朴素贝叶斯分类器 示范程序 Python

教案

# -*- coding: utf-8 -*-
"""
Created on Sat Mar 25 21:32:34 2017
@author: Yuan Sheng
"""
import matplotlib.pyplot as plt
import numpy as np
import random
##################################    
def createDataSet2():
    "生成两块随机点"
    groupA = []
    groupB = []
    direction = [1, -1]
    for i in range(0, 200):
            groupA.append([50 + random.choice(direction) * random.choice(range(50)), 50 + random.choice(direction) * random.choice(range(50))])
            groupB.append([150 + random.choice(direction) * random.choice(range(50)), 150 + random.choice(direction) * random.choice(range(50))])
    return groupA, groupB
##################################    
def distance(A, B):
    "欧氏距离"
    return np.sqrt((A[0] - B[0])**2 + (A[1] - B[1])**2)
def P_test_of_class(test, group_a, group_b):
    "计算 P(测试点|类别 A),  P(测试点|类别 B) 可以不看"
    # 计算特征符合的最小距离
    LEAST_DIST = 20
    total_sample = len(group_a) + len(group_b)   
    count_a, count_b = 0, 0
    # 计数 A
    for pt in group_a:
        if (distance(test, pt) <= LEAST_DIST):
            count_a += 1;
    # 计数 B
    for pt in group_b:
        if (distance(test, pt) <= LEAST_DIST):
            count_b += 1;
    # P(测试点|类别 A)
    p_test_A = float(count_a) / float(total_sample)
    # P(测试点|类别 B)
    p_test_B = float(count_b) / float(total_sample)
    return p_test_A, p_test_B
def P_class(group_a, group_b):
    "计算P(类别 A)和P(类别 B)"
    p_A = float(len(group_a)) / float(len(group_a) + len(group_b))
    p_B = 1. - p_A
    return p_A, p_B
##################################
def naive_bayes(test, group_a, group_b):
    """核心函数. 示范用，没有安全检查
    # 根据贝叶斯公式：
    # P(类别 A | 测试点) = [P(测试点 | 类别 A) * P(类别 A)] / P(测试点)
    # P(类别 B | 测试点) = [P(测试点 | 类别 B) * P(类别 B)] / P(测试点)
    # 哪个概率大，测试点即属于哪个类别。
    # 因为 2 个表达式<分母相同>，所以<只比较分子>就可以了！"""
    # P(测试点|类别 A),  P(测试点|类别 B)
    p_test_A, p_test_B = P_test_of_class(test, group_a, group_b)
    # P(类别 A), P(类别 B)
    p_A, p_B = P_class(group_a, group_b)
    # # 贝叶斯公式的分子
    # P(测试点 |类别 A) * P(类别 A)
    num_A_test = p_test_A * p_A
    # P(测试点 |类别 B) * P(类别 B)
    num_B_test = p_test_B * p_B
    # # 返回值 0-无法分类；1-A类；2-B类。
    if (num_A_test == 0. and num_B_test == 0.):
        ret = 0
    else:
        if num_A_test >= num_B_test:
            ret = 1
        else:
            ret = 2
    return ret, num_A_test, num_B_test
##################################    
def draw_plot(group_a, group_b, cls, num_a, num_b):
    "画图表，可以不看"
    x, y, color, size = [], [], [], []
    for pt in group_a:
        x.append(pt[0])
        y.append(pt[1])
        color.append('b')
        size.append(40)
    for pt in group_b:
        x.append(pt[0])
        y.append(pt[1])
        color.append('r')
        size.append(40)
    plt.xlabel('Chocolate per-day')
    plt.ylabel('Ice Cream per-day')
    plt.scatter(x,y,size,color) 
    x1 = [test[0]]
    y1 = [test[1]]
    text = 'None'
    color2 = 'k'
    text_num_A = 'P(A | x,y) = P(x,y | A) * P(A) / P(x,y) = ' + str(num_a) + " / P(x,y)"
    text_num_B = 'P(B | x,y) = P(x,y | B) * P(B) / P(x,y) = ' + str(num_b) + " / P(x,y)"    
    if cls == 2: 
        text = 'B'
        color2 = 'r'
    elif cls == 1:
        text = 'A'
        color2 = 'b'        
    plt.scatter(x1, y1, [200], ['g'])
    plt.text(200, 0, text,
        verticalalignment='bottom', horizontalalignment='right',
        color=color2, fontsize=20)
    plt.text(-45, 225, text_num_A,
        verticalalignment='bottom', horizontalalignment='left',
        color='k', fontsize=12)
    plt.text(-45, 205, text_num_B,
        verticalalignment='bottom', horizontalalignment='left',
        color='k', fontsize=12)        
    plt.show()
##################################
if __name__ == '__main__':
    groupA, groupB = createDataSet2()
    # 测试点， 可以自己修改试试
    test = [100., 100.]
    cls, num_a, num_b = naive_bayes(test, groupA, groupB)
    draw_plot(groupA, groupB, cls, num_a, num_b)
    print cls