自学机器学习之logistic回归

基于logictic回归和sigmoid函数的分类，sigmoid函数很简单：f(x)= 1/(1+exp(-z))

其中最主要的就是回归系数的确定，

回归系数的确定就采用最优化的思想：比如牛顿法或者梯度下降（上升），

其中梯度下降就要用到高数中梯度和偏导数的概念，具体的数学可以参考高数书，下面直接上代码。

下面代码用python实现logistic回归，主要参考机器学习实战：

from math import  exp

from numpy import *
def loadDataset():

dataMat = []
labelMat = []
fr =  open('testSet.txt')
for line in fr.readlines():
lineArr = line.strip().split()#删除每行首尾空格，并生成切片
dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
labelMat.append(lineArr[2])

return  dataMat,labelMat

def sigmoid(inx):
return  1.0/(1+exp(-inx))#构造sigmoid函数

def gradAscrnt(dataMatIn,classLabelIs):
dataMatrix = mat(dataMatIn)#把列表转换成矩阵
labelMat = mat(classLabelIs).transpose()#变转换成矩阵并转置
labelMat = labelMat.astype('float64')
m,n = shape(dataMatrix)
alpha = 0.001
maxCycles = 500
weights =ones((n,1))
weights = weights.astype('float64')
for k in range(maxCycles):
h = sigmoid(dataMatrix*weights)
error = (labelMat-h)
weights = weights+alpha*dataMatrix.transpose()*error
'''这里梯度上升算法并不是严格意义上的梯度上升，
这里只是按照差值的方向调整回归系数'''

return weights

下面画出决策边界

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
4000
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()

plotBestFit(weights.getA())

'''改进后的随机梯度上升算法'''

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+j+i)+0.0001
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