Fisher准则线性分类器设计.doc
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Fisher准则线性分类器设计.doc
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一、基于Fisher准则线性分类器设计
1、实验内容:
已知有两类数据和二者的概率已知=0.6,=0.4。
中数据点的坐标对应一一如下:
数据:
x=
0.23311.52070.64990.77571.05241.1974
0.29080.25180.66820.56220.90230.1333
-0.54310.9407-0.21260.0507-0.08100.7315
0.33451.0650-0.02470.10430.31220.6655
0.58381.16531.26530.8137-0.33990.5152
0.7226-0.20150.4070-0.1717-1.0573-0.2099
y=
2.33852.19461.67301.63651.78442.0155
2.06812.12132.47971.51181.96921.8340
1.87042.29481.77142.39391.56481.9329
2.20272.45681.75231.69912.48831.7259
2.04662.02262.37571.79872.08282.0798
1.94492.38012.23732.16141.92352.2604
z=
0.53380.85141.08310.41641.11760.5536
0.60710.44390.49280.59011.09271.0756
1.00720.42720.43530.98690.48411.0992
1.02990.71271.01240.45760.85441.1275
0.77050.41291.00850.76760.84180.8784
0.97510.78400.41581.03150.75330.9548
数据点的对应的三维坐标为
x2=
1.40101.23012.08141.16551.37401.1829
1.76321.97392.41522.58902.84721.9539
1.25001.28641.26142.00712.18311.7909
1.33221.14661.70871.59202.93531.4664
2.93131.83491.83402.50962.71982.3148
2.03532.60301.23272.14651.56732.9414
y2=
1.02980.96110.91541.49010.82000.9399
1.14051.06780.80501.28891.46011.4334
0.70911.29421.37440.93871.22661.1833
0.87980.55920.51500.99830.91200.7126
1.28331.10291.26800.71401.24461.3392
1.18080.55031.47081.14350.76791.1288
z2=
0.62101.36560.54980.67080.89321.4342
0.95080.73240.57841.49431.09150.7644
1.21591.30491.14080.93980.61970.6603
1.39281.40840.69090.84000.53811.3729
0.77310.73191.34390.81420.95860.7379
0.75480.73930.67390.86511.36991.1458
数据的样本点分布如下图:
1)请把数据作为样本,根据Fisher选择投影方向的原则,使原样本向量在该方向上的投影能兼顾类间分布尽可能分开,类内样本投影尽可能密集的要求,求出评价投影方向的函数,并在图形表示出来。
并在实验报告中表示出来,并求使取极大值的。
用matlab完成Fisher线性分类器的设计,程序的语句要求有注释。
2)根据上述的结果并判断(1,1.5,0.6)(1.2,1.0,0.55),(2.0,0.9,0.68),(1.2,1.5,0.89),(0.23,2.33,1.43),属于哪个类别,并画出数据分类相应的结果图,要求画出其在上的投影。
3)回答如下问题,分析一下的比例因子对于Fisher判别函数没有影响的原因。
2、实验代码
x1=[0.23311.52070.64990.77571.05241.1974
0.29080.25180.66820.56220.90230.1333
-0.54310.9407-0.21260.0507-0.08100.7315
0.33451.0650-0.02470.10430.31220.6655
0.58381.16531.26530.8137-0.33990.5152
0.7226-0.20150.4070-0.1717-1.0573-0.2099];
x2=[2.33852.19461.67301.63651.78442.0155
2.06812.12132.47971.51181.96921.8340
1.87042.29481.77142.39391.56481.9329
2.20272.45681.75231.69912.48831.7259
2.04662.02262.37571.79872.08282.0798
1.94492.38012.23732.16141.92352.2604];
x3=[0.53380.85141.08310.41641.11760.5536
0.60710.44390.49280.59011.09271.0756
1.00720.42720.43530.98690.48411.0992
1.02990.71271.01240.45760.85441.1275
0.77050.41291.00850.76760.84180.8784
0.97510.78400.41581.03150.75330.9548];
%将x1、x2、x3变为行向量
x1=x1(:
);x2=x2(:
);x3=x3(:
);
%计算第一类的样本均值向量m1
m1
(1)=mean(x1);
m1
(2)=mean(x2);
m1(3)=mean(x3);
%计算第一类样本类内离散度矩阵S1
S1=zeros(3,3);
fori=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
%w2的数据点坐标
x4=[1.40101.23012.08141.16551.37401.1829
1.76321.97392.41522.58902.84721.9539
1.25001.28641.26142.00712.18311.7909
1.33221.14661.70871.59202.93531.4664
2.93131.83491.83402.50962.71982.3148
2.03532.60301.23272.14651.56732.9414];
x5=[1.02980.96110.91541.49010.82000.9399
1.14051.06780.80501.28891.46011.4334
0.70911.29421.37440.93871.22661.1833
0.87980.55920.51500.99830.91200.7126
1.28331.10291.26800.71401.24461.3392
1.18080.55031.47081.14350.76791.1288];
x6=[0.62101.36560.54980.67080.89321.4342
0.95080.73240.57841.49431.09150.7644
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- 关 键 词:
- Fisher 准则 线性 分类 设计