核心提示：Fisher分类器...
function fisher
x1=[0.2331 1.5207 0.6499 0.7757 1.0524 1.1974
0.2908 0.2518 0.6682 0.5622 0.9023 0.1333
-0.5431 0.9407 -0.2126 0.0507 -0.0810 0.7315
0.3345 1.0650 -0.0247 0.1043 0.3122 0.6655
0.5838 1.1653 1.2653 0.8137 -0.3399 0.5152
0.7226 -0.2015 0.4070 -0.1717 -1.0573 0.2099];
x2=[2.3385 2.1946 1.6730 1.6365 1.7844 2.0155
2.0681 2.1213 2.4797 1.5118 1.9692 1.8340
1.8704 2.2948 1.7714 2.3939 1.5648 1.9329
2.2027 2.4568 1.7523 1.6991 2.4883 1.7259
2.0466 2.0226 2.3757 1.7987 2.0828 2.0798
1.9449 2.3801 2.2373 2.1614 1.9235 2.2604];
x3=[0.5338 0.8514 1.0831 0.4164 1.1176 0.5536
0.6071 0.4439 0.4928 0.5901 1.0927 1.0756
1.0072 0.4272 0.4353 0.9869 0.4841 1.0992
1.0299 0.7127 1.1024 0.4576 0.8544 1.1275
0.7705 0.4129 1.0085 0.7676 0.8418 0.8784
0.9751 0.7840 0.4158 1.0315 0.7533 0.9548];
%将x1,x2,x3变为列向量
x1=x1(:);
x2=x2(:);
x3=x3(:);
%计算第一类的样本均值向量
m1(1)=mean(x1);
m1(2)=mean(x2);
m1(3)=mean(x3);
%计算第一类样本类内散度矩阵S1
S1=zeros(3,3);
for i=1:36
S1=S1+[-M1(1)+X1(I)-m1(2)+x2(i)-m1(3)+x3(i)]'*[-m1(1)+x1(i)-m1(2)+x2(i)-m1(3)+x3(i)];
end
x4=[1.4010 1.2301 2.0814 1.1655 1.3740 1.1829
1.7632 1.9739 2.4152 2.5890 2.8472 1.9539
1.2500 1.2864 1.2614 2.0071 2.1831 1.7909
1.3322 1.1466 1.7087 1.5920 2.9353 1.4664
2.9313 1.8349 1.8340 2.5096 2.7198 2.3148
2.0353 2.6030 1.2327 2.1465 1.5673 2.9414];
x5=[1.0298 0.9611 0.9154 1.4901 0.8200 0.9399
1.1405 1.0678 0.8050 1.2889 1.4601 1.4334
0.7091 1.2942 1.3744 0.9387 1.2266 1.1833
0.8798 0.5592 0.5150 0.9983 0.9120 0.7126
1.2833 1.1029 1.2680 0.7140 1.2446 1.3392
1.1808 0.5503 1.4708 1.1435 0.7679 1.1288];
x6=[0.6210 1.3656 0.5498 0.6708 0.8932 1.4342
0.9508 0.7324 0.5784 1.4943 1.0915 0.7644
1.2159 1.3049 1.1408 0.9398 0.6197 0.6603
1.3928 1.4084 0.6909 0.8400 0.5381 1.3729
0.7731 0.7319 1.3439 0.8142 0.9586 0.7379
0.7548 0.7393 0.6739 0.8651 1.3699 1.1458];
x4=x4(:);
x5=x5(:);
x6=x6(:);
%计算第二类的样本均值向量m2
m2(1)=mean(x4);
m2(2)=mean(x5);
m2(3)=mean(x6);
%计算第二类样本类内散度矩阵S2
S2=zeros(3,3);
for i=1:36
S2=S2+[-m2(1)+x4(i)-m2(2)+x5(i)-m2(3)+x6(i)]'*[-m2(1)+x4(i)-m2(2)+x5(i)-m2(3)+x6(i)];
end
%总类内散度矩阵
Sw=zeros(3,3);
Sw=S1+S2;
%样本类间散度矩阵Sb
Sb=zeros(3,3);
Sb=(m1-m2)'*(m1-m2);
%最优解W
W=S^-1*(m1-m2)'
%将W变为单位向量以方便计算投影
W=W/sqrt(sum(W.^2));
%计算一维Y空间中的各类样本均值M1及M2
for i=1:36
y(i)=W'*[x1(i) x2(i) x3(i)]';
end
M1=mean(y)
for i=1:36
y(i)=W'*[x4(i) x5(i) x6(i)]';
end
M2=mean(y)
%利用当P(w1)与P（w2）已知的公式计算wo
p1=0.6;p2=0.4;
W0=-(M1+M2)/2+(log(p2/p1))/(36+36-2);
%计算将样本投影到最佳方向上以后的新坐标
X1=[x1*W(1)+x2*W(2)+x3*W(3)]';
X2=[x4*W(1)+x5*W(2)+x6*W(3)]';%计算投影得到的长度
XX1=[W(1)*X1;W(2)*X1;W(3)*X1];
XX2=[W(1)*X2;W(2)*X2;W(3)*X2];%得到新坐标
%绘制样本点
figure(1)
plot3(x1,x2,x3,'r*') %第一类
hold on
plot3(x4,x5,x6,'bp') %第二类
legend('第一类点','第二类点')
title('Fisher线性判别函数')
W1=5*W;
%画出最佳方向
line([-W1(1),W1(1)],[-W1(2),W1(2)],[-W1(3),W1(3)],'color','b');
%判别已给点的分类
a1=[1,1,5,0.6]';
a2=[1.2,1.0,0.55]';
a3
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