主成分分析matlab程序

1、新華學(xué)院2011數(shù)學(xué)建模Matlab編程實(shí)現(xiàn)主成分分析 .程序結(jié)構(gòu)及函數(shù)作用在軟件Matlab中實(shí)現(xiàn)主成分分析可以采取兩種方式實(shí)現(xiàn)：一是通過(guò)編程來(lái)實(shí)現(xiàn)；二是直接調(diào)用Matlab種自帶程序?qū)崿F(xiàn)。下面主要主要介紹利用Matlab的矩陣計(jì)算功能編程實(shí)現(xiàn)主成分分析。1程序結(jié)構(gòu)Cwprint.m 主函數(shù) 子函數(shù) Cwfac.mCwscore.mCwstd.m2函數(shù)作用Cwstd.m用總和標(biāo)準(zhǔn)化法標(biāo)準(zhǔn)化矩陣Cwfac.m計(jì)算相關(guān)系數(shù)矩陣；計(jì)算特征值和特征向量；對(duì)主成分進(jìn)行排序；計(jì)算各特征值貢獻(xiàn)率；挑選主成分（累計(jì)貢獻(xiàn)率大于85%），輸出主成分個(gè)數(shù)；計(jì)算主成分載荷Cwscore.m計(jì)算各主成分得分、綜合得分

2、并排序Cwprint.m讀入數(shù)據(jù)文件；調(diào)用以上三個(gè)函數(shù)并輸出結(jié)果3.源程序3.1 cwstd.m總和標(biāo)準(zhǔn)化法標(biāo)準(zhǔn)化矩陣%cwstd.m,用總和標(biāo)準(zhǔn)化法標(biāo)準(zhǔn)化矩陣function std=cwstd(vector)cwsum=sum(vector,1); %對(duì)列求和a,b=size(vector); %矩陣大小,a為行數(shù),b為列數(shù)for i=1:a for j=1:b std(i,j)= vector(i,j)/cwsum(j); endend3.2 cwfac.m計(jì)算相關(guān)系數(shù)矩陣%cwfac.mfunction result=cwfac(vector);fprintf('相關(guān)系數(shù)矩陣:

3、n')std=CORRCOEF(vector) %計(jì)算相關(guān)系數(shù)矩陣fprintf('特征向量(vec)及特征值(val)：n')vec,val=eig(std) %求特征值(val)及特征向量(vec)newval=diag(val) ;y,i=sort(newval) ; %對(duì)特征根進(jìn)行排序，y為排序結(jié)果，i為索引fprintf('特征根排序：n')for z=1:length(y) newy(z)=y(length(y)+1-z);endfprintf('%gn',newy)rate=y/sum(y);fprintf('n貢獻(xiàn)

4、率：n')newrate=newy/sum(newy)sumrate=0;newi=;for k=length(y):-1:1 sumrate=sumrate+rate(k); newi(length(y)+1-k)=i(k); if sumrate>0.85 break; end end %記下累積貢獻(xiàn)率大85%的特征值的序號(hào)放入newi中fprintf('主成分?jǐn)?shù)：%gnn',length(newi);fprintf('主成分載荷：n')for p=1:length(newi) for q=1:length(y) result(q,p)=sqr

5、t(newval(newi(p)*vec(q,newi(p); endend %計(jì)算載荷disp(result)3.3 cwscore.m%cwscore.m,計(jì)算得分function score=cwscore(vector1,vector2);sco=vector1*vector2;csum=sum(sco,2);newcsum,i=sort(-1*csum);newi,j=sort(i);fprintf('計(jì)算得分：n')score=sco,csum,j %得分矩陣：sco為各主成分得分；csum為綜合得分；j為排序結(jié)果 3.4 cwprint.m%cwprint.mfu

6、nction print=cwprint(filename,a,b); %filename為文本文件文件名，a為矩陣行數(shù)(樣本數(shù))，b為矩陣列數(shù)(變量指標(biāo)數(shù))fid=fopen(filename,'r')vector=fscanf(fid,'%g',a b);fprintf('標(biāo)準(zhǔn)化結(jié)果如下：n')v1=cwstd(vector)result=cwfac(v1);cwscore(v1,result);4.程序測(cè)試?yán)}4.1原始數(shù)據(jù)中國(guó)大陸35個(gè)大城市某年的10項(xiàng)社會(huì)經(jīng)濟(jì)統(tǒng)計(jì)指標(biāo)數(shù)據(jù)見下表。城 市名 稱年底總?cè)丝?萬(wàn)人) 非農(nóng)業(yè)人口比(%) 農(nóng) 業(yè)

7、總產(chǎn)值(萬(wàn)元)工業(yè)總產(chǎn)值(萬(wàn)元)客運(yùn)總量(萬(wàn)人)貨運(yùn)總量(萬(wàn)噸)地方財(cái)政預(yù)算內(nèi)收入(萬(wàn)元)城鄉(xiāng)居民年底儲(chǔ)蓄余額(萬(wàn)元)在崗職工人數(shù)(萬(wàn)人)在崗職工工資總額(萬(wàn)元)北 京1 249.900.597 81 843 42719 999 70620 32345 5622 790 86326 806 646410.805 773 301天 津910.170.580 91 501 13622 645 5023 25926 3171 128 07311 301 931202.682 254 343石 家 莊875.400.233 22 918 6806 885 7682 9291 911352 3487 0

8、95 87595.60758 877太 原299.920.656 3236 0382 737 7501 93711 895203 2773 943 10088.65654 023呼和浩特207.780.441 2365 343816 4522 3512 623105 7831 396 58842.11309 337沈 陽(yáng)677.080.629 91 295 4185 826 7337 78215 412567 9199 016 998135.451 152 811大 連545.310.494 61 879 7398 426 38510 78019 187709 2277 556 79694.1

9、5965 922長(zhǎng) 春691.230.406 81 853 2105 966 3434 8109 532357 0964 803 744102.63884 447哈 爾 濱927.090.462 72 663 8554 186 1236 7207 520481 4436 450 020172.791 309 151上 海1 313.120.738 42 069 01954 529 0986 40644 4854 318 50025 971 200336.845 605 445南 京537.440.534 1989 19913 072 73714 26911 193664 2995 680 47

10、2113.811 357 861杭 州616.050.355 61 414 73712 000 79617 88311 684449 5937 425 96796.901 180 947寧 波538.410.254 71 428 23510 622 86622 21510 298501 7235 246 35062.15824 034合 肥429.950.318 4628 7642 514 1254 8931 517233 6281 622 93147.27369 577福 州583.130.273 32 152 2886 555 3518 8517 190467 5245 030 22069

11、.59680 607廈 門128.990.486 5333 3745 751 1243 7282 570418 7582 108 33146.93657 484南 昌424.200.398 8688 2892 305 8813 6743 189167 7142 640 46062.08479 ,555濟(jì) 南557.630.408 51 486 3026 285 8825 91511 775460 6904 126 97083.31756 696青 島702.970.369 32 382 32011 492 03613 40817 038658 4354 978 045103.52961 704

12、鄭 州615.360.342 4677 4255 287 60110 4336 768387 2525 135 33884.66696 848武 漢740.200.586 91 211 2917 506 0859 79315 442604 6585 748 055149.201 314 766長(zhǎng) 沙582.470.310 71 146 3673 098 1798 7065 718323 6603 461 24469.57596 986廣 州685.000.621 41 600 73823 348 13922 00723 8541 761 49920 401 811182.813 047 594

13、深 圳119.850.793 1299 66220 368 2958 7544 2741 847 9089 519 90091.261 890 338南 寧285.870.406 4720 4861 149 6915 1303 293149 7002 190 91845.09371 809海 口54.380.835 444 815717 4615 3452 356115 1741 626 80019.01198 138重 慶3 072.340.206 74 168 7808 585 52552 44125 124898,9129 090 969223.731 606 804成 都1 003.5

14、60.3351 935 5905 894 28940 14019 632561 1897 479 684132.891 200 671貴 陽(yáng)321.500.455 7362 0612 247 93415 7034 143197 9081 787 74855.28419 681昆 明473.390.386 5793 3563 605 7295 60412 042524 2164 127 90088.11842 321西 安674.500.409 4739 9053 665 94210 3119 766408 8965 863 980114.01885 169蘭 州287.590.544 5259

15、 4442 940 8841 8324 749169 5402 641 56865.83550 890西 寧133.950.522 765 848711 3101 7461 46949 134855 05127.21219 251銀 川95.380.570 9171 603661 2262 1061 19374 758814 10323.72178 621烏魯木齊158.920.824 478 5131 847 2412 6689 041254 8702 365 50855.27517 6224.2運(yùn)行結(jié)果>> cwprint('cwbook.txt',35,10)

16、fid =6數(shù)據(jù)標(biāo)準(zhǔn)化結(jié)果如下：v1 =0.0581 0.0356 0.0435 0.0680 0.0557 0.1112 0.1194 0.1184 0.1083 0.13920.0423 0.0346 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 0.0087 0.0174 0.0234 0.01580.00

17、97 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 0.02780.0253 0.0295 0.0443 0.0286 0.0295 0.0468 0.0304 0.0334 0.0248 0.02330.0321 0.0242 0.0437 0.0203 0.0132 0.0233 0.0153 0.0212 0.0270 0.02130.0431 0.0276 0.0628 0.0142

18、0.0184 0.0184 0.0206 0.0285 0.0455 0.03160.0610 0.0440 0.0488 0.1853 0.0176 0.1086 0.1848 0.1148 0.0888 0.13520.0250 0.0318 0.0233 0.0444 0.0391 0.0273 0.0284 0.0251 0.0300 0.03270.0286 0.0212 0.0334 0.0408 0.0490 0.0285 0.0192 0.0328 0.0255 0.02850.0250 0.0152 0.0337 0.0361 0.0609 0.0251 0.0215 0.0

19、232 0.0164 0.01990.0200 0.0190 0.0148 0.0085 0.0134 0.0037 0.0100 0.0072 0.0125 0.00890.0271 0.0163 0.0508 0.0223 0.0243 0.0175 0.0200 0.0222 0.0183 0.01640.0060 0.0290 0.0079 0.0195 0.0102 0.0063 0.0179 0.0093 0.0124 0.01590.0197 0.0237 0.0162 0.0078 0.0101 0.0078 0.0072 0.0117 0.0164 0.01160.0259

20、0.0243 0.0350 0.0214 0.0162 0.0287 0.0197 0.0182 0.0220 0.01820.0327 0.0220 0.0562 0.0391 0.0367 0.0416 0.0282 0.0220 0.0273 0.02320.0286 0.0204 0.0160 0.0180 0.0286 0.0165 0.0166 0.0227 0.0223 0.01680.0344 0.0349 0.0286 0.0255 0.0268 0.0377 0.0259 0.0254 0.0393 0.03170.0271 0.0185 0.0270 0.0105 0.0

21、239 0.0140 0.0139 0.0153 0.0183 0.01440.0318 0.0370 0.0377 0.0793 0.0603 0.0582 0.0754 0.0901 0.0482 0.07350.0056 0.0472 0.0071 0.0692 0.0240 0.0104 0.0791 0.0421 0.0240 0.04560.0133 0.0242 0.0170 0.0039 0.0141 0.0080 0.0064 0.0097 0.0119 0.00900.0025 0.0497 0.0011 0.0024 0.0146 0.0057 0.0049 0.0072

22、 0.0050 0.00480.1428 0.0123 0.0983 0.0292 0.1437 0.0613 0.0385 0.0402 0.0590 0.03870.0466 0.0199 0.0456 0.0200 0.1100 0.0479 0.0240 0.0331 0.0350 0.02900.0149 0.0271 0.0085 0.0076 0.0430 0.0101 0.0085 0.0079 0.0146 0.01010.0220 0.0230 0.0187 0.0123 0.0154 0.0294 0.0224 0.0182 0.0232 0.02030.0313 0.0

23、244 0.0174 0.0125 0.0283 0.0238 0.0175 0.0259 0.0300 0.0213 0.0134 0.0324 0.0061 0.0100 0.0050 0.0116 0.0073 0.0117 0.0173 0.01330.0062 0.0311 0.0016 0.0024 0.0048 0.0036 0.0021 0.0038 0.0072 0.00530.0044 0.0340 0.0040 0.0022 0.0058 0.0029 0.0032 0.0036 0.0063 0.00430.0074 0.0491 0.0019 0.0063 0.007

24、3 0.0221 0.0109 0.0105 0.0146 0.0125相關(guān)系數(shù)矩陣:std =1.0000 -0.3444 0.8425 0.3603 0.7390 0.6215 0.4039 0.4967 0.6761 0.4689-0.3444 1.0000 -0.4750 0.3096 -0.3539 0.1971 0.3571 0.2600 0.1570 0.30900.8425 -0.4750 1.0000 0.3358 0.5891 0.5056 0.3236 0.4456 0.5575 0.37420.3603 0.3096 0.3358 1.0000 0.1507 0.766

25、4 0.9412 0.8480 0.7320 0.86140.7390 -0.3539 0.5891 0.1507 1.0000 0.4294 0.1971 0.3182 0.3893 0.25950.6215 0.1971 0.5056 0.7664 0.4294 1.0000 0.8316 0.8966 0.9302 0.90270.4039 0.3571 0.3236 0.9412 0.1971 0.8316 1.0000 0.9233 0.8376 0.95270.4967 0.2600 0.4456 0.8480 0.3182 0.8966 0.9233 1.0000 0.9201

26、0.97310.6761 0.1570 0.5575 0.7320 0.3893 0.9302 0.8376 0.9201 1.0000 0.93960.4689 0.3090 0.3742 0.8614 0.2595 0.9027 0.9527 0.9731 0.9396 1.0000特征向量(vec)：vec =-0.1367 0.2282 -0.2628 0.1939 0.6371 -0.2163 0.3176 -0.1312 -0.4191 0.2758-0.0329 -0.0217 0.0009 0.0446 -0.1447 -0.4437 0.4058 -0.5562 0.5487

27、 0.0593-0.0522 -0.0280 0.2040 -0.0492 -0.5472 -0.4225 0.3440 0.3188 -0.4438 0.2401 0.0067 -0.4176 -0.2856 -0.2389 0.1926 -0.4915 -0.4189 0.2726 0.2065 0.3403 0.0404 0.1408 0.0896 0.0380 -0.1969 -0.0437 -0.4888 -0.6789 -0.4405 0.1861-0.0343 0.2360 0.0640 -0.8294 0.0377 0.2662 0.1356 -0.1290 0.0278 0.

28、37820.2981 0.4739 0.5685 0.2358 0.1465 -0.1502 -0.2631 0.1245 0.2152 0.36440.1567 0.3464 -0.6485 0.2489 -0.4043 0.2058 -0.0704 0.0462 0.1214 0.38120.4879 -0.5707 0.1217 0.1761 0.0987 0.3550 0.3280 -0.0139 0.0071 0.3832-0.7894 -0.1628 0.1925 0.2510 -0.0422 0.2694 0.0396 0.0456 0.1668 0.3799特征值(val)va

29、l =0.0039 0 0 0 0 0 0 0 0 00 0.0240 0 0 0 0 0 0 0 00 0 0.0307 0 0 0 0 0 0 0 0 0 0 0.0991 0 0 0 0 0 0 0 0 0 0 0.1232 0 0 0 0 0 0 0 0 0 0 0.2566 0 0 0 00 0 0 0 0 0 0.3207 0 0 00 0 0 0 0 0 0 0.5300 0 00 0 0 0 0 0 0 0 2.3514 00 0 0 0 0 0 0 0 0 6.2602特征根排序：6.260222.351380.5300470.3206990.2566390.1232410.

30、09909150.03070880.02403550.00393387各主成分貢獻(xiàn)率：newrate =0.6260 0.2351 0.0530 0.0321 0.0257 0.0123 0.0099 0.0031 0.0024 0.0004第一、二主成分的載荷： 0.690 1 -0.6427 0.148 3 0.8414 0.600 7 -0.6805 0.851 5 0.3167 0.465 6 -0.6754 0.946 3 0.0426 0.911 7 0.3299 0.953 7 0.1862 0.958 9 0.0109 0.950 6 0.2558第一、二、三、四主成分的得分：score = 0.718 5 0.049 9 0.768 4 2.0000 0.380 6 0