Logistic 回归梯度上升优化函数

In [183]:

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

In [184]:

def sigmoid(inX):

return 1.0/(1+exp(-inX))

批量梯度下降

In [185]:

def gradAscent(dataMatIn, classLabels):

dataMatrix = mat(dataMatIn)

labelMat = mat(classLabels).transpose()

m,n = shape(dataMatrix)

alpha = 0.001

maxCycles = 500

weights = ones((n,1))

for k in range(maxCycles):

h = sigmoid(dataMatrix*weights) #   h是一个矩阵

error = (labelMat - h)

weights = weights + alpha * dataMatrix.transpose() * error

return weights 

随机梯度下降

In [186]:

def stocGradAscent0(dataMatrix, classLabels):

m,n = shape(dataMatrix)

alpha = 0.01

weights = ones(n)

#weights = [0.1,0.1,0.1]

for i in range(m):

h = sigmoid(sum(dataMatrix[i]*weights))#  h是一个数值

print dataMatrix[i]

print weights

print dataMatrix[i]*weights

error = classLabels[i] - h

weights = weights + alpha * error * dataMatrix[i]

return weights

sum()的参数是一个list 下面是改进的随机梯度上升算法：

In [187]:

def stocGradAscent1(dataMatrix, classLabels, numIter=150):

m,n = shape(dataMatrix)

weights = ones(n)

#weights = [0.1,0.1,0.1]

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))#  h是一个数值

error = classLabels[randIndex] - h

weights = weights + alpha * error * dataMatrix[randIndex]

del(dataIndex[randIndex])

return weights

In [188]:

#import logRegres

In [189]:

dataArr,labelMat = loadDataSet()

In [190]:

#weights=gradAscent(dataArr,labelMat)

weights=stocGradAscent1(array(dataArr),labelMat,500)

In [191]:

def plotBestFit(wei):

import matplotlib.pyplot as plt

weights = wei

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()

h = subplot(m,n,p)/subplot(mnp) 将figure划分为m×n块，在第p块创建坐标系，并返回它的句柄。当m,n,p<10时，可以简化为subplot(mnp)或者subplot mnp （注：subplot（m,n,p）或者subplot（mnp）此函数最常用：subplot是将多个图画到一个平面上的工具。其中，m表示是图排成m行，n表示图排成n列，也就是整个figure中有n个图是排成一行的，一共m行，如果第一个数字是2就是表示2行图。p是指你现在要把曲线画到figure中哪个图上，最后一个如果是1表示是从左到右第一个位置。 ）

In [192]:

from numpy import *

#reload

print weights

plotBestFit(weights)