感知机示例程序

教案

# -*- coding: utf-8 -*-
"""
Created on Wed Mar 22 21:47:27 2017
@author: Yuan Sheng
"""
import random
import matplotlib.pyplot as plt
import numpy as np
# 训练集 ((x1, x2), y)
train_set = ( ((1, 1), -1), ((3, 3), 1), ((3, 4), 1) )
# 准备训练出来的直线参数
w1, w2, b = 0, 0, 0
eta = 1 # 学习率
##################################
def y_of_line(x, A, B, C):
    "根据直线方程求 y"
    if (A == 0 and B == 0):
        return x, [0] * 50
    elif (A != 0 and B == 0):
        x = [-1 * (C / float(A))] * 50
        y = np.linspace(0, 5, 50)
        return x, y
    else:
        return x, [-1.0 * (A / float(B)) * val - (C / float(B)) for val in x]
##################################    
def draw_plot():
    "分类结束后画图"
    global train_set, w1, w2, b
    plt.xlim(0, 5)
    plt.ylim(0, 5)
    plt.xlabel('x1')
    plt.ylabel('x2')
    # 实例点
    for simple in train_set:
        x1, x2, y = simple[0][0], simple[0][1], simple[1]
        color = 'r'
        if y == 1 : color = 'b'        
        shape = 'x'
        if y == 1 : shape = '+'
        plt.scatter(x1, x2, 120, color, shape)
    # 直线
    x = np.linspace(0, 5, 50)
    x, y = y_of_line(x, w1, w2, b)
    plt.plot(x, y, 'g')
##################################    
def is_err_simple(_x1, _x2, _y):
    "判断一个点是否误分类. x1:横坐标; x2:纵坐标; y:标注分类"
    global w1, w2, b
    return _y * (w1 * _x1 + w2 * _x2 + b) <= 0
##################################    
def train():
    "算法的核心过程，即训练模型的过程"
    global train_set, w1, w2, b
    go_through = False
    cnter = 0
    while (cnter < 1000):        
        err_list = [] # 存放一个步骤中所有的误分类点
        for simple in train_set:
            x1, x2, y = simple[0][0], simple[0][1], simple[1]
            # 找到误分类点则加入 err_list
            if is_err_simple(x1, x2, y):
                err_list.append(simple)
        # 如果分类完成则结束循环
        if len(err_list) == 0:
            go_through = True
            break
        # 随机选择一个误分类点
        err_simple = random.choice(err_list)
        # 调整直线参数
        w1 += eta * err_simple[1] * err_simple[0][0]
        w2 += eta * err_simple[1] * err_simple[0][1]
        b += eta * err_simple[1]            
        # 计数
        cnter += 1
    model = "f(x1,x2) = sign(%d*x1 + %d*x2 + %d)" % (w1, w2, b);
    print model
    return go_through
##################################    
if __name__ == "__main__":
    train()
    draw_plot()