机器学习逻辑回归牛顿法python

数据集来自http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex4/ex4.html

image.png

import numpy as np
import matplotlib.pyplot as plt

#逻辑回归 牛顿法

#加载数据,shu
def load_data(file):
    data,label = [],[]
    for line in file.readlines():
        lineArr = line.strip().split()
        data.append([1.0, float(lineArr[0] ), float( lineArr[1])] )
    for i in range(80):
        if i < 40 : 
            label.append(1)
        else :
            label.append(0)
    xmat = np.mat(data)                 #x集，共80个
    ymat = np.mat(label).reshape(80,1)  #标签集
    return xmat,ymat

def w_calc (xmat,ymat,maxIter = 7):
    W = np.zeros((3,1))
    m = xmat.shape[0]                       #80
    for i in range(maxIter):
        h = 1.0/(1+np.exp(-(xmat*W)) )     #sigmoid函数 (80,1)
        grad = (1.0/m)*xmat.T*(h-ymat)     #梯度 (3,1) = (3,80) * (80,1)  重点
        H = (1.0/m)*xmat.T*np.diag((h*(1-h).T).A[0] ).T*xmat  #(3,3) =(3,80)*(80,1)*(1,80)*(80,3)
        W -= np.linalg.inv(H)*grad       #(3,1) = 
    return W

file = open("ex4x.dat")
xmat,ymat = load_data(file)
W = w_calc(xmat,ymat)
print('w:',W)

w0=W[0,0]
w1=W[1,0]
w2=W[2,0]

plotx1 = np.arange(20,50,2)
plotx2 = -w0/w2-w1/w2*plotx1   #x2轴
plt.plot(plotx1,plotx2,c='r',label='decision boundary')

plt.scatter(xmat[:,1][ymat==0].A,xmat[:,2][ymat==0].A,marker='o',label='label=neg')
plt.scatter(xmat[:,1][ymat==1].A,xmat[:,2][ymat==1].A,marker='+',label='lebel=pos')
plt.grid()
plt.legend()
plt.show()

其中求海森矩阵是重点，之前看了很多代码都没有用到 np.diag() 求对角矩阵，导致结果不准确。这样写了后由于牛顿法下降很快，迭代7次左右即可。