朴素贝叶斯分类Python演示

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt

'''
朴素贝叶斯分类器的原理

事件H的先验概率P(H)，即无条件概率
事件H在X发生时的后验概率P(H|X)

这里面H通常是指某一个分类
X是指样本事件
P(H|X)就表示在样本X发生的情况下，分类H的概率
假设有N个分类H1到HN，那么P(Hi|X)最大的分类就是我们要找的，假设是Hk
因为在X发生的情况下，Hk发生的概率最大

P(H|X) = [P(X|H)*P(H)]/P(X)

分类器的构造
条件如下
1.每个元组有N个属性 X = ｛x1 , x2 , ... , xn｝，分别对应属性｛A1 ... An｝，并且属性之间相互独立
2.当前有M个训练元组，并且知道它们的分类标号
3.一共有K个分类C1 ... Ck，并且知道每个分类的先验概率，如果不知道则拟定其为1/K

问题是
对于任意给定的新的元组Xgive，确定其分类Cget，使得P(Cget|Xgive)最大（相对于其它分类）

解析
P(Ci|X) = [P(X|Ci)*P(Ci)]/P(X)
对于所有的分类｛C｝，P(X)是不变的（其实是未知的），为了使P(Ci|X)最大，
只需要使P(X|Ci)*P(Ci)最大
如果P(Ci)取1/K，则只要使P(X|Ci)最大
由于X = ｛x1 , x2 , ... , xn｝，分别对应属性｛A1 ... An｝，并且各个属性之间没有关联
则P(X|Ci)*P(Ci) = P(x1|Ci)*P(x2|Ci)*...*P(xn|Ci) * P(Ci)

P(xi|Ci)由训练元组得到
分为两种情况
如果Ai为离散值，则P(xi|Ci)等于【属于Ci的训练元组中，Ai=xi的元组个数】/【属于Ci的元组总数】
如果Ai为连续值，则假定Ci中的Ai服从高斯分布，计算出高斯分布的参数，分别为平均值和标准差
P(xi|Ci)等于xi处的概率密度

'''

'''
问题一：训练元组从何而来？

'''

#加载训练数据
#文件格式：属性标号，是否连续【yes|no】，属性说明
attribute_file_dest = 'F:\\bayes_categorize\\attribute.dat'
attribute_file = open(attribute_file_dest)

#文件格式：rec_id,attr1_value,attr2_value,...，attrn_value,class_id
trainning_data_file_dest = 'F:\\bayes_categorize\\trainning_data.dat'
trainning_data_file = open(trainning_data_file_dest)

#文件格式：class_id,class_desc
class_desc_file_dest = 'F:\\bayes_categorize\\class_desc.dat'
class_desc_file = open(class_desc_file_dest)

attr_dict = {}
for line in attribute_file :
line = line.strip()
fld_list = line.split(',')
attr_dict[int(fld_list[0])] = tuple(fld_list[1:])

class_dict = {}
for line in class_desc_file :
line = line.strip()
fld_list = line.split(',')
class_dict[int(fld_list[0])] = fld_list[1]

trainning_data_dict = {}
class_member_set_dict = {}
for line in trainning_data_file :
line = line.strip()
fld_list = line.split(',')
rec_id = int(fld_list[0])
a1 = int(fld_list[1])
a2 = int(fld_list[2])
a3 = float(fld_list[3])
c_id = int(fld_list[4])

if c_id not in class_member_set_dict :
class_member_set_dict[c_id] = set()
class_member_set_dict[c_id].add(rec_id)
trainning_data_dict[rec_id] = (a1 , a2 , a3)

attribute_file.close()
class_desc_file.close()
trainning_data_file.close()

class_possibility_dict = {}
for c_id in class_member_set_dict :
class_possibility_dict[c_id] = (len(class_member_set_dict[c_id]) + 0.0)/len(trainning_data_dict)

#等待分类的数据
data_to_classify_file_dest = 'F:\\bayes_categorize\\trainning_data_new.dat'
data_to_classify_file = open(data_to_classify_file_dest)
data_to_classify_dict = {}
for line in data_to_classify_file :
line = line.strip()
fld_list = line.split(',')
rec_id = int(fld_list[0])
a1 = int(fld_list[1])
a2 = int(fld_list[2])
a3 = float(fld_list[3])
c_id = int(fld_list[4])
data_to_classify_dict[rec_id] = (a1 , a2 , a3 , c_id)
data_to_classify_file.close()

diff_cnt = 0
#对于每一个待分类元组，对于每一个分类计算P(X|Ci)*P(Ci)，寻找取得最大值的分类
for rec_id in data_to_classify_dict :

res_class_id = 0
max_P_X_Ci = 0.0
a1_x1 = data_to_classify_dict[rec_id][0]
a2_x2 = data_to_classify_dict[rec_id][1]
a3_x3 = data_to_classify_dict[rec_id][2]
for c_id in class_possibility_dict :
P_Ci = class_possibility_dict[c_id]
#求P_x1_Ci
cnt_Ci = len(class_member_set_dict[c_id])
cnt_x1_Ci = len([tmp_rec_id for tmp_rec_id in trainning_data_dict \
if trainning_data_dict[tmp_rec_id][0] == a1_x1 and tmp_rec_id in class_member_set_dict[c_id]])
P_x1_Ci = (cnt_x1_Ci + 0.0) / cnt_Ci
#求P_x2_Ci
cnt_Ci = len(class_member_set_dict[c_id])
cnt_x2_Ci = len([tmp_rec_id for tmp_rec_id in trainning_data_dict \
if trainning_data_dict[tmp_rec_id][1] == a2_x2 and tmp_rec_id in class_member_set_dict[c_id]])
P_x2_Ci = (cnt_x2_Ci + 0.0) / cnt_Ci
#求P_x3_Ci
#按正态分布处理，取标准差和平均值
a3_data = [ trainning_data_dict[tmp_rec_id][2] for tmp_rec_id in trainning_data_dict \
if tmp_rec_id in class_member_set_dict[c_id] ]
a3_std_err = np.sqrt(np.var(a3_data))
a3_mean = np.mean(a3_data)
P_x3_Ci = mlab.normpdf(a3_x3 , a3_mean , a3_std_err )

res = P_x1_Ci * P_x2_Ci * P_x3_Ci * P_Ci
if res > max_P_X_Ci :
max_P_X_Ci = res
res_class_id = c_id

if res_class_id == 0 :
print 'error 2'

if res_class_id != data_to_classify_dict[rec_id][3] :
print 'different'
print res_class_id
print data_to_classify_dict[rec_id]
diff_cnt += 1

print diff_cnt

产生测试数据的脚本：
# -*- coding: utf-8 -*-
import numpy as np
from random import random as rdn

#attr : a1 离【1 -- 10 】, a2 离【1 -- 10 】, a3 连【1 -- 100】正态分布

#class : c1 , c2 , c3 , c4 , c5 , c6 , c7 , c8

#data : 1 - 1000

'''
c1 : a1[1 - 3] a2[4 - 10] a3[<= 50]
c2 : a1[1 - 3] a2[4 - 10] a3[> 50]
c3 : a1[1 - 3] a2[1 - 3] a3[> 30]
c4 : a1[1 - 3] a2[1 - 3] a3[<= 30]
c5 : a1[4 - 10] a2[4 - 10] a3[<= 50]
c6 : a1[4 - 10] a2[4 - 10] a3[> 50]
c7 : a1[4 - 10] a2[1 - 3] a3[> 30]
c8 : a1[4 - 10] a2[1 - 3] a3[<= 30]
'''

data_file = open('F:\\bayes_categorize\\trainning_data_new.dat' , 'w')
a3_data = np.random.randn(1000 ) * 30 + 50

for i in range(1 , 1001 ) :
rec_id = i
a1 = int(rdn()*10) + 1
if a1 > 10 :
a1 = 10

a2 = int(rdn()*10) + 1
if a2 > 10 :
a2 = 10

a3 = a3_data[i-1]

c_id = 0
if a1 <= 3 and a2 >= 4 and a3 <= 50 :
c_id = 1
elif a1 <= 3 and a2 >= 4 and a3 > 50 :
c_id = 2
elif a1 <= 3 and a2 < 4 and a3 > 30 :
c_id = 3
elif a1 <= 3 and a2 < 4 and a3 <= 30 :
c_id = 4
elif a1 > 3 and a2 >= 4 and a3 <= 50 :
c_id = 5
elif a1 > 3 and a2 >= 4 and a3 > 50 :
c_id = 6
elif a1 > 3 and a2 < 4 and a3 > 30 :
c_id = 7
elif a1 > 3 and a2 < 4 and a3 <= 30 :
c_id = 8
else :
print 'error'

str_line = str(rec_id) + ',' + str(a1) + ',' + str(a2) + ',' + str(a3) + ',' + str(c_id) + '\n'
data_file.write(str_line)
data_file.close()

配置文件：
1,no,
2,no,
3,yes,