Fisher分类器Matlab

Fisher分类器用于解决二类线性可分问题。

Fisher准则基本原理：找到一个最合适的投影轴，使两类样本在该轴上投影之间的距离尽可能远，而每一类样本的投影尽可能紧凑，从而使分类效果为最佳。

例如上图中：通过将方块点和圆点向w1投影，然后再在设置合适的阈值即可将方块和圆点分离。

 

Matlab程序如下：

[html]  view plain   copy

1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
2. %By Shelley from NCUT，April 2nd 2011  
3. %Email:just_for_h264@163.com  
4. %本m文件实现fisher算法，并对两个二维正态分布随机序列  
5. %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  
6. %还是第二类  
7. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
8.   
9. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
10. %分别产生x轴和y轴都为正态分布的随机序列  
11. %假设x轴和y轴序列相互独立，可产生二维正态分布随机序列  
12. %w1、w2分别用来保存两个训练集的横坐标和纵坐标  
13. %用normrnd函数产生正态分布函数  
14. %normrnd（mean,omega,[row,column]）  
15. %mean:均值;omega:标准差  
16. %row:产生随机序列的行数;column:产生随机序列的列数  
17. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
18.  X1 = normrnd(40,10,[200,1]);  
19.  Y1 = normrnd(40,10,[200,1]);  
20.  w1=[X1, Y1];  
21.  X2 = normrnd(5 ,10,[100,1]);  
22.  Y2 = normrnd(0 ,10,[100,1]);  
23.  w2=[X2, Y2];  
24.    
25. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
26. %以下部分为fisher算法的实现  
27. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
28. %计算样本均值  
29. m1=mean(w1)';  
30. m2=mean(w2)';  
31. %s1、s2分别代表表示第一类、第二类样本的类内离散度矩阵  
32. s1=zeros(2);  
33. [row1,colum1]=size(w1);  
34. for i=