主成分分析报告matlab程序

1、标准实用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2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.计算各主成分得分、综合得分并排序Cwpri nt.m读入数据文件；调用以上三个函数并输出结果3. 源程序3.1 cwstd

2、.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);% 对歹U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.mfun cti on result=cwfac(vector);fprintf('相关系数矩阵:n')std=CORRCOEF(vector)%计算相关系数矩阵fprintf('

3、;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)n ewval=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:le ngth(y)n ewy(z)=y(le ngth(y)+1-z);endfprin tf('%gn', newy)rate=y/sum(y);fprintf('n 贡献率：n')n ewrate=n ewy/sum( newy)sumrate=0;n

4、 ewi=;for k=le ngth(y):-1:1sumrate=sumrate+rate(k);newi(le ngth(y)+1-k)=i(k);if sumrate>0.85 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',le ngth( newi);fprintf('主成分载荷：n')for p=1:le ngth( newi)for q=1:le ngth(y)result(q,p)=sqrt( newval( newi(p)*vec(q, newi(p);endend%计

5、算载荷disp(result)3.3 cwscore.m%cwscore.m 计算得分fun cti on score=cwscore(vector1,vector2);sco=vector1*vector2;csum=sum(sco,2);n ewcsum,i=sort(-1*csum);n ewi,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 cwpri nt.m%cwpri nt.mfun cti on prin t=cwpri nt(file name,a,

6、b);%filename为文本文件文件名，a为矩阵行数(样本数),b为矩阵列数(变量 指标数)fid=fope n(filen ame,'r')vector=fsca nf(fid,'%g',a b);fprintf('标准化结果如下：n')v仁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。年底总人口（万人）非 农业 人口比（%）农业 总产值 （万元）工业 总产值（万元）客运 总量（万人）货运总量（万

7、吨）地方财 政预算内收入（万元）城乡居 民年底 储蓄余 额（万元）在岗 职工 人数（万人）在岗职 工工资 总额（万元）10.5971 84319 99920452 79026 806410.805 773249.908427706323562863646301910.170.5801 50122 6453261 12811 301202.682 25491365022593170739313430.2332 9186 885217 095875.402680768929911352 34887595.60758 877299.920.656236 0382 737111203 2773 943

8、88.65654 0233750937895100207.780.4412365 343816 45223512623105 7831 39658842.11309 337677.080.6291 2955 826715567 9199 016135.451 15290.4944181 8797338 42678210412199987 556811545.31709 22794.15965 92267393857801877960.4061 8535 966494 803691.23810357 096102.63884 4478210343532744927.090.4622 6634 1

9、8667481 4436 450172.791 309785512372052002015110.7382 06954 5296444 31825 971336.845 605313.124019098406485500200445537.440.534989 19913 0721411664 2995 680113.811 3571737269193472861616.050.3551 41412 0001711449 5937 42596.901 1806737796883684967947538.410.2541 42810 6222210501 7235 24662.15824 034

10、72358662152983500.3182 514411 622429.95628 764893517233 62847.27369 5774125931583.130.2732 1526 55587467 5245 03069.59680 6073288351851190220128.990.48650.398333 3745 7511242 3053728325703418 7582 1083312 64046.93657 484424.20688 289167 71462.08479 ,5558881674189460禾 北京天津庄太原耐特沈阳大连长春“滨上海南京杭州宁波合肥福州厦门南

11、昌 城名 石 呼 哈济南557.630.40851 4863026 285882591511775460 6904 12697083.31756 696青岛702.970.36932 38232011 4920361340817038658 4354 978045103.52961 704郑 州615.360.3424677 4255 287601104336768387 2525 13533884.66696 848武 汉740.200.58691 2112917 506085979315442604 6585 748055149.201 314766长 沙582.470.31071 146

12、3673 09817987065718323 6603 46124469.57596 986广685.000.6211 60023 34822231 76120 401182.813 047州4738139007854499811594深 圳119.850.7931299 66220 368295875442741 8479089 51990091.261 890338南/宁285.870.4064720 4861 14969151303293149 7002 19091845.09371 809海 口54.380.835444 815717 46153452356115 1741 62680

13、019.01198 138重30.2064 1688 5855225898,9129 090223.731 606庆072.347780525441124969804成 都1003.560.3351 9355905 8942894014019632561 1897 479684132.891 200671贵 阳321.500.4557362 0612 247934157034143197 9081 78774855.28419 681昆 明473.390.3865793 3563 605729560412042524 2164 12790088.11842 321西 安674.500.4094

14、739 9053 665942103119766408 8965 863980114.01885 169州287.590.5445259 4442 94088418324749169 5402 64156865.83550 890西/宁133.950.522765 848711 3101746146949 134855 05127.21219 251银 川95.380.5709171 603661 2262106119374 758814 10323.72178 621乌鲁木 齐158.920.824478 5131 84724126689041254 8702 36550855.27517

15、6224.2运行结果>> cwpri nt('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.

16、01740.02340.01580.00970.02630.00860.00280.00640.00640.00450.00620.01110.00750.03150.03750.03050.01980.02130.03760.02430.03980.03570.02780.02530.02950.04430.02860.02950.04680.03040.03340.02480.02330.03210.02420.04370.02030.01320.02330.01530.02120.02700.02130.04310.02760.06280.01420.01840.01840.02060.

17、02850.04550.03160.06100.04400.04880.18530.01760.10860.18480.11480.08880.13520.02500.03180.02330.04440.03910.02730.02840.02510.03000.03270.02860.02120.03340.04080.04900.02850.01920.03280.02550.02850.02500.01520.03370.03610.06090.02510.02150.02320.01640.01990.02000.01900.01480.00850.01340.00370.01000.

18、00720.01250.00890.02710.01630.05080.02230.02430.01750.02000.02220.01830.01640.00600.02900.00790.01950.01020.00630.01790.00930.01240.01590.01970.02370.01620.00780.01010.00780.00720.01170.01640.01160.02590.02430.03500.02140.01620.02870.01970.01820.02200.01820.03270.02200.05620.03910.03670.04160.02820.

19、02200.02730.02320.02860.02040.01600.01800.02860.01650.01660.02270.02230.01680.03440.03490.02860.02550.02680.03770.02590.02540.03930.03170.02710.01850.02700.01050.02390.01400.01390.01530.01830.01440.03180.03700.03770.07930.06030.05820.07540.09010.04820.07350.00560.04720.00710.06920.02400.01040.07910.

20、04210.02400.04560.01330.02420.01700.00390.01410.00800.00640.00970.01190.00900.00250.04970.00110.00240.01460.00570.00490.00720.00500.00480.14280.01230.09830.02920.14370.06130.03850.04020.05900.03870.04660.01990.04560.02000.11000.04790.02400.03310.03500.02900.01490.02710.00850.00760.04300.01010.00850.

21、00790.01460.01010.02200.02300.01870.01230.01540.02940.02240.01820.02320.02030.03130.02440.01740.01250.02830.02380.01750.02590.03000.02130.01340.03240.00610.01000.00500.01160.00730.01170.01730.01330.00620.03110.00160.00240.00480.00360.00210.00380.00720.00530.00440.03400.00400.00220.00580.00290.00320.

22、00360.00630.00430.00740.04910.00190.00630.00730.02210.01090.01050.01460.0125相关系数矩阵：std =1.0000-0.3444 0.84250.36030.7390 0.6215 0.4039 0.4967 0.67610.4689-0.34441.0000-0.47500.3096-0.35390.19710.35710.26000.15700.30900.8425 -0.47501.00000.33580.5891 0.5056 0.3236 0.4456 0.55750.37420.36030.30960.335

23、81.00000.1507 0.76640.9412 0.84800.73200.86140.7390 -0.35390.58910.15071.0000 0.4294 0.1971 0.3182 0.38930.25950.62150.19710.50560.76640.42941.00000.83160.89660.93020.90270.40390.35710.32360.94120.19710.83161.00000.92330.83760.95270.49670.26000.44560.84800.31820.89660.92331.00000.92010.97310.67610.1

24、5700.55750.73200.38930.93020.83760.92011.00000.93960.46890.30900.37420.86140.25950.90270.95270.97310.93961.0000特征向量(vec)：vec =-0.13670.2282-0.26280.19390.6371-0.21630.3176-0.1312-0.41910.2758-0.0329-0.02170.00090.0446-0.1447-0.44370.4058-0.55620.54870.0593-0.0522-0.02800.2040-0.0492-0.5472-0.42250.3

25、4400.3188-0.44380.2401 0.0067-0.4176-0.2856-0.23890.1926-0.4915-0.41890.2726 0.20650.3403 0.0404 0.14080.08960.0380-0.1969-0.0437-0.4888-0.6789 -(0.44050.1861-0.03430.23600.0640-0.82940.03770.26620.1356-0.12900.02780.37820.29810.47390.56850.23580.1465-0.1502-0.26310.12450.21520.36440.15670.3464-0.64

26、850.2489-0.40430.2058-0.07040.04620.12140.38120.4879-0.57070.1217 0.17610.0987 0.35500.3280-0.01390.00710.3832-0.7894-0.16280.19250.2510-0.04220.26940.03960.04560.16680.3799特征值(val)val =0.0039000000.0240000000.0307000000.099100000000000000000000000002.3514006.2602000000000000000000000000.1232000000.

27、2566000000.3207000000.53000000000000特征根排序：6.260222.351380.5300470.3206990.2566390.1232410.09909150.03070880.02403550.00393387各主成分贡献率:n ewrate =0.62600.23510.05300.03210.02570.01230.00990.00310.00240.0004第一、二主成分的载荷:文案大全标准实用0.690 10.148 30.600 70.851 50.465 60.946 30.911 70.953 70.958 90.950 6-0.64270.8414-0.68050.3167-0.67540.04260.32990.18620.01090.2558文案大全标准实用文案大全标准实用第一、二、三、四主成分的得分:scor