基于-Fisher準(zhǔn)則線性分類器設(shè)計

1、基于 Fisher 準(zhǔn)則線性分類器設(shè)計專 業(yè)：電子信息工程學(xué)生：子龍學(xué) 號： 201316040117-、實驗類型設(shè)計型：線性分類器設(shè)計（FiSher準(zhǔn)則）1、實驗?zāi)康谋緦嶒炛荚谧屚瑢W(xué)進一步了解分類器的設(shè)計概念，能夠根據(jù)自己的設(shè)計對線性分類器有更深刻地認(rèn)識，理解FiSher準(zhǔn)則方法確定最佳線性分界面方法的原理，以及Lagrande乘子求解的原理。三、實驗條件matlab軟件四、實驗原理線性判別函數(shù)的一般形式可表示成g (X) WTX Wo其中X1WXd根據(jù)FiSher選擇投影方向WdW的原則，即使原樣本向量在該方向上的投影能兼顧類間分布盡可能分開，類樣本投影盡可能密集的要求，用以評價投影方向W

2、的函數(shù)為:JF(W)（幣帀2）22 S2* 1WSW (m1 m2)上面的公式是使用 FiSher準(zhǔn)則求最佳法線向量的解，該式比較重要。另外，該式這種形式的運算，我們稱為線性變換，其中m1 m2式一個向量，SWI是SW的逆矩陣，如m m2 是d維，SW和SW都是d× d維，得到的 W 也是一個d維的向量。向量W*就是使FiSher準(zhǔn)則函數(shù)JF(W)達(dá)極大值的解，也就是按FiSher準(zhǔn)則將d維X 空間投影到一維 Y空間的最佳投影方向， 該向量W*的各分量值是對原 d維特征向量求加權(quán) 和的權(quán)值。以上討論了線性判別函數(shù)加權(quán)向量W的確定方法，并討論了使 FiSher準(zhǔn)則函數(shù)極大的d維向量W*

3、的計算方法，但是判別函數(shù)中的另一項Wo尚未確定，一般可采用以下幾種方法確定Wo如或者WoWom1 m22NImINim mN2或當(dāng)P( )1與p( )2已知時可用WoITi1m22ln p( 1)/ p( 2)N1 N2 2當(dāng)W確定之后，則可按以下規(guī)則分類,WTXWTXw0XIWOX2使用FiSher準(zhǔn)則方法確定最佳線性分界面的方法是一個著名的方法，盡管提出該方法 的時間比較早，仍見有人使用。五、實驗容已知有兩類數(shù)據(jù) I和2二者的概率已知 p( )1=0.6， p( )2 =0.4。1中數(shù)據(jù)點的坐標(biāo)對應(yīng)一一如下:數(shù)據(jù)：x1 =0.23311.52070.64990.77571.05241.19

4、740.29080.25180.66820.56220.90230.1333-0.54310.9407-0.21260.0507-0.08100.73150.33451.0650-0.02470.10430.31220.66550.58381.16531.26530.8137-0.33990.51520.7226-0.20150.4070-0.1717-1.0573-0.2099x2 =2.33852.19461.67301.63651.78442.01552.06812.12132.47971.51181.96921.83401.87042.29481.77142.39391.56481.9

5、3292.20272.45681.75231.69912.48831.72592.04662.02262.37571.79872.08282.07981.94492.38012.23732.16141.92352.2604x3 =0.53380.85141.08310.41641.11760.55360.60710.44390.49280.59011.09271.07561.00720.42720.43530.98690.48411.09921.02990.71271.01240.45760.85441.12750.77050.41291.00850.76760.84180.87840.975

6、10.78400.41581.03150.75330.95482 數(shù)據(jù)點的對應(yīng)的三維坐標(biāo)為 x1 =1.4010 1.2301 2.0814 1.1655 1.3740 1.18291.7632 1.9739 2.4152 2.5890 2.8472 1.95391.25001.28641.26142.00712.18311.79091.33221.14661.70871.59202.93531.46642.93131.83491.83402.50962.71982.31482.03532.60301.23272.14651.56732.9414x2 =1.02980.96110.91541.

7、49010.82000.93991.14051.06780.80501.28891.46011.43340.70911.29421.37440.93871.22661.18330.87980.55920.51500.99830.91200.71261.28331.10291.26800.71401.24461.33921.18080.55031.47081.14350.76791.1288x3 =0.62101.36560.54980.67080.89321.43420.95080.73240.57841.49431.09150.76441.21591.30491.14080.93980.61

8、970.66031.39281.40840.69090.84000.53811.37290.77310.73191.34390.81420.95860.73790.75480.73930.67390.86511.36991.1458數(shù)據(jù)的樣本點分布如下圖：圖1 :樣本點分布圖六、實驗要求1）請把數(shù)據(jù)作為樣本，根據(jù)FiSher選擇投影方向 W的原則，使原樣本向量在該方向上的投影能兼顧類間分布盡可能分開，類樣本投影盡可能密集的要求， 求出評價投影方向 W的函數(shù)，并在圖形表示出來。并在實驗報告中表示出 來，并求使JF（W）取極大值的W。用matlab完成FiSher線性分類器的設(shè) 計，程序的語句要求

9、有注釋。2）根據(jù)上述的結(jié)果并判斷（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），屬于哪個類別，并畫出數(shù)據(jù)分類 相應(yīng)的結(jié)果圖，要求畫出其在W上的投影。3）回答如下問題，分析一下W的比例因子對于FiSher判別函數(shù)沒有影響的原因。七、實驗結(jié)果1、源代碼x1=0.23311.52070.64990.77571.05241.19740.29080.25180.66820.56220.90230.1333-0.54310.9407-0.21260.0507-0.08100.73150.33451.0650

10、-0.02470.10430.31220.66550.58381.16531.26530.8137-0.33990.51520.7226-0.20150.4070-0.1717-1.0573-0.2099'y1=2.33852.19461.67301.63651.78442.01552.06812.12132.47971.51181.96921.83401.87042.29481.77142.39391.56481.93292.20272.45681.75231.69912.48831.72592.04662.02262.37571.79872.08282.07981.94492.38

11、012.23732.16141.92352.2604'z1=0.53380.85141.08310.41641.11760.55360.60710.44390.49280.59011.09271.07561.00720.42720.43530.98690.48411.09921.02990.71271.01240.45760.85441.12750.77050.41291.00850.76760.84180.87840.97510.78400.41580.9548'%存儲第一類點x2=1.40101.23012.08141.16551.37401.18291.76321.973

12、92.41522.58902.84721.95391.25001.28641.26142.00712.18311.79091.33221.14661.70871.59202.93531.46642.93131.83491.83402.50962.71982.31482.03532.60301.23272.14651.56732.9414'y2=1.02980.96110.91541.49010.82000.93991.14051.06780.80501.28891.46011.43340.70911.29421.37440.93871.22661.18330.87980.55920.5

13、1500.99830.91200.71261.28331.10291.26800.71401.24461.33921.18080.55031.47081.14350.76791.1288'z2=0.62101.36560.54980.67080.89321.43420.95080.73240.57841.49431.09150.76441.21591.30491.14080.93980.61970.66031.39281.40840.69090.84000.53811.37291.03150.75330.7731 0.7319 1.3439 0.8142 0.9586 0.73790.

14、86511.36990.7548 0.7393 0.67391.1458'%存儲第二類點Pw1=0.6Pw2=0.4 %求第一類點的均值向量 m1 m1x=mean(x1(:)%全部平均m1y=mean(y1(:)%全部平均m1z=mean(z1(:)%全部平均m1=m1xm1ym1z %求第二類點的均值向量 m2 m2x=mean(x2(:)%全部平均m2y=mean(y2(:)%全部平均m2z=mean(z2(:)%全部平均m2=m2xm2ym2z%求第一類類離散矩陣 S1S1=zeros(3,3) for i=1:36S1=S1+(x1(i),y1(i),z1(i)'-m

15、1)*(x1(i),y1(i),z1(i)'-m1)' end%求第二類類離散矩陣 S2S2=zeros(3,3) for i=1:36S2=S2+(x2(i),y2(i),z2(i)'-m2)*(x2(i),y2(i),z2(i)'-m2)' end%求總類離散度矩陣 SwSw=S1+S2%求向量 W*W=(inv(Sw)*(m1-m2) %畫出決策面 x=0:.1:2.5 y=0:.1:3X,Y=meshgrid(x,y) Z=(W(1)*X+W(2)*Y)/(-W(3) mesh(X,Y,Z)%保持 hold on %透視決策面 hidden of

16、f %求第一類樣品的投影值均值Y1=0 for i=1:36Y1=Y1+W'*x1(i),y1(i),z1(i)'endM1=Y1/36 %求第二類樣品的投影值均值Y2=0 for i=1:36Y2=Y2+W'*x2(i),y2(i),z2(i)' endM2=Y2/36 %選取閾值 Y0Y0=(M1+M2)/2+(log(Pw1)/log(Pw2)/70 %判定未知樣品類別X1=1,1.5,0.6'if W'*X1>Y0disp( ' 點 X1(1,1.5,0.6)屬于第一類')plot3(1,0.5,0.6, '

17、or')elsedisp(' 點 X1(1,1.5,0.6)屬于第二類')plot3(1,0.5,0.6, 'ob')endX2=1.2,1.0,0.55'if W'*X2>Y0disp(' 點 X2(1.2,1.0,0.55)屬于第一類')plot3(1.2,1.0,0.55,'or')elsedisp(' 點 X2(1.2,1.0,0.55)屬于第二類')plot3(1.2,1.0,0.55,'ob')endX3=2.0,0.9,0.68'if W'

18、*X3>Y0disp(' 點 X3(2.0,0.9,0.68)屬于第一類')plot3(2.0,0.9,0.68,'or')elsedisp(' 點 X3(2.0,0.9,0.68)屬于第二類')plot3(2.0,0.9,0.68,'ob')endX4=1.2,1.5,0.89'if W'*X4>Y0disp(' 點 X4(1.2,1.5,0.89)屬于第一類')plot3(1.2,1.5,0.89,'or')elsedisp(' 點 X4(1.2,1.5,0.

19、89)屬于第二類')plot3(12,1.5,089, end'ob')X5=023,2.33,143'if W*X5>Y0disp( '點X5(0.23,2.33,1.43)屬于第一類)plot3(0.23,2.33,1.43,'or')elsedisp( '點X5(0.23,2.33,1.43)屬于第二類')plot3(0.23,2.33,1.43,'ob')end2、決策面圖2 :決策面（紅色代表第一類，藍(lán)色代表第二類）5Jl3、參數(shù)決策面向量W =-0.07980.2005-0.0478閾值Y0 =0.1828 樣本點分類 X1 =1.00001.50000.6000點 X1(1,1.5,0.6) 屬于第一類X2 =1.20001.00000.5500點 X2(1.2,1.0,0.55) 屬于第二類X3 =2.00000.90000.6800點 X3(2.0,0.9,0.68) 屬于第二類X4 =1.20001.50000.8900點 X4(1.2,1.5,0.89) 屬于第二類X5 =0.23002.33001.4300點 X5(0.23