模式識別實驗最小錯誤率下的貝葉斯決策.docx

模式識別實驗報告題目： 最小錯誤率貝葉斯決策 一、 實驗內(nèi)容1，實驗原理2，實驗步驟1）從iris.txt 文件（課程郵箱-文件中心）中讀取估計參數(shù)用的樣本，每一類樣本抽出前40個，分別求其均值； （2）求每類樣本的協(xié)方差矩陣、逆矩陣以及協(xié)方差矩陣的行列式； （3）對三個類別，分別取每組剩下的 10個樣本，每兩組進(jìn)行分類。由于每類樣本都相等，且每類選取用作訓(xùn)練的樣本也相等，在每兩組進(jìn)行分類時，待分類樣本的類先驗概率為0.5。將各個樣本代入判別函數(shù)既公式(5)，進(jìn)行分類。3，實驗要求（1）復(fù)習(xí)最小錯誤率貝葉斯決策原理，寫出實驗代碼，實現(xiàn)對三類樣本的分類； （2）計算分類的正確率，畫出三維空間的樣本分類圖； （3）分析實驗結(jié)果，完成實驗報告。二、實驗代碼（1），clear% 原始數(shù)據(jù)導(dǎo)入iris=load(iris.txt);N=40;%每組取N=40個樣本%求第一類樣本均值for i = 1:Nfor j = 1:4w1(i,j) = iris(i,j+1);endendsumx1 = sum(w1,1);for i=1:4meanx1(1,i)=sumx1(1,i)/N;end%求第二類樣本均值for i = 1:Nfor j = 1:4w2(i,j) = iris(i+50,j+1);endendsumx2 = sum(w2,1);for i=1:4meanx2(1,i)=sumx2(1,i)/N;end%求第三類樣本均值for i = 1:Nfor j = 1:4w3(i,j) = iris(i+100,j+1);endendsumx3 = sum(w3,1);for i=1:4meanx3(1,i)=sumx3(1,i)/N;end（2），%求第一類樣本協(xié)方差矩陣z1(4,4) = 0;var1(4,4) = 0;for i=1:4for j=1:4for k=1:Nz1(i,j)=z1(i,j)+(w1(k,i)-meanx1(1,i)*(w1(k,j)-meanx1(1,j);endvar1(i,j) = z1(i,j) / (N-1);endend%求第二類樣本協(xié)方差矩陣z2(4,4) = 0 ;var2(4,4) = 0;for i=1:4for j=1:4for k=1:Nz2(i,j)=z2(i,j)+(w2(k,i)-meanx2(1,i)*(w2(k,j)-meanx2(1,j);endar2(i,j) = z2(i,j) / (N-1);endend%求第三類樣本協(xié)方差矩陣z3(4,4) = 0 ;var3(4,4) = 0;for i=1:4for j=1:4for k=1:Nz3(i,j)=z3(i,j)+(w3(k,i)-meanx3(1,i)*(w3(k,j)-meanx3(1,j);endvar3(i,j) = z3(i,j) /( N-1);endend%求各類的協(xié)方差矩陣逆矩陣及行列式var1_inv = ;var1_det = ;var2_inv = ;var2_det = ;var3_inv = ;var3_det = ;var1_inv = inv(var1);var2_inv = inv(var2);var3_inv = inv(var3);var1_det = det(var1);var2_det = det(var2);var3_det = det(var3);（3），M=10;for i = 1:Mfor j = 1:4test(i,j) = iris(i+50,j+1); % 取測試數(shù)據(jù)endendt1=0;t2=0;t3=0;for i = 1:Mx=test(i,1);y=test(i,2);z=test(i,3);h=test(i,4);g1 = (-0.5)*(x,y,z,h-meanx1)*var1_inv*(x,y,z,h-meanx1) - 0.5*log(abs(var1_det) +log(0.5); % p1g2 = (-0.5)*(x,y,z,h-meanx2)*var2_inv*(x,y,z,h-meanx2) - 0.5*log(abs(var2_det) +log(0.5); % p2if g1g2t1=t1+1; %若g1g2,則屬于第一類，否則屬于第二類，并統(tǒng)計屬于每一類的個數(shù)elset2=t2+1;endend三、實驗結(jié)果（1）第一類樣本均值：5.03753.45251.460.235第二類樣本均值：6.012.784.31751.35第三類樣本均值：6.62252.965.60751.99（2）每類樣本的協(xié)方差矩陣、逆矩陣以及協(xié)方差矩陣的行列式第一類樣本的協(xié)方差矩陣：0.1311217948717950.09721153846153840.01333333333333330.01326923076923080.09721153846153840.1302500000000000.002153846153846140.01196153846153850.01333333333333330.002153846153846140.02964102564102570.005025641025641030.01326923076923080.01196153846153850.005025641025641030.00951282051282051逆矩陣：18.8146188042527-13.3847352886752-6.47453636800065-5.99346924772421-13.384735288675218.25047066457185.95329943788004-7.42342518317483-6.474536368000655.9532994378800439.4922929094642-19.3184124732768-5.99346924772421-7.42342518317483-19.3184124732768133.021717057711協(xié)方差矩陣的行列式：1.56318133831812e-06第二類樣本的協(xié)方差矩陣：0000000000000000逆矩陣：InfInfInfInfInfInfInfInfInfInfInfInfInfInfInfInf協(xié)方差矩陣的行列式：0第三類樣本的協(xié)方差矩陣：0.4679423076923080.1104102564102560.3577756410256410.05125641025641030.1104102564102560.1132307692307690.08107692307692310.04625641025641030.3577756410256410.08107692307692310.3453269230769230.05930769230769230.05125641025641030.04625641025641030.05930769230769230.0742564102564103逆矩陣：12.0677437364511-4.88916379648501-12.10821285122384.38637019494952-4.8891637964850114.82114235555433.00369869101398-8.25671873361937-12.10821285122383.0036986910139815.7866851329687-6.121877645562624.38637019494952-8.25671873361937-6.1218776455626220.4719162879598協(xié)方差矩陣的行列式：0.000142786635162081（3）各類樣本代入公式分類得：第一類樣本：5.113750000000003.791250000000000.5200000000000000.5175000000000003.791250000000005.079750000000000.08399999999999960.4665000000000000.5200000000000000.08399999999999961.156000000000000.1960000000000000.5175000000000000.4665000000000000.1960000000000000.371000000000000第二類樣本：10.67600000000003.378000000000006.713000000000002.040000000000003.378000000000004.324000000000003.154000000000001.770000000000006.713000000000003.154000000000007.937750000000002.875000000000002.040000000000001.770000000000002.875000000000001.68000000000000第三類樣本：18.24975000000004.3060000000000013.95325000000001.999000000000004.306000000000004.416000000000003.162000000000001.8040000000000013.95325000000003.1620000000000013.46775000000002.313000000000001.999000000000001.804000000000002.313000000000002.89600000000000三維空間分類圖：四 實驗心得首先感謝老師給予我們這次試驗的機(jī)會，通過這次試驗，我更深入了解了最小錯誤率貝葉斯決策原理，通過計算期望，可以對現(xiàn)實問題進(jìn)行數(shù)學(xué)計算，從而獲