主成分分析法MATLAB实现.docx

1、主成分分析法MATLAB实现MATLAB结课作业指导老师：Maa：信管121:桂亚东学号:8利用Matlab i程实现主成分分林欄述Matlab i言是当今国际上科学界（尤其是自动腔制领域）最具影响力、也是最有 活力的狀件。它起源于葩阵运算，并已经发展成一种高IS集成的廿算机培言。它 提哄了強大的科学运算、灵活的程序设it流程、高质量的图形可視化与界面设廿、 与其他程序和培言的便捷接口的功能。Matlab培言在各国高校与研究单位起着 重大的作用。主成分分折是把原来多个变量则为少数几个妹合指标的一种貌计分 折方法，从数学角度来看，这是一种降绒处理技术。1.1主成分分析廿算步骤1it算相关系数矩阵

2、在（353）式中，；j=19 29，为原变量的力与M之间的相关系数，其廿算公式为riJ =为（心-耳）（-兀）（弘-可吩（切一石尸V1 z因为R是实对称矩阵（即厶），所以只需廿算上三用元素或下三舟元素即可。2廿算特征值与特征向量首先解特征方程AJ-R = O，通常用雅可比法（Jacobi ）求岀特征值 兄& = 1,2,丿），并使其按大小噸序排列，-,0；滋后分别求 岀对应干特征值人的特征向量勺（心1,2，丿）。这里要求I.|=1, 其J=l中表示向量的第/个分量。3廿算主成分硫献率及累itfi S率主成分的贡献率为- （/ = 1,2, ,/?）Jt=l（心1,2,丿）Jt=l一般取累计贡献

3、率达85-95%的特征值2,九,，九所对应的第一、第 二，第m （mwp） f主成分。4it算主成分载荷其计算公式为hj = P（G，x_/） = eij Q，j = 12 ,p） （ 3）得到各主成分的载荷以后，还可以按照（3.5.2）武进一步计算，得到各主成 分的得分IniZ11 可 2z=灯3.“I “22.函数作用Cwstd.m一用总和标准化法标准化矩阵Cwfac.m一廿算相关系数矩阵;计算特征值和特征向量；对主成分进行排序；廿算各特征值质献率；挑选主成分（累廿质献率大于85%输出主成分个；廿算主成分数荷Cwscore.m it算各主威分得分、综合得分并排序Cwprint.m一读入数据

4、文件;调用以上三个函数并输岀结果3 源程序3.1cwstd.m总和标准化法标准化矩阵%cwstd.m.用总和标准化法标准化矩阵function std 二 cwstd(vector)cwsum=sum(vector,1); % 对列求和a,b=size(vector); %拒阵大小,a为行数,b为列数for i=1:afor j=1:bstd(i,j)= vector(ij)/cwsum(j);endend3.2cwfac.m it算相关系数矩阵%cwfac.mfunction result=cwfac(vector);fprintfCffl关系数矩阵:n)std=CORRCOEF(vecto

5、r) % it 算相关系数拒阵fprintf(将征向量(vec)及符征 ffi(val)： n)vec,val=eig(std) % 求特征值(val)及特征向量(vec) nev/val=diag(val);(y,i=sort(newval); %对特征根进行井序,y为排序结果，i为索引 fprintfCU 征根 H 序:W)forz=1:length(y)newy(z)=y(length(y)+1-z);endfprintf(%gnnewy)rate=y/sum(y);fprintf(n 贡献率:n)nevjrate=nev/y/sum(nev/y)sumrate=O;newi=);for

6、 k=length(y):-1:1sumrate=sumrate+rate(k);newi(length(y)+1-k)=i(k);if sumrate0.85 break;endend %记卞累枳质献率大85%的特征個的序号笊人newi中fprintf(注成分数:%gnn,length(newi);fprintf(注成分我荷：n)for p=1:length(newi)for q=1:length(y) result(q,p)=sqrt(newval(newi(p)*vec(q?newi(p);endend %廿算我荷disp(result)3.3cwscore.m%cwscore.m, i

7、t 算得分function score=cv/score(vector1 ,vector2);sco=vector1 *vector2;csum=sum(sco,2);newcsumti=sort(-1 *csum);(newi,j=sort(i);fprintfCit 算得分:n*)score=scoJcsumj%得分矩H： sco Ji各主成分得分;csum为综合得分；j为U序结果3.4cwprint.m%cwprint.mfunction print二cwprint(filenameab);%filename 文本文件文件名,a为矩眸行数(样本数),b为矩阵列数(变量指标数) tid=f

8、open(filename/r,)vector=f scant (f id, %o1, a b);fprintf(标准化给果如下:n)v1 二 cwstd(vector)result 二 cwfac(v1);cwscore(v1 jesult);4.程序测试4.1原始数据中国大陆35个大城市某年的10 Bitt会经济标数据见下表。城帀年辰非农业农业工业容运地方u或城乡居艮在岗职在岗职工总人口人口比总产值收人年 Ktii 余瀑工人数工资忠竄（牙人）(%)（H元）（万元）（万人）（万盹）（JJ 元）OJ元)（耳人）（JJ 元）北京1249.900.5978184342719999706203234

9、5562279086326806646410.805773301天津910.170.5809150113622645502325926317112807311301931202.682254343石家圧875.400.23322918680688576829291911352348709587595.60758877299.920.65632360382737750193711895203277394310088.65654023呼和浩特207.780.441236534381645223512623105783139658842.11309337n677.080.62991295418582

10、67337782154125679199016998135.451152811大连545.310.4946187973984263851078019187709227755679694.15965922长春691.230.406818532105966343481095323570964803744102.63884447927.090.462726638554186123672075204814436450020172.791309151上涸1313.120.7384206901954529098640644485431850025971200336.845605445甫京537.440.5

11、3419891991307273714269111936642995680472113.811357861616.050.35561414737120007961788311684449593742596796.901180947538.410.25471428235106228662221510298501723524635062.15824034台肥429.950.3184628764251412548931517233628162293147.27369577福卅583.130.27332152288655535188517190467524503022069.59680607n128.

12、990.4865333374575112437282570418758210833146.93657484南昌424.200.3988688289230588136743189167714264046062.08479 ,555557.630.408514863026285882591511775460690412697083.31756696702.970.369323823201149203613408170386584354978045103.52961704州615.360.34246774255287601104336768387252513533884.66696848武汉740.

13、200.5869121129175060859793154426046585748055149.201314766长沙582.470.31071146367309817987065718323660346124469.57596986广州685.000.62141600738233481392200723854176149920401811182.813047594深n119.850.793129966220368295875442741847908951990091.261890338甫285.870.4064720486114969151303293149700219091845.0937

14、1809海口54.380.83544481571746153452356115174162680019.011981383072.340.2067416878085855255244125124898.9129090969223.7316068041003.560.3351935590589428940140196325611897479684132.891200671贵讯321.500.45573620612247934157034143197908178774855.28419681n明473.390.38657933563605729560412042524216412790088.11

15、842321西安674.500.409473990536659421031197664088965863980114.01885169兰卅287.590.5445259444294088418324749169540264156865.83550890西133.950.522765848711310174614694913485505127.21219251和II95.380.5709171603661226210611937475881410323.72178621乌曾木齐158.920.824478513184724126689041254870236550855.275176224.2运

16、行结果 cwprint( cwbook.txt1,35.10)fid =6数据标准化结果如下:v1 =0.0581 0.0356 0.0435 0.0680 0.0557 0.1112 0.1194 0.1184 0.10830.13920.04230.0346 0.0354 0.0770 0.0089 0.0642 0.0483 0.0499 0.0534 0.05440.0407 0.0139 0.0688 0.0234 0.0080 0.0047 0.0151 0.0314 0.0252 0.01830.0139 0.0391 0.0056 0.0093 0.0053 0.0290 0.

17、0087 0.0174 0.0234 0.01580.0097 0.0263 0.0086 0.0028 0.0064 0.0064 0.0045 0.0062 0.0111 0.00750.0315 0.0375 0.0305 0.0198 0.0213 0.0376 0.0243 0.0398 0.0357 0.02780.02530.02950.04430.02860.0295 0.0468 0.0304 0.0334 0.02480.02330.03210.02420.04370.02030.01320.02330.01530.02120.02700.02130.04310.02760

18、.0628 0.0142 0.0184 0.0184 0.0206 0.0285 0.0455 ID.03160.06100.04400.04880.1853 0.01760.10860.18480.1148 0.0888 ID.13520.02500.03180.02330.04440.0391 0.0273 0.0284 0.0251 0.03000.03270.02860.02120.03340.04080.0490 0.0285 0.0192 0.0328 0.02550.02850.02500.01520.03370.03610.06090.0251 0.0215 0.0232 0.

19、01640.01990.02000.01900.01480.00850.01340.00370.01000.00720.0125 0.00890.02710.01630.05080.02230.02430.01750.02000.02220.0183 0.01640.00600.02900.00790.01950.01020.00630.01790.00930.0124 0.01590.01970.02370.01620.00780.01010.00780.00720.01170.0164 0.01160.02590.02430.03500.02140.01620.02870.01970.01

20、820.02200.01820.03270.02200.05620.03910.03670.04160.02820.02200.02730.02320.02860.02040.01600.01800.02860.01650.01660.02270.02230.01680.03440.03490.02860.02550.02680.03770.02590.02540.03930.03170.02710.01850.02700.01050.02390.01400.0139 0.0153 0.01830.01440.03180.03700.03770.07930.06030.05820.07540.

21、09010.0482 0.07350.00560.04720.00710.06920.02400.01040.07910.04210.02400.04560.01330.02420.01700.00390.01410.00800.00640.00970.01190.00900.00250.0497 0.0011 0.0024 0.0146 0.0057 0.0049 0.0072 0.00500.00480.14280.01230.09830.02920.1437 0.0613 0.0385 0.0402 0.05900.03870.04660.01990.04560.02000.11000.

22、0479 0.0240 0.0331 0.03500.02900.01490.02710.00850.00760.04300.01010.00850.00790.01460.01010.02200.02300.01870.01230.01540.02940.02240.01820.02320.02030.03130.02440.01740.01250.02830.02380.01750.02590.03000.02130.01340.03240.00610.01000.00500.01160.00730.01170.01730.01330.00620.03110.00160.00240.004

23、80.00360.00210.00380.00720.00530.00440.03400.00400.00220.00580.00290.00320.00360.0063 0.00430.00740.04910.00190.00630.00730.02210.01090.01050.01460.0125相关系数矩阵:std =1.0000-0.34440.84250.36030.73900.62150.40390.49670.67610.4689-0.34441.0000-0.47500.3096-0.35390.19710.35710.26000.15700.30900.8425-0.475

24、01.00000.33580.58910.50560.32360.44560.55750.37420.36030.30960.33581.00000.15070.76640.94120.84800.73200.86140.7390-0.35390.58910.15071.00000.42940.19710.31820.38930.25950.62150.19710.50560.76640.42941.00000.83160.89660.93020.90270.40390.35710.32360.94120.1971 0.8316 1.0000 0.9233 0.8376 0.95270.496

25、70.26000.44560.84800.31820.89660.92331.00000.92010.97310.6761 0.15700.55750.73200.3893 0.93020.8376 0.92011.00000.93960.4689 0.30900.37420.86140.2595 0.90270.9527 0.97310.93961.0000特征向量(vec)：vec =-0.1367 0.2282-0.26280.19390.6371 -0.21630.3176 -0.1312-0.41910.2758-0.0329 -0.02170.00090.0446-0.1447 -

26、0.44370.4058 -0.55620.54870.0593-0.0522 -0.0280 0.2040 -0.0492 -0.5472 -0.4225 0.3440 0.3188 -0.44380.2401 0.0067 -0.4176 -0.2856 0.2389 0.1926 -0.4915 -0.4189 0.2726 0.20650.34030.04040.14080.08960.0380 -0.1969-0.0437 -0.4888-0.6789-0.44050.1861-0.03430.23600.0640-0.82940.0377 0.26620.1356 -0.12900.02780.37820.29810.47390.56850.23580.1465 -0.1502-0.2631 0.12450.21520.36440.15670.3464-0.6485