【机器学习系列】logistic回归python实现

说明

这里采用梯度下降法（gradient descent）学习logistic回归模型的参数，如果数据量比较大，速度会变慢，可以在迭代过程中改用其他学习方法。如果需要优化，请参考 @zouxy09 的文章

  http://blog.csdn.net/zouxy09/article/details/20319673，不明白logistic回归原理的也可以参考这篇文章。

logistic回归最终需要求解的参数是w，即回归系数。且回归问题最终转化为无约束的优化问题，求解方法为梯度下降法，用来求最终的对数似然函数L(w)的最大值。

参考资料

 @zouxy09 的”logistic回归“写的特别好，主要细节都说清楚了，链接地址： http://blog.csdn.net/zouxy09/article/details/20319673 。

代码

LR.py

from numpy import *
import matplotlib.pyplot as plt

def loadDataset(filename):
	train_x = []
	train_y = []
	fileIn = open(filename)
	for line in fileIn.readlines():
		lineArr = line.strip().split()
		train_x.append([1.0, float(lineArr[0]), float(lineArr[1])])
		train_y.append(float(lineArr[2]))
	return train_x, train_y

def sigmoid(inX):
    return 1.0/(1+exp(-inX))

def trainLR(train_x,train_y,alpha=0.001,iternum=1000):
    matx=mat(train_x)
    maty=mat(train_y).transpose()
    m,n = shape(matx)
    weights = ones((n,1))
    for i in range(iternum):
        weights = weights + alpha * matx.transpose() * ( maty - sigmoid( matx * weights ))
    return weights.getA() # convert mat to array

def testLR(test_x,test_y,weights):
    test_size = len(test_y)
    matchCount = 0
    for i in range(test_size):
        predict_y = 0
        if sum([test_x[i][j]*weights[j] for j in range(len(weights))]) > 0:
            predict_y = 1
        if predict_y == int(test_y[i]):
            matchCount += 1
    return matchCount / float(test_size)

def plotLR(cur_x,cur_y,weights,figIndex):

    ax = plotLR.fig.add_subplot(figIndex)

    posx = []; posy = []
    negx = []; negy = []
    for i in range(len(cur_y)):
        if int(cur_y[i]) == 1:
            posx.append(cur_x[i][1])
            posy.append(cur_x[i][2])
        else:
            negx.append(cur_x[i][1])
            negy.append(cur_x[i][2])

    ax.scatter(posx,posy,30,c='r',marker='s')
    ax.scatter(negx,negy,30,c='b',marker='^')

    minX = min(min(posx),min(negx))
    maxX = max(max(posx),max(negx))
    xs = arange( minX - 1.0 , maxX + 1.0 , 0.1)
    ys=(-weights[0]-weights[1]*xs)/weights[2]
    ax.plot(xs,ys)
    plt.xlabel('X1')
    plt.ylabel('X2')

if __name__ == '__main__':
    print "Step 1. load dataset"
    train_x,train_y = loadDataset("trainset.txt")
    test_x,test_y = loadDataset("testset.txt")

    print "\nStep 2. train"
    weights = trainLR(train_x,train_y)

    print "\nStep 3. test"
    accuracy = testLR(test_x, test_y, weights)
    print 'The classify accuracy is: %.3f%%' % (accuracy * 100)

    print "\nStep 4. show the result"
    plotLR.fig = plt.figure()
    plotLR(train_x,train_y,weights,121)
    plotLR(test_x,test_y,weights,122)
    plt.show()

注：在testLR中，当w·x > 0 时，预测为正例，否则为负例。

运行结果