感知机

理论知识是参考的《统计学习方法》

代码需要用到numpy和matplotlib.pyplot

import numpy as np import matplotlib.pyplot as plt def perceptron_v2(x,y,mu): #omg与x维度相同 omg = np.zeros((1,x.shape[1])) b = 0 finish_flag = False while finish_flag == False: finish_flag = True; for i in range(len(y)): #若有误分类点，则继续计算 if y[i] * (np.dot(omg, x[i]) + b) <= 0: finish_flag = False omg += mu * y[i] * x[i] b += mu * y[i] break omg = omg[0] #如果是二维数据，则将结果可视化 if x.shape[1] == 2: for i in range(x.shape[0]): #正实例点 if y[i] == 1: plt.scatter(x[i,0],x[i,1],c = 'b') #负实例点 else: plt.scatter(x[i,0],x[i,1],c = 'r') #超平面的在水平轴上的端点取x[:,]的最大值和最小值 x0 = np.array((x[:,0].min(),x[:,0].max())) y0 = np.array(((-1 * b - omg[0] * x0[0]) / omg[1], (-1 * b - omg[0] * x0[1]) / omg[1])) plt.plot(x0,y0,c='g') return omg,b

测试

x = np.array([[3,3],[4,3],[1,1]]) y = np.array([1,1,-1]) mu = 1 perceptron_v2(x,y,mu)

结果

(array([1., 1.]), -3) #输出的omg和b的值

对偶形式

def perceptron_dual(x,y,mu): g = np.empty([x.shape[0],x.shape[0]]) for i in range(x.shape[0]): for j in range(x.shape[0]): g[i,j] = np.dot(x[i],x[j]) alpha = np.zeros((1,x.shape[0])) alpha = alpha[0] b = 0 finish_flag = False while finish_flag == False: finish_flag = True; for i in range(len(y)): temp = 0 for j in range(len(y)): temp += alpha[j] * y[j] * g[i,j] if y[i] * (temp + b) <= 0: finish_flag = False alpha[i] += mu b += mu * y[i] break return alpha,b

在对偶性形式中画超平面，只需由α计算出ω，再利用第一段代码中的画图语句即可