主分量分析与统计模式识别实验报告

辽宁工程技术大学上机实验报告成绩成绩实验名称主分量分析与统计模式识别院系理学院专业信科班级09-1班姓名学号日期雷雨明09110101072011-12-20实验目的简述本次实验目的：1、 了解教学选定的统计分析软件的基本特点2、 会用统计软件进行数据描述3、 会用统计软件完成实际问题的主分量分析4、 会用统计软件完成实际问题的统计模式识别实验准备你为本次实验做了哪些准备：认真学习了课本上关于典型相关分析的知识，同时巩固概率的基础，结，不懂得地方上网收集并查找有关资料。进行总实验进度本次共有 1个练习，完成1 个。实验总结本次实验的收获、体会、经验、问题和教训：1、使用MATLAB求自相关系数、互相关系数、典型相关系数和组合系数：function[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca（X,Y）% CCA由两组变量的相关矩阵求典型相关系数和典型变量% 语法％[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca（X,Y）% X――第1组多维随机变量的“n^p”数据矩阵% Y――第2组多维随机变量的“n^q”数据矩阵% R――X与Y的相关系数矩阵% CCORR――典型相关系数% ALPHA――X的典型变量（系数）% BETA——Y的典型变量（系数）% LAMDA――典型决策系数（典型相关系数的平方）% Rxx-X的自相关系数矩阵% RyyY的自相关系数矩阵% RxyX与Y的互相关系数矩阵[n,p]=size(X);[n,q]=size(Y);Z=[X,Y];% 求相关系数矩阵以及剖分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';% 求典型变量(系数)和典型相关系数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));输入14个城市的收入矩阵和支出矩阵：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];调用M文件函数：[R,CCORR,ALPHA,BETA,LAMDA,Rxx,Ryy,Rxy]=cca(X,Y)结果为：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求典型相关系数的巴泰勒特检验：function[Prob,QEST,DF]=ccorrtest(LAMDA)% CCORRTEST进行典型相关系数显著性的逐一检验( BARTLETT方法）%语法[Prob,QEST,DF]=ccorrtest(LAMDA)% LAMDA——典型决策系数，函数CCA的第5个输出% Prob检验的最小显者性概率值向量（检验的p值）% QEST——Bartlett检验统计量的值向量% DF——Bartlett检验统计量的自由度向量QEST=[];Prob=[];DF=[];p=4;q=10;

n=14;