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贝叶斯分类器的matlab实现

贝叶斯分类原理：

1) 在已知P(Wi)，P(X|Wi)(i=1,2)及给出待识别的X的情况下，根据贝叶斯公式计算出后验概率P(Wi|X) ;

2) 根据1)中计算的后验概率值，找到最大的后验概率，则样本X属于该类

举例：

解决方案：

但对于两类来说，因为分母相同，所以可采取如下分类标准：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%

%By Shelley from NCUT，April 14th 2011

%Email:just_for_h264@https://www.wendangku.net/doc/8814309193.html,

%此程序利用贝叶斯分类算法，首先对两类样本进行训练，

%进而可在屏幕上任意取点，程序可输出属于第一类，还是第二类%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%

clear;

close all

%读入两类训练样本数据

load data

%求两类训练样本的均值和方差

u1=mean(Sample1);

u2=mean(Sample2);

sigm1=cov(Sample1);

sigm2=cov(Sample2);

%计算两个样本的密度函数并显示

x=-20:0.5:40;

y= -20:0.5:20;

[X,Y] = meshgrid(x,y);

F1 = mvnpdf([X(:),Y(:)],u1,sigm1);

F2 = mvnpdf([X(:),Y(:)],u2,sigm2);

P1=reshape(F1,size(X));

P2=reshape(F2,size(X));

figure(2)

surf(X,Y,P1)

hold on

surf(X,Y,P2)

shading interp

colorbar

title('条件概率密度函数曲线'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%

%以下为测试部分

%利用ginput随机选取屏幕上的点（可连续取10个点）

%程序可根据点的位置自动地显示出属于那个类

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%

pw1=0.4;pw2=0.6;

figure(1)

plot(Sample1(:,1),Sample1(:,2),'r.')

hold on

plot(Sample2(:,1),Sample2(:,2),'b.')

for i=1:10

[u,v]=ginput(1);

plot(u,v,'m*');

P1=pw1*mvnpdf([u,v],u1,sigm1);

P2=pw2*mvnpdf([u,v],u2,sigm2);

hold all

if(P1>P2)

disp('it belong to the first class');

else

disp('it belong to the second class');

end;

end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%

结果示意：

两个样本的密度函数曲线：

测试结果：

命令窗口中显示：

it belong to the first class

it belong to the second class

it belong to the first class

分析可知在第一类周围有八个随机的测试点，在第二类周围有两个随机的测试点，与命令窗口中的结果相符合。