贝叶斯分类器（matlab）

目标

下表由雇员数据库的训练数据组成。数据已泛化。例如，age“3135”表示年龄在31~35之间。对于给定的行，count表示department、status、age和salary在该行具有给定值的元组数。

Department	Status	Age	Salary	Count
Sales	Senior	31-35	46K-50K	30
Sales	junior	26-30	26K-30K	40
Sales	junior	31-35	31K-35K	40
sysytems	junior	21-25	46K-50K	20
sysytems	Senior	31-35	66K-70K	5
sysytems	junior	26-30	46K-50K	3
sysytems	Senior	41-45	66K-70K	3
marketing	Senior	36-40	46K-50K	10
marketing	junior	31-35	41K-45K	4
secretary	Senior	45-60	36K-40K	4
secretary	junior	26-30	26K-30K	6

贝叶斯定理：

拉普拉斯校准法（拉普拉斯估计法）：可以假定训练数据库D很大，以至于对每个计数加1造成的估计概率的变化可以忽略不计，但可以方便地避免概率值为为零。这种概率估计技术成为拉普拉斯校准或拉普拉斯估计法。如果对q个计数都加上1，则必须在用于计算概率地对应分母上加上q。

未使用拉普拉斯校准的朴素贝叶斯（matlab）

主程序：experiment_02.m
使用的自定义函数：Get_judge.m %调用的分类器
涉及到的数据文件：data.xlsx
三个文件夹放到同一级别目录下：

data.xlsx里面涉及的内容：

主函数experiment_02.m

clc;clear
%%朴素贝叶斯做分类
data=xlsread("data.xlsx","Sheet1","A2:G12");
career=data(:,1);%职业     1:sales    2:systems    3:marketing    4:secretary
label=data(:,2);%分类      0为junior  1为senior
%要预测的分类
sample=[2,26,30,46,50];
%%需要得到：职业2分类是1的概率；age在26-30分类是1的概率；收入在46-50之间分类是1的概率
[p1,p2]=get_judge(data,sample);
%%判断是哪个分类p1为senior
if p1>p2
    sample_label=1
else
    sample_label=0
end

Get_judge.m %调用的分类器

function [p1,p2]= get_judge(data,sample)
%%需要判断有没有出现0值的情况，使用拉普拉斯校准
%junior和senior的概率
count=sum(data(:,7));
count_se=sum((data(:,2)==1).*data(:,7))
count_ju=sum((data(:,2)==0).*data(:,7))
p_se=count_se/count
p_ju=count_ju/count
%首先判断senior，junior里面是职业2的概率
% d_count=sum(data(find(data(:,1)==sample(1)),7));%职业是该样本的总人数
% d_count=sum( (data(:,1)==sample(1)).*data(:,7));
d_count_se=sum( (data(:,1) ==sample(1) & data(:,2)==1).*data(:,7));
d_count_ju=sum( (data(:,1) ==sample(1) & data(:,2)==0).*data(:,7));
p_de_1=d_count_se/count_se;
p_de_0=d_count_ju/count_ju;
%接着判断senior，junior是age:26-30之间是的概率
% age_count=sum( (data(:,3)==sample(2)).*data(:,7));
age_count_se=sum( (data(:,3)==sample(2) & data(:,2)==1).*data(:,7));
age_count_ju=sum( (data(:,3)==sample(2) & data(:,2)==0).*data(:,7));
p_age_1=age_count_se/count_se;
p_age_0=age_count_ju/count_ju;


%判断senior,junior中是salary:46-50的概率
% sal_count=sum( (data(:,5)==sample(4)).*data(:,7));
sal_count_se=sum((data(:,5)==sample(4) & data(:,2)==1).*data(:,7));
sal_count_ju=sum((data(:,5)==sample(4) & data(:,2)==0).*data(:,7));
p_sal_1=sal_count_se/count_se;
p_sal_0=sal_count_ju/count_ju;
%%开始计算p1
%p_senior的概率

p1=p_de_1*p_age_1*p_sal_1*p_se

%%同理计算p2
p2=p_de_0*p_age_0*p_sal_0*p_ju

结果

分类结果为junior(sample_label=0)

添加了拉普拉斯校准后的分类器

程序入口：experiment_02.m(需要调用新的分类函数，下面给出改过的函数)
相关文件：get_judge2.m，data.xlsx（同上）

experiment_02.m

clc;clear
%%朴素贝叶斯做分类
data=xlsread("data.xlsx","Sheet1","A2:G12");
career=data(:,1);%职业     1:sales    2:systems    3:marketing    4:secretary
label=data(:,2);%分类      0为junior  1为senior
%要预测的分类
sample=[2,26,30,46,50];
%%需要得到：职业2分类是1的概率；age在26-30分类是1的概率；收入在46-50之间分类是1的概率
[p1,p2]=get_judge2(data,sample);
%%判断是哪个分类p1为senior
if p1>p2
    sample_label=1
else
    sample_label=0
end
    

get_judge2.m

function [p1,p2]= get_judge2(data,sample)
%%需要判断有没有出现0值的情况，使用拉普拉斯校准
%junior和senior的概率
count=sum(data(:,7));
count_se=sum((data(:,2)==1).*data(:,7))
count_ju=sum((data(:,2)==0).*data(:,7))
p_se=count_se/count
p_ju=count_ju/count
%首先判断senior，junior里面是职业2的概率
% d_count=sum(data(find(data(:,1)==sample(1)),7));%职业是该样本的总人数
% d_count=sum( (data(:,1)==sample(1)).*data(:,7));
d_count_se=sum( (data(:,1) ==sample(1) & data(:,2)==1).*data(:,7));
if d_count_se==0
    d_count_se=1
    count_se=count_se+length(unique(data(:,1)));
    count=count+length(unique(data(:,1)));
end
d_count_ju=sum( (data(:,1) ==sample(1) & data(:,2)==0).*data(:,7));
if d_count_ju==0
    d_count_ju=1
    count_ju=count_ju+length(unique(data(:,1)));
    count=count+length(unique(data(:,1)));
end
p_de_1=d_count_se/count_se;
p_de_0=d_count_ju/count_ju;
%接着判断senior，junior是age:26-30之间是的概率
% age_count=sum( (data(:,3)==sample(2)).*data(:,7));
age_count_se=sum( (data(:,3)==sample(2) & data(:,2)==1).*data(:,7));
if age_count_se==0
    age_count_se=1
    count_se=count_se+length(unique(data(:,3)));
    count=count+length(unique(data(:,3)));
end
age_count_ju=sum( (data(:,3)==sample(2) & data(:,2)==0).*data(:,7));
if age_count_ju==0
    age_count_ju=1
    count_ju=count_ju+length(unique(data(:,3)));
    count=count+length(unique(data(:,3)));
end
p_age_1=age_count_se/count_se;
p_age_0=age_count_ju/count_ju;


%判断senior,junior中是salary:46-50的概率
% sal_count=sum( (data(:,5)==sample(4)).*data(:,7));
sal_count_se=sum((data(:,5)==sample(4) & data(:,2)==1).*data(:,7));
if sal_count_se==0
    sal_count_se=1
    count_se=count_se+length(unique(data(:,5)))
end
sal_count_ju=sum((data(:,5)==sample(4) & data(:,2)==0).*data(:,7));
if sal_count_ju==0
    sal_count_ju=1
    count_ju=count_ju+length(unique(data(:,5)))
end
p_sal_1=sal_count_se/count_se;
p_sal_0=sal_count_ju/count_ju;
%%开始计算p1
%p_senior的概率

p1=p_de_1*p_age_1*p_sal_1*p_se

%%同理计算p2
p2=p_de_0*p_age_0*p_sal_0*p_ju

data.xlsx

结果

添加了拉普拉斯校准后的分类器：

上述哪里如果有问题的话，还请指教。