主分量分析與統(tǒng)計(jì)模式識(shí)別實(shí)驗(yàn)報(bào)告

遼寧工程技術(shù)大學(xué)上機(jī)實(shí)驗(yàn)報(bào)告成績(jī)成績(jī)實(shí)驗(yàn)名稱(chēng)主分量分析與統(tǒng)計(jì)模式識(shí)別院系理學(xué)院專(zhuān)業(yè)信科班級(jí)09-1班姓名學(xué)號(hào)日期雷雨明09110101072011-12-20實(shí)驗(yàn)?zāi)康暮?jiǎn)述本次實(shí)驗(yàn)?zāi)康模?、 了解教學(xué)選定的統(tǒng)計(jì)分析軟件的基本特點(diǎn)2、 會(huì)用統(tǒng)計(jì)軟件進(jìn)行數(shù)據(jù)描述3、 會(huì)用統(tǒng)計(jì)軟件完成實(shí)際問(wèn)題的主分量分析4、 會(huì)用統(tǒng)計(jì)軟件完成實(shí)際問(wèn)題的統(tǒng)計(jì)模式識(shí)別實(shí)驗(yàn)準(zhǔn)備你為本次實(shí)驗(yàn)做了哪些準(zhǔn)備：認(rèn)真學(xué)習(xí)了課本上關(guān)于典型相關(guān)分析的知識(shí)，同時(shí)鞏固概率的基礎(chǔ)，結(jié)，不懂得地方上網(wǎng)收集并查找有關(guān)資料。進(jìn)行總實(shí)驗(yàn)進(jìn)度本次共有 1個(gè)練習(xí)，完成1 個(gè)。實(shí)驗(yàn)總結(jié)本次實(shí)驗(yàn)的收獲、體會(huì)、經(jīng)驗(yàn)、問(wèn)題和教訓(xùn)：1、使用MATLAB求自相關(guān)系數(shù)、互相關(guān)系數(shù)、典型相關(guān)系數(shù)和組合系數(shù)：function[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca（X,Y）% CCA由兩組變量的相關(guān)矩陣求典型相關(guān)系數(shù)和典型變量% 語(yǔ)法％[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca（X,Y）% X――第1組多維隨機(jī)變量的“n^p”數(shù)據(jù)矩陣% Y――第2組多維隨機(jī)變量的“n^q”數(shù)據(jù)矩陣% R――X與Y的相關(guān)系數(shù)矩陣% CCORR――典型相關(guān)系數(shù)% ALPHA――X的典型變量（系數(shù)）% BETA——Y的典型變量（系數(shù)）% LAMDA――典型決策系數(shù)（典型相關(guān)系數(shù)的平方）% Rxx-X的自相關(guān)系數(shù)矩陣% RyyY的自相關(guān)系數(shù)矩陣% RxyX與Y的互相關(guān)系數(shù)矩陣[n,p]=size(X);[n,q]=size(Y);Z=[X,Y];% 求相關(guān)系數(shù)矩陣以及剖分R=corrcoef(Z);Rxx=R(1:p,1:p);Ryy=R(p+1:end,p+1:end);Rxy=R(1:p,p+1:end);Ryx=Rxy';% 求典型變量(系數(shù))和典型相關(guān)系數(shù)MF=sqrtm(inv(Rxx))*Rxy*inv(Ryy)*Ryx*sqrtm(inv(Rxx));MG=sqrtm(inv(Ryy))*Ryx*inv(Rxx)*Rxy*sqrtm(inv(Ryy));[LF,LAMDA]=eigs(MF);[LG,LAMDA]=eigs(MG);LAMDA=diag(LAMDA)';CCORR=sqrt(LAMDA)：ALPHA=LF'*sqrtm(inv(Rxx));BETA=LG'*sqrtm(inv(Ryy));輸入14個(gè)城市的收入矩陣和支出矩陣：X=[14339.5,2735.7,166.0,6719.3;15820.3,1630.3,625.2,7147.1;10546.8,1214.1,482.0,7843.9;9121.3,820.7,133.6,6710.9;10789.1,1267.4,342.5,6239.0;8601.8,932.569.7,6523.3;10081.3,3246.1,161.3,5395.5;10287.9,2661.35,228.6,6483.9;8386.3,805.93,163.3,4348.3;10570.9,1763.32,128.9,6172.6;18229.9,875.51,223.6,5181.1;7763.1,1008.03,97.6,5637.6;8091.2,701.54,93.0,5034.5;9213.0,2997.52,331.7,6285.9];Y=[5384.8,2139.7,1032.0,1448.0,2428.3,2359.3,1364.9,804.6,2742.6,2974.4;6145.2,1676.0,994.8,1128.2,2519.6,1741.8,1741.6,623.6,4909.4,3381.0;4671.4,1490.8,719.8,1080.9,2095.5,1374.7,1572.2,704.4,2741.0,1392.2;4041.1,975.7,473.1,895.4,1196.7,1090.2,900.6,433.8,4121.7,1291.5;4779.8,1583.5,712.9,976.6,1321.4,1291.6,907.7,545.9,4564.7,1662.7;4470.3,1118.6,675.9,1129.9,1110.8,1032.8,1402.4,382.1,1668.5,1428.1;4190.9,1457.6,560.7,1061.3,1356.6,1305.4,1460.6,408.5,3165.4,1272.6;4511.3,1528.4,819.5,953.6,1074.4,1159.7,1409.2,767.2,2270.6,1407.4;3462.7,1274.2,594.9,759,795.4,1046.8,820.8,293.5,1760.0,864.5;4202.2,1284.5,718.9,766.8,1624,959.9,1056.2,458.2,1884.1,1812.7;4358.1,2034.9,878.5,1450.5,1963.2,1661.4,995.8,580.5,4699.0,2873.4;3566.7,1321.5,805.0,717.8,939.3,850.2,1815.1,306.4,2629.4,662.8;3478.9,1121.3,487.7,892.6,1238.6,745.4,1006.3,347.5,2442.5,781.9;3771.7,1131.7,619.7,671.0,2071.3,1136.1,1065.1,502.7,3865.4,1205.7];調(diào)用M文件函數(shù)：[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca(X,Y)結(jié)果為：R=1.00000.10380.46000.18010.68560.84250.72850.78290.72340.79220.09380.10381.00000.13470.18920.24280.25700.21340.05820.34840.36710.24340.46000.13471.00000.56560.65930.31280.40950.15740.65550.40520.31210.18010.18920.56561.00000.65860.11290.35180.22480.54650.36090.45940.68560.24280.65930.65861.0000|0.62370.73860.63260.70260.76790.42820.84250.25700.31280.11290.62371.00000.82400.79720.58770.86450.21560.72850.21340.40950.35180.73860.82401.00000.58220.60420.74450.50970.78290.05820.15740.22480.63260.79720.58221.00000.52770.80650.16620.72340.34840.65550.54650.70260.58770.60420.52771.00000.75970.25480.79220.36710.40520.36090.76790.86450.74450.80650.75971.00000.20830.09380.24340.31210.45940.42820.21560.50970.16620.25480.20831.00000.59930.44290.52000.64810.71650.69080.66940.58430.66190.73950.25120.59270.02490.58090.20390.42360.33490.21920.29020.48800.3981-0.06360.93350.17150.48930.35710.85090.77420.78440.75190.78630.84580.17270.5993 0.5927 0.93350.4429 0.0249 0.17150.5200 0.5809 0.48930.6481 0.2039 0.35710.7165 0.4236 0.85090.6908 0.3349 0.77420.6694 0.2192 0.78440.5843 0.2902 0.75190.6619 0.4880 0.78630.7395 0.3981 0.84580.2512 -0.0636 0.17271.0000 0.2588 0.63660.2588 1.0000 0.51760.6366 0.5176 1.0000CCORR=1.00000.98360.77330.69860.00000-0.0000iALPHA=1.1025 -0.0247 -0.3264 -0.11880.0147 0.2741 0.4174 0.6025-0.2476 0.5608 0.9426 -1.03100.1094 0.8077 -0.8106 0.2825BETA=0.8800-0.41910.2378-0.17790.27010.2035-0.1424-0.0673-0.0539-1.58910.6468-0.2576-0.1332-0.24200.42720.03630.19440.55970.1581-0.41470.12632.5015-1.9085-1.95240.01500.17420.5043-0.2760-0.03700.81531.85540.21771.60840.94531.0838|

-1.7459-1.1047-1.14150.6308-2.4252-0.7595-0.23090.06780.3667-1.01550.18260.40380.93251.0110-0.24340.33400.13380.2439-0.7907-1.2854-0.2060-0.37230.7995-0.01200.8094LAMDA=1.0000 0.9674 0.5981 0.48810.0000-0.0000Rxx=1.00000.10380.46000.18010.10381.00000.13470.18920.46000.13471.00000.56560.18010.18920.56561.0000Ryy=1.00000.62370.73860.63260.70260.76790.42820.7165 0.42360.85090.62371.00000.82400.79720.58770.86450.21560.69080.33490.77420.73860.82401.00000.58220.60420.74450.50970.66940.21920.78440.63260.79720.58221.00000.52770.80650.16620.58430.29020.75190.70260.58770.60420.52771.00000.75970.25480.66190.48800.78630.76790.86450.74450.80650.75971.00000.20830.73950.39810.84580.42820.21560.50970.16620.25480.20831.00000.2512-0.06360.17270.71650.69080.66940.58430.66190.73950.25121.00000.25880.63660.42360.33490.21920.29020.48800.3981-0.06360.25881.00000.51760.85090.77420.78440.75190.78630.84580.17270.63660.51761.0000Rxy=0.68560.84250.72850.78290.72340.79220.09380.59930.59270.93350.24280.25700.21340.05820.34840.36710.24340.44290.02490.17150.65930.31280.40950.15740.65550.40520.31210.52000.58090.48930.65860.11290.35180.22480.54650.36090.45940.64810.20390.35712、用MATLAB求典型相關(guān)系數(shù)的巴泰勒特檢驗(yàn)：function[Prob,QEST,DF]=ccorrtest(LAMDA)% CCORRTEST進(jìn)行典型相關(guān)系數(shù)顯著性的逐一檢驗(yàn)( BARTLETT方法）%語(yǔ)法[Prob,QEST,DF]=ccorrtest(LAMDA)% LAMDA——典型決策系數(shù)，函數(shù)CCA的第5個(gè)輸出% Prob檢驗(yàn)的最小顯者性概率值向量（檢驗(yàn)的p值）% QEST——Bartlett檢驗(yàn)統(tǒng)計(jì)量的值向量% DF——Bartlett檢驗(yàn)統(tǒng)計(jì)量的自由度向量QEST=[];Prob=[];DF=[];p=4;q=10;

n=14;