主成分分析实施报告matlab程序.docx

1、.Matlab 编程实现主成分分析. 程序结构及函数作用在软件 Matlab 中实现主成分分析可以采取两种方式实现：一是通过编程来实现；二是直接调用 Matlab 种自带程序实现。下面主要主要介绍利用 Matlab 的矩阵计算功能编程实现主成分分析。1 程序结构Cwprint.m主函数子函数Cwstd.mCwfac.mCwscore.m2 函数作用Cwstd.m用总和标准化法标准化矩阵Cwfac.m计算相关系数矩阵；计算特征值和特征向量；对主成分进行排序；计算各特征值贡献率；挑选主成分（累计贡献率大于85%），输出主成分个数；计算主成分载荷Cwscore.m计算各主成分得分、综合得分并排序Cw

2、print.m 读入数据文件；调用以上三个函数并输出结果优质范文.3. 源程序3.1 cwstd.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=cwstd(vector)cwsum=sum(vector,1);%对列求和a,b=size(vector);%矩阵大小 ,a 为行数 ,b 为列数for i=1:afor j=1:bstd(i,j)= vector(i,j)/cwsum(j);endend3.2 cwfac.m计算相关系数矩阵%cwfac.mfunction result=cwfac(vector);fprintf(相关系数矩阵 :n)s

3、td=CORRCOEF(vector)% 计算相关系数矩阵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) ;%对特征根进行排序， y 为排序结果， i 为索引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贡献率： n)newrate=newy/sum(newy)sumrat

4、e=0;newi=;for k=length(y):-1:1sumrate=sumrate+rate(k);newi(length(y)+1-k)=i(k);if sumrate0.85 break;endend%记下累积贡献率大85%的特征值的序号放入newi 中fprintf(主成分数： %gnn,length(newi);fprintf(主成分载荷： n)优质范文.for p=1:length(newi)for q=1:length(y)result(q,p)=sqrt(newval(newi(p)*vec(q,newi(p); endend%计算载荷disp(result)3.3 cw

5、score.m%cwscore.m,计算得分function score=cwscore(vector1,vector2);sco=vector1*vector2;csum=sum(sco,2);newcsum,i=sort(-1*csum);newi,j=sort(i);fprintf(计算得分： n)score=sco,csum,j%得分矩阵： sco 为各主成分得分； csum为综合得分； j 为排序结果3.4 cwprint.m%cwprint.mfunction print=cwprint(filename,a,b);%filename 为文本文件文件名， a 为矩阵行数 ( 样本数

6、 ) ，b 为矩阵列数 ( 变量指标数 )fid=fopen(filename,r)vector=fscanf(fid,%g,a b);fprintf(标准化结果如下： n)v1=cwstd(vector)result=cwfac(v1);cwscore(v1,result);4. 程序测试例题4.1 原始数据中国大陆 35 个大城市某年的10 项社会经济统计指标数据见下表。优质范文.年底非农 业工业客运 货运地方财城乡居在岗在岗职农业政民年底职工城总量 总量工工资市人口 总产值 总产值预算内储蓄余人数名总人口( 万( 万总额称比收入(万额( 万(万人)(万元)(万元)人 )吨 )( 万元)(

7、%)元 )( 万元)人)北10.591 84319 99920452 79026 806410.85 773京249.907 84277063235628636460301天910.170.581 50122 6453261 12811 301202.62 254津0 91365022593170739318343石 家0.232 9186 885217 095庄875.403 2680768929911 352 34887595.60758 877太299.920.65236 0382 737111203 2773 94388.65654 023原6 3750937895100呼和浩0.44

8、365 343 816 45222105 7831 39642.11309 337特207.781 2351623588沈0.621 2955 8267159 016135.41 152阳677.089 9418733782412 567 9199985811大545.310.491 8798 4261019709 2277 55694.15965 922连4 6739385780187796长691.230.401 8535 96649357 0964 803102.6884 447春6 82103438105327443哈 尔0.462 6634 186676 450172.71 309滨

9、927.092 7855123720520 481 4430209151上10.732 06954 5296444 31825 971336.85 605海313.128 40190984064855002004445南537.440.53989 19913 0721411664 2995 680113.81 357京4 17372691934721861杭0.351 41412 00017117 4251 180州616.055 6737796883684 449 59396796.90947宁538.410.251 42810 6222210501 7235 24662.15824 034

10、波4 7235866215298350合429.950.31628 7642 51441233 6281 62247.27369 577肥8 4125893517931福583.130.272 1526 55587467 5245 03069.59680 607州3 3288351851190220厦128.990.48333 3745 75132418 7582 10846.93657 484门6 5124728570331南424.200.39688 2892 30533167 7142 64062.08479 ,55昌8 88816741894605优质范文.济南青岛郑州武汉长沙广州深圳

11、南宁海口重庆成都贵阳昆明西安兰州557.630.401 4866 2858 5302882702.970.362 38211 4929 3320036615.360.34677 4255 2872 4601740.200.581 2117 5066 9291085582.470.311 1463 0980 7367179685.000.621 60023 3481 4738139119.850.79299 66220 3683 1295285.870.40720 4861 1496 469154.380.8344 815 717 4615 430.204 1688 585072.346 778

12、052510.331 9355 894003.565590289321.500.45362 0612 2475 7934473.390.38793 3563 6056 5729674.500.40739 9053 6659 4942287.590.54259 4442 9404 5884511460 6904 12683.31756 69691577597013174 978103.5408038 658 4350452961 704106387 2525 13584.66696 848433768338915604 6585 748149.21 314793442055076685323 6

13、603 46169.57596 98670671824422231 76120 401182.83 0470078544998111594841 8479 51991.261 890754274908900338532 190130293 149 70091845.09371 80952115 1741 62619.01198 1383453568005225898,9129 090223.71 606441124969380440197 479132.81 200140632 561 1896849671154197 9081 78755.28419 6817031437485124 127

14、604042 524 21690088.11842 3211095 863114.0311766 408 8969801885 16914169 5402 64165.83550 890832749568西宁银川乌鲁木齐133.950.5265 848 711 3101149 134 855 051 27.21219 2512 774646995.380.57171 603 661 2262174 758 814 103 23.72178 6210 9106193158.920.8278 5131 84729254 8702 36555.27517 6224 4241668041508优质范文

15、.4.2 运行结果 cwprint(cwbook.txt,35,10) fid =6数据标准化结果如下：v1 =0.05810.03560.04350.06800.05570.11120.11940.11840.10830.13920.04230.03460.03540.07700.00890.06420.04830.04990.05340.05440.04070.01390.06880.02340.00800.00470.01510.03140.02520.01830.01390.03910.00560.00930.00530.02900.00870.01740.02340.01580.00

16、970.02630.00860.00280.00640.00640.00450.00620.01110.00750.03150.03750.03050.01980.02130.03760.02430.03980.03570.02780.02530.02950.04430.02860.02950.04680.03040.03340.02480.02330.03210.02420.04370.02030.01320.02330.01530.02120.02700.02130.04310.02760.06280.01420.01840.01840.02060.02850.04550.03160.06

17、100.04400.04880.18530.01760.10860.18480.11480.08880.13520.02500.03180.02330.04440.03910.02730.02840.02510.03000.03270.02860.02120.03340.04080.04900.02850.01920.03280.02550.02850.02500.01520.03370.03610.06090.02510.02150.02320.01640.01990.02000.01900.01480.00850.01340.00370.01000.00720.01250.00890.02

18、710.01630.05080.02230.02430.01750.02000.02220.01830.01640.00600.02900.00790.01950.01020.00630.01790.0093优质范文.0.01240.01590.01970.02370.01620.00780.01010.00780.00720.01170.01640.01160.02590.02430.03500.02140.01620.02870.01970.01820.02200.01820.03270.02200.05620.03910.03670.04160.02820.02200.02730.023

19、20.02860.02040.01600.01800.02860.01650.01660.02270.02230.01680.03440.03490.02860.02550.02680.03770.02590.02540.03930.03170.02710.01850.02700.01050.02390.01400.01390.01530.01830.01440.03180.03700.03770.07930.06030.05820.07540.09010.04820.07350.00560.04720.00710.06920.02400.01040.07910.04210.02400.045

20、60.01330.02420.01700.00390.01410.00800.00640.00970.01190.00900.00250.04970.00110.00240.01460.00570.00490.00720.00500.00480.14280.01230.09830.02920.14370.06130.03850.04020.05900.03870.04660.01990.04560.02000.11000.04790.02400.03310.03500.02900.01490.02710.00850.00760.04300.01010.00850.00790.01460.010

21、10.02200.02300.01870.01230.01540.02940.02240.01820.02320.02030.03130.02440.01740.01250.02830.02380.01750.02590.03000.02130.01340.03240.00610.01000.00500.01160.00730.01170.01730.01330.00620.03110.00160.00240.00480.00360.00210.00380.00720.00530.00440.03400.00400.00220.00580.00290.00320.00360.00630.004

22、30.00740.04910.00190.00630.00730.02210.01090.01050.01460.0125相关系数矩阵 :std =优质范文.1.0000-0.3444 0.84250.36030.7390 0.6215 0.4039 0.49670.67610.4689-0.34441.0000-0.47500.3096-0.3539 0.19710.35710.26000.15700.30900.8425-0.4750 1.0000 0.33580.5891 0.5056 0.3236 0.44560.55750.37420.36030.30960.33581.00000.

23、15070.76640.94120.84800.73200.86140.7390-0.3539 0.5891 0.15071.0000 0.4294 0.1971 0.31820.38930.25950.62150.19710.50560.76640.42941.00000.83160.89660.93020.90270.40390.35710.32360.94120.19710.83161.00000.92330.83760.95270.49670.26000.44560.84800.31820.89660.92331.00000.92010.97310.67610.15700.55750.

24、73200.38930.93020.83760.92011.00000.93960.46890.30900.37420.86140.25950.90270.95270.97310.93961.0000特征向量 (vec)：vec =-0.13670.2282-0.26280.19390.6371 -0.21630.3176-0.1312-0.41910.2758-0.0329-0.0217 0.0009 0.0446-0.1447 -0.44370.4058-0.55620.54870.0593-0.0522-0.0280 0.2040 -0.0492 -0.5472 -0.4225 0.34

25、40 0.3188-0.44380.2401 0.0067 -0.4176 -0.2856 -0.2389 0.1926 -0.4915-0.41890.27260.20650.34030.04040.14080.08960.0380-0.1969-0.0437 -0.4888 -0.6789-0.4405 0.1861-0.03430.23600.0640-0.82940.03770.26620.1356 -0.12900.02780.37820.29810.4739 0.5685 0.2358 0.1465-0.1502-0.26310.12450.21520.36440.15670.34

26、64-0.64850.2489-0.40430.2058-0.07040.04620.12140.38120.4879-0.57070.12170.17610.09870.35500.3280-0.01390.00710.3832-0.7894-0.16280.19250.2510-0.04220.26940.03960.0456优质范文.0.16680.3799特征值 (val)val =0.003900000000000.024000000000000.030700000000000.099100000000000.123200000000000.256600000000000.32070

27、0000000000.530000000000002.351400000000006.2602特征根排序：6.260222.351380.5300470.3206990.2566390.1232410.09909150.03070880.02403550.00393387各主成分贡献率：newrate =0.6260 0.2351 0.0530 0.0321 0.0257 0.0123 0.0099 0.0031优质范文.0.00240.0004第一、二主成分的载荷：0.690 1-0.64270.148 30.84140.600 7-0.68050.851 50.31670.465 6-0.67540.946 30.04260.911 70.32990.953 70.18620.958 90.01090.950 60.2558第一、二、三、四主成分的得分：score =0.718 50.049 90.768 42.00000.380 60.038 60.419 24.00000.184 8-0