# -*- coding:utf-8 -*-
from numpy import *
#加载数据集
def loadDataSet():
dataMat = []
labelMat = []
fp = open("C:\\Users\\Rainey\\Desktop\\testSet.txt")
for line in fp.readlines():
lineArr = line.strip().split() #删除文件中多余的字符
dataMat.append([1.0,float(lineArr[0]), float(lineArr[1])])
labelMat.append(float(lineArr[2]))
return dataMat,labelMat
#定义Sigmoid函数
def sigmoid(inX):
return 1.0/(1+exp(-inX))
#定义求解最佳回归系数,Logistic回归梯度上升优化算法
def gradAscent(dataMatIn,classLabels):
dataMatrix = mat(dataMatIn) #将数组转为矩阵
labelMat = mat(classLabels).transpose() #转置
m,n = shape(dataMatrix) #返回矩阵的行和列
alpha = 0.001 #初始化 alpha的值
maxCycles = 500 #最大迭代次数
weights = ones((n,1)) #初始化最佳回归系数
for i in range(0,maxCycles):
#引用原书的代码，求梯度
#dataMatrix*weights，100×3和3×1的矩阵相乘，得到100×1的矩阵
h = sigmoid(dataMatrix*weights)
#h的取值为0~1，因而error为误差
error = labelMat - h
weights = weights + alpha * dataMatrix.transpose() * error
return weights
#随机梯度上升算法
def stocGradAscent0(dataMatrix, classLabels):
m,n = shape(dataMatrix)
alpha = 0.01
weights = ones(n)
for i in range(m):
h = sigmoid(sum(dataMatrix[i]*weights)) #此处h为具体数值
error = classLabels[i] - h #error也为具体数值
weights = weights + alpha*error*dataMatrix[i] #每次对一个样本进行处理，更新权值
return weights
#改进的随机梯度上升算法，收敛得更快
def stocGradAscent1(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+i+j)+0.0001 #alpha迭代次数不断变小，1.非严格下降，2.不会到0
#随机选取样本更新系数weights,每次随机从列表中选取一个值，用过后删除它再进行下一次迭代
randIndex = int(random.uniform(0, len(dataIndex)))#每次迭代改变dataIndex,而m是不变的，故不用unifor(0, m)
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex] - h
weights = weights + alpha*error*dataMatrix[randIndex]
del(dataIndex[randIndex])
return weights
#分析数据，画出决策边界
def plotBestFit(wei,dataMatrix,labelMat):
import matplotlib.pyplot as plt
weights = wei #将矩阵wei转化为list
dataArr = array(dataMatrix) #将矩阵转化为数组
n = shape(dataMatrix)[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) #x为numpy.arange格式，并且以0.1为步长从-3.0到3.0切
#拟合曲线为0 = w0*x0+w1*x1+w2*x2, 故x2 = (-w0*x0-w1*x1)/w2, x0为1,x1为x, x2为y,故有
y = (-weights[0]-weights[1] * x)/weights[2]
ax.plot(x,y)
plt.xlabel("x1") #X轴的标签
plt.ylabel("x2") #Y轴的标签
plt.show()
if __name__=="__main__":
dataMatrix,labelMat = loadDataSet()
weight = stocGradAscent1(array(dataMatrix), labelMat)
plotBestFit(weight,dataMatrix,labelMat)
梯度上升
随机梯度上升
改进的随机梯度上升
样本集为:
-0.017612 14.053064 0
-1.395634 4.662541 1
-0.752157 6.538620 0
-1.322371 7.152853 0
0.423363 11.054677 0
0.406704 7.067335 1
0.667394 12.741452 0
-2.460150 6.866805 1
0.569411 9.548755 0
-0.026632 10.427743 0
0.850433 6.920334 1
1.347183 13.175500 0
1.176813 3.167020 1
-1.781871 9.097953 0
-0.566606 5.749003 1
0.931635 1.589505 1
-0.024205 6.151823 1
-0.036453 2.690988 1
-0.196949 0.444165 1
1.014459 5.754399 1
1.985298 3.230619 1
-1.693453 -0.557540 1
-0.576525 11.778922 0
-0.346811 -1.678730 1
-2.124484 2.672471 1
1.217916 9.597015 0
-0.733928 9.098687 0
-3.642001 -1.618087 1
0.315985 3.523953 1
1.416614 9.619232 0
-0.386323 3.989286 1
0.556921 8.294984 1
1.224863 11.587360 0
-1.347803 -2.406051 1
1.196604 4.951851 1
0.275221 9.543647 0
0.470575 9.332488 0
-1.889567 9.542662 0
-1.527893 12.150579 0
-1.185247 11.309318 0
-0.445678 3.297303 1
1.042222 6.105155 1
-0.618787 10.320986 0
1.152083 0.548467 1
0.828534 2.676045 1
-1.237728 10.549033 0
-0.683565 -2.166125 1
0.229456 5.921938 1
-0.959885 11.555336 0
0.492911 10.993324 0
0.184992 8.721488 0
-0.355715 10.325976 0
-0.397822 8.058397 0
0.824839 13.730343 0
1.507278 5.027866 1
0.099671 6.835839 1
-0.344008 10.717485 0
1.785928 7.718645 1
-0.918801 11.560217 0
-0.364009 4.747300 1
-0.841722 4.119083 1
0.490426 1.960539 1
-0.007194 9.075792 0
0.356107 12.447863 0
0.342578 12.281162 0
-0.810823 -1.466018 1
2.530777 6.476801 1
1.296683 11.607559 0
0.475487 12.040035 0
-0.783277 11.009725 0
0.074798 11.023650 0
-1.337472 0.468339 1
-0.102781 13.763651 0
-0.147324 2.874846 1
0.518389 9.887035 0
1.015399 7.571882 0
-1.658086 -0.027255 1
1.319944 2.171228 1
2.056216 5.019981 1
-0.851633 4.375691 1
-1.510047 6.061992 0
-1.076637 -3.181888 1
1.821096 10.283990 0
3.010150 8.401766 1
-1.099458 1.688274 1
-0.834872 -1.733869 1
-0.846637 3.849075 1
1.400102 12.628781 0
1.752842 5.468166 1
0.078557 0.059736 1
0.089392 -0.715300 1
1.825662 12.693808 0
0.197445 9.744638 0
0.126117 0.922311 1
-0.679797 1.220530 1
0.677983 2.556666 1
0.761349 10.693862 0
-2.168791 0.143632 1
1.388610 9.341997 0
0.317029 14.739025 0
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