据集，链接: https://pan.baidu.com/s/1dEE1QJR 密码: 6nnh

我们拿到一些数据点，用一条直线对这些点进行拟合（该线称为最佳拟合直线），这个拟合过程就叫做回归。利用Logistic回归进行分类的主要思想是：根据现有数据对分类边界线建立回归公式，以此进行分类。“回归”一词源于最佳拟合，表示要找到最佳拟合参数集。其实，回归也就是个名字，不用太纠结。

代码中还会用到Sigmoid函数和梯度上升，这个在CS231n系列课程里激活函数那部分已经详细讲解过，这里就不在赘述。

2.Logistic回归分类的代码实现

#coding:utf-8

#Logistic回归梯度上升优化算法
#导入numpy
from numpy import *

#打开测试文件，进行逐行读取
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

#sigmoid函数定义
def sigmoid(inX):
return 1.0/(1+exp(-inX))

#梯度上升算法
def gradAscent(dataMatIn, classLabels):
dataMatrix = mat(dataMatIn)             #convert to NumPy matrix
labelMat = mat(classLabels).transpose() #convert to NumPy matrix
m,n = shape(dataMatrix)
alpha = 0.001
maxCycles = 500
weights = ones((n,1))
for k in range(maxCycles):              #heavy on matrix operations
h = sigmoid(dataMatrix*weights)     #matrix mult
error = (labelMat - h)              #vector subtraction
weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
return weights

#画出数据集和Logistic回归最佳拟合直线的函数
def plotBestFit(weights):
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()
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()

#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]
return weights

#改进的随机梯度下降
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
m,n = shape(dataMatrix)
weights = ones(n)   #initialize to all ones
for j in range(numIter):
dataIndex = range(m)
for i in range(m):
alpha = 4/(1.0+j+i)+0.0001    #apha decreases with iteration, does not
randIndex = int(random.uniform(0,len(dataIndex)))#go to 0 because of the constant
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex] - h
weights = weights + alpha * error * dataMatrix[randIndex]
del(dataIndex[randIndex])
return weights

#Logistic回归分类函数
def classifyVector(inX, weights):
prob = sigmoid(sum(inX*weights))
if prob > 0.5: return 1.0
else: return 0.0

#便利函数，整理好训练集和测试集数据
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)
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

#多次测试求平均值，这个测试结果不太稳定，在35%左右
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))

又完成一个实战咯！O(∩_∩)O