机器学习之感知机python实现

一. 理论基础

1. 损失函数

L(w,b)=−∑i=0myi(wxi+b)

2. 更新参数

w=w+α∑i=0mxiyi

b=b+α∑i=0myi

二. python实现

1. 代码

Perceptron.py

#encoding=utf-8'''implements the perceptron'''import numpy as npimport matplotlib.pyplot as pltimport pandas as pdclass Perceptron:    def __init__(self, alpha=0.1, iterator_num=100):        self.alpha = alpha        self.iterator_num = iterator_num    def train(self, x_train, y_train):        x_train = np.mat(x_train)        y_train = np.mat(y_train)        [m, n] = x_train.shape        self.theta = np.mat(np.zeros((n, 1)))        self.b = 0        self.__stochastic_gradient_decent__(x_train, y_train)    def __gradient_decent__(self, x_train, y_train):        x_train = np.mat(x_train)        y_train = np.mat(y_train)        for i in xrange(self.iterator_num):            self.theta = self.theta + self.alpha * x_train.T * y_train            self.b = self.b + self.alpha * np.sum(y_train)    def __stochastic_gradient_decent__(self, x_train, y_train):        x_train = np.mat(x_train)        y_train = np.mat(y_train)        [m, n] = x_train.shape        for i in xrange(self.iterator_num):            for j in xrange(m):                self.theta = self.theta + self.alpha * x_train[j].T * y_train[j]                 self.b = self.b + self.alpha * y_train[j]def main():    '''    test unit    '''    print "step 1: load data..."    data = pd.read_csv('/home/LiuYao/Documents/MarchineLearning/data.csv')    # data = data.ix[0:30, :]    x = np.mat(data[['x', 'y']].values)    y = np.mat(data['label'].values).T    y[y == 0] = -1    print y[y == 1]    print "positive samples : ", y[y == 1].shape    print "nagetive samples : ", y[y == -1].shape    ## step 2: training...    print "step 2: training..."    perceptron = Perceptron(alpha=0.1,iterator_num=100)    perceptron.train(x, y)    ## step 3: show the decision boundary    print "step 3: show the decision boundary..."       print perceptron.theta    x_min = np.min(x[:, 0])    x_max = np.max(x[:, 0])    y_min = (-perceptron.b - perceptron.theta[0] * x_min) / perceptron.theta[1]    y_max = (-perceptron.b - perceptron.theta[0] * x_max) / perceptron.theta[1]    plt.plot([x_min, x_max], [y_min[0,0], y_max[0,0]])    plt.scatter(x[:, 0].getA(), x[:, 1].getA(), c=y.getA())    plt.show()if __name__ == '__main__':    main()

2. 结果

最终结果会有一些问题，不知道为什么，请知道的大神解答一下,梯度下降和随机梯度下降都试了，结果一样。
* 用前三十个数据的时候，分界面正确；
* 用前60个数据的时候，分界面就离谱了。
* 所有数据的时候分界面明显有一些偏差；

前30个数据

前60个数据

所有数据

数据如下：

x,y,label10.6,13.5,012.55,12.1,012.05,13.95,010.85,15.05,07.5,12.75,09.45,11.25,08.95,13.3,08.45,15.5,012.15,12.2,05.15,8.25,017.45,6.0,018.55,5.8,116.1,4.45,113.95,6.75,115.4,7.85,117.7,9.25,119.3,9.8,120.5,8.1,18.15,2.05,111.7,4.9,121.1,4.6,121.1,9.75,117.65,11.4,16.95,9.9,15.8,12.05,17.35,10.0,08.15,11.05,07.4,11.65,04.55,11.35,04.4,15.2,04.2,16.6,07.85,17.1,013.45,18.95,015.35,18.9,018.35,17.1,016.85,15.75,015.75,10.8,013.95,9.25,010.25,10.7,09.85,12.05,014.25,17.45,010.15,17.55,07.0,14.1,04.85,11.8,04.75,8.6,03.25,6.65,01.9,9.55,02.1,14.75,01.5,10.9,05.75,9.65,07.65,8.1,09.6,9.1,010.1,2.0,112.2,2.75,18.0,6.3,16.8,5.1,17.35,3.65,19.5,4.65,113.05,7.7,117.85,5.15,124.35,7.4,120.4,13.1,114.55,15.4,124.95,11.05,122.15,11.15,122.85,5.85,122.5,4.15,119.3,1.6,115.6,0.25,114.5,1.55,114.5,3.95,110.35,7.1,113.65,6.75,114.0,5.55,112.15,4.8,110.5,4.15,122.95,8.75,121.25,7.05,117.05,7.9,117.05,7.9,1