主成分分析实施报告matlab程序

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Cwprint.m读入数据文件；调用以上三个函数

2、并输出结果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);fprintfC相关系数矩阵：n)std=CORRCOEF(vector)%计算相关系数矩阵fprin

3、tfC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fprintfC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)sumrate=0;newi=;for k=length(y)：-1:1sumrate=sumrate

4、+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);fprintfC主成分载荷：n)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 cwscore.m%cwscore.m,计算得分function score=cwscore(vector1,ve

5、ctor2);sco=vector1*vector2;csum=sum(sco,2);newcsum,i=sort(-1*csum);newi,j=sort(i);fprintfC 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 区为矩阵行数(样本数)，b 矩阵列数(变量指标数)fid=fopen(filename,r)vector=fscanf(fid,%g,a b);fpr

6、intfC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。城市名称北京天津石家庄太原呼和浩特沈阳大连非客运货运地方财城乡居在岗在岗职年底农业农业工业总量总量政民年底职工工工资总人口人口总产值总产值（万（万预算内储蓄余人数总额（万人）比（万元）（万元）人）吨）收入（万额（万（万元）(%)元）（万元）人）10.591 84319 99920452 79026 806410.85 773249.907 84277063235628636

7、4603010.581 50122 6453261 12811 301202.62 254910.170 913650225931707393183430.232 9186 885217 095875.403 2680768929911352 34887595.60758 8770.652 7371113 943299.926 3236 038750937895203 27710088.65654 0230.44221 396207.781 2365 343816 452351623105 78358842.11309 3370.621 2955 8267159 016135.41 15267

8、7.089 9418733782412567 91999858110.491 8798 42610197 556545.314 6739385780187709 22779694.15965 922长春哈尔滨上海南京杭州宁波合肥福州厦门南昌0.401 8535 966494 803102.6691.23357 096884 4476 821034381053274430.462 6634 186676 450172.71 309927.09481 4432 7855123720520020915110.732 06954 5296444 31825 971336.85 605313.128 4

9、01909840648550020044450.5313 07214115 680113.81 357537.44989 199664 2994 173726919347218610.351 41412 00017117 4251 180616.05449 59396.905 67377968836849679470.251 42810 62222105 246538.41501 72362.15824 0344 72358662152983500.312 514411 622429.95628 764233 62847.27369 5778 41258935179310.272 1526 5

10、55875 030583.13467 52469.59680 6073 32883518511902200.485 751322 108128.99333 374418 75846.93657 4846 51247285703310.392 305332 640479 ,55424.20688 289167 71462.088 88816741894605济0.40 1 486 6 2855114 126557.63460 69083.31 756 696南8 5302882915 775970青0.36 2 382 11 492 13 174 978 103.5702.97658 43596

11、1 704岛9 3320036408 0380452郑0.345 287 1065 135615.36677 425387 25284.66 696 848州2 4601433 768338武0.58 1 211 7 5069155 748 149.2 1 314740.20604 658汉6 9291085793 4420550766长0.31 1 146 3 098853 461582.47323 66069.57 596 986沙0 7367179706 718244广0.62 1 600 23 348 22 23 1 761 20 401 182.8 3 047685.00州1 473

12、8139007 8544998111594深0.7920 368 841 847 9 5191 890119.85299 66291.26圳3 1295754 274908900338南0.401 149532 190285.87720 486149 70045.09 371 809宁6 4691130 293918海0.83521 62654.3844 815 717 461115 17419.01 198 138口5 4345 356800重30.20 4 168 8 585 52 259 090 223.7 1 606898,912庆072.34 6 7780525441 1249693

13、804成10.331 9355 894都003.565590289贵0.452 247321.50362 061阳5 7934昆0.383 605473.39793 356明6 5729西0.403 665674.50739 905安9 4942兰0.542 940287.59259 444州4 5884西0.52133.9565 848711 310宁2 7银0.5795.38171 603661 226川0 9乌鲁木0.821 847158.9278 513齐4 424140197 479132.81 200561 18914063268496711541 787197 90855.284

14、19 6817031437485124 127524 21688.11842 3216040429001095 863114.0408 896885 1693117669801142 641169 54065.83550 8908327495681149 134855 05127.21219 2517464692174 758814 10323.72178 621106193292 365254 87055.27517 6226680415084.2运行结果 cwprint(cwbook.txt,35,10)fid =数据标准化结果如下：v1 =0.05810.03560.04350.0680

15、0.05570.11120.11940.11840.10830.13920.04230.03460.03540.07700.00890.06420.04830.04990.05340.05440.04070.01390.06880.02340.00800.00470.01510.03140.02520.01830.01390.03910.00560.00930.00530.02900.00870.01740.02340.01580.00970.02630.00860.00280.00640.00640.00450.00620.01110.00750.03150.03750.03050.0198

16、0.02130.03760.02430.03980.03570.02780.02530.02950.04430.02860.02950.04680.03040.03340.0248 0.02330.03210.02420.04370.02030.01320.02330.01530.02120.02700.02130.04310.02760.06280.01420.01840.01840.02060.02850.04550.03160.06100.04400.04880.18530.01760.10860.18480.11480.08880.13520.02500.03180.02330.044

17、40.03910.02730.02840.02510.03000.03270.02860.02120.03340.04080.04900.02850.01920.03280.02550.02850.02500.01520.03370.03610.06090.02510.02150.02320.01640.01990.02000.01900.01480.00850.01340.00370.01000.00720.01250.00890.02710.01630.05080.02230.02430.01750.02000.02220.01830.01640.00600.02900.00790.019

18、50.01020.00630.01790.00930.01240.01590.01970.02370.01620.00780.01010.00780.00720.01170.01640.01160.02590.02430.03500.02140.01620.02870.01970.01820.03270.02200.05620.03910.03670.04160.02820.02200.02730.02320.02860.02040.01600.01800.02860.01650.01660.02270.02230.01680.03440.03490.02860.02550.02680.037

19、70.02590.02540.03930.03170.02710.01850.02700.01050.02390.01400.01390.01530.01830.01440.03180.03700.03770.07930.06030.05820.07540.09010.04820.07350.00560.04720.00710.06920.02400.01040.07910.04210.02400.04560.01330.02420.01700.00390.01410.00800.00640.00970.01190.00900.00250.04970.00110.00240.01460.005

20、70.00490.00720.00500.00480.14280.01230.09830.02920.14370.06130.03850.04020.05900.03870.04660.01990.04560.02000.11000.04790.02400.03310.03500.02900.01490.02710.00850.00760.04300.01010.00850.00790.02200.02300.0232 0.02030.03130.02440.0300 0.02130.01340.03240.0173 0.01330.00620.03110.0072 0.00530.00440

21、.03400.0063 0.00430.00740.04910.0146 0.0125相关系数矩阵:std =1.00000.67610.4689-0.34440.15700.30900.0187 0.01230.01740.01250.00610.01000.00160.00240.00400.00220.00190.0063-0.34440.84251.0000-0.47500.36030.30960.01540.02940.02830.02380.00500.01160.00480.00360.00580.00290.00730.02210.7390 0.6215-0.3539 0.19

22、710.02240.01820.01750.02590.00730.01170.00210.00380.00320.00360.01090.01050.4039 0.49670.3571 0.26000.8425 -0.47501.00000.33580.5891 0.5056 0.3236 0.44560.55750.37420.36030.30960.73200.86140.7390 -0.35390.38930.25950.62150.19710.93020.90270.40390.35710.83760.95270.49670.26000.92010.97310.67610.15701

23、.00000.93960.46890.30900.93961.00000.33581.00000.58910.15070.50560.76640.32360.94120.44560.84800.55750.73200.37420.8614特征向量(vec):vec =0.1507 0.76640.9412 0.84801.0000 0.42940.1971 0.31820.4294 1.00000.8316 0.89660.1971 0.83160.3182 0.89660.3893 0.93020.2595 0.90271.0000 0.92330.9233 1.00000.8376 0.9

24、2010.9527 0.9731-0.13670.2282 -0.26280.19390.6371 -0.2163 0.3176 -0.1312-0.41910.2758-0.0329-0.02170.00090.0446 -0.1447 -0.4437 0.4058 -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 -0.4915-0.41890.2726 0.20650.3403 0

25、.0404 0.14080.0896 0.0380-0.1969-0.0437 -0.4888 -0.6789 -0.44050.1861-0.03430.23600.0640 -0.8294 0.0377 0.2662 0.1356 -0.12900.02780.37820.29810.47390.5685 0.23580.1465 -0.1502 -0.2631 0.12450.21520.36440.15670.3464-0.6485 0.2489 -0.4043 0.2058 -0.0704 0.04620.12140.38120.4879-0.57070.1217 0.17610.0

26、987 0.3550 0.3280 -0.01390.00710.3832-0.7894-0.1628 0.1925 0.2510 -0.0422 0.2694 0.0396 0.04560.16680.3799特征值(val)val =0.003900000000000.024000000000000.030700000000000.099100000000000.123200000000000.256600000000000.320700000000000.530000000000002.351400000000006.2602特征根排序：6.260222.351380.5300470.3

27、206990.2566390.1232410.09909150.03070880.02403550.00393387各主成分贡献率：newrate =0.6260 0.2351 0.0530 0.0321 0.0257 0.0123 0.0099 0.00310.00240.0004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 60.946 30.911 70.953 70.958 90.950 6-0.67540.04260.32990.18620.01090.2558第一、二、三、四主成分的得分：score =