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随机抽取管理学院10名学生，对其4门课程的考试成绩进行统计，如下表所示，这4门课程分别为多元统计分析1X ，运筹学2X ，经济学3X ，管理学4X . 使用主成分分析方法对学生成绩进行分析.>> x1=[77 63 75 55 31 67 70 66 70 57]; >> x2=[82 78 73 72 55 81 81 81 68 73]; >> x3=[67 80 71 63 60 82 78 73 72 55]; >> x4=[81 81 81 68 73 67 80 71 63 60];>> data=[x1;x2;x3;x4]'; %输入观测值数据矩阵 >> [n,m]=size(data);>> for i=1:m %将数据矩阵中心标准化sddata(:,i)=(data(:,i)-mean(data(:,i)))./std(data(:,i),1); end>> [P,score,egenvalue,t2]=princomp(sddata) %做主成分分析 P =-0.5511 0.3268 -0.3624 0.6769 -0.5588 0.3358 -0.2089 -0.7289 -0.5110 -0.1193 0.8460 0.0944 -0.3505 -0.8753 -0.3307 -0.0398score =-1.3489 -0.2567 -1.2840 -0.0315 -1.2458 -0.9740 0.5341 -0.2698 -0.8704 -0.7467 -0.5863 0.7336 1.1642 0.3096 -0.2225 -0.2707 3.3634 -1.5690 0.3950 -0.0572 -1.1054 0.8480 1.1534 -0.2345 -1.5954 -0.5212 0.0958 -0.1867 -0.6992 0.4872 0.1005 -0.4105 0.4738 0.9799 0.5768 1.03061.8637 1.4430 -0.7628 -0.3031egenvalue = 2.7502 0.9334 0.5275 0.2334 t2 =3.8620 2.4333 3.8297 1.0034 7.0609 3.9724 1.3834 1.1732 6.29124.9906>> for k=1:mgxl(k)=sum(egenvalue(1:k))/sum(egenvalue); end>> gxl %输出累计贡献率 gxl =0.6188 0.8288 0.9475 1.0000>> plot(score(:,1),score(:,2),'r+') %画出第一第二主成分的散点图 >> gname第一主成分43211X X X X Y 0.3505-0.5110-0.5588--0.5511=，所有科目考试成绩的系数均为负，且差异不大，故1Y 可解释为学生的综合学习成绩，该主成分得分越小（散点图中的位置越靠左），综合成绩越好.第二主成分43212X X X X Y 0.8753-0.1193-0.33580.3268+=，数学科目考试成绩的系数均为正，专业科目考试成绩的系数均为负，故2Y 可解释为学生的数学科目与专业科目学习成绩的差异，该主成分得分绝对值越大则差异越大，由散点图可以看出，10号学生的数学科目明显优于其专业科目成绩，而5号学生的数学科目明显差于其专业科目成绩.>> Y1=score(:,1);ZF=(sum(data'))'; %提取第一主成分得分，求每个学生的总分 >>for k=1:norder(k,1)=find(Y1==min(Y1));Y1(order(k,1))=inf; %按第一主成分得分由高到低排序order(k,2)=find(ZF==max(ZF));ZF(order(k,2))=-inf; %按总分由高到低排序 end >> orderorder =7 7 1 1 2 2 6 3 3 6 8 8 9 9 4 4 10 10 5 5两种排序方式下3号学生和6号学生的排序结果相反，原因在于43211X X X X Y 0.3505-0.5110-0.5588--0.5511可见，这四个科目成绩的重要性是依次递减的，3号学生的总分虽略高于6号学生，但他的最高分出现在重要性最低的第4科.>> R=sddata'*sddata./n %求标准化数据的样本相关矩阵R =1.0000 0.7867 0.5322 0.28900.7867 1.0000 0.5749 0.27680.5322 0.5749 1.0000 0.39750.2890 0.2768 0.3975 1.0000建模2011A主成分分析-聚类分析：data1=[7.84 153.80 44.31 20.56 266.00 18.20 35.38 72.35 5.93 146.20 45.05 22.51 86.00 17.20 36.18 94.594.90 439.20 29.07 64.56 109.00 10.60 74.32 218.376.56 223.90 40.08 25.17 950.00 15.40 32.28 117.356.35 525.20 59.35 117.53 800.00 20.20 169.96 726.02 14.08 1092.90 67.96 308.61 1040.00 28.20 434.80 966.738.94 269.80 95.83 44.81 121.00 17.80 62.91 166.739.62 1066.20 285.58 2528.48 13500.00 41.70 381.64 1417.867.41 1123.90 88.17 151.64 16000.00 25.80 172.36 926.848.72 267.10 65.56 29.65 63.00 21.70 36.94 100.415.93 201.40 45.19 24.90 259.00 14.60 35.88 102.659.17 287.00 43.94 45.77 168.00 19.70 62.74 223.165.72 193.70 80.35 26.57 111.00 19.80 57.64 89.084.49 359.50 258.15 123.27 77.00 12.90 106.47 853.985.51 516.40 91.97 89.04 189.00 19.80 121.72 494.80 11.45 1044.50 94.78 136.97 202.00 22.30 472.48 602.046.14 445.40 82.69 167.39 144.00 18.40 111.24 389.807.84 347.90 57.65 97.14 213.00 19.60 70.82 307.247.41 345.70 159.45 71.03 85.00 18.10 89.34 380.928.50 614.00 744.46 130.55 156.00 32.80 228.64 1013.475.51 257.20 54.64 29.01 104.00 13.20 87.68 223.279.84 1213.50 920.84 1364.85 115.00 142.50 181.48 1818.479.39 325.80 172.29 104.89 82.00 31.50 90.90 429.293.30 212.10 50.13 38.62 139.00 10.60 66.98 186.224.09 90.50 35.02 11.82 16.00 10.40 29.09 46.846.14 583.40 95.25 233.70 155.00 21.10 97.47 311.025.31 366.40 42.34 64.65 188.00 17.40 67.11 182.653.69 323.90 35.14 34.66 50.00 13.90 65.48 253.16 21.87 424.50 73.40 59.72 1520.00 27.80 83.70 175.71 18.38 630.00 96.68 114.81 645.00 34.80 130.36 1626.02 10.53 635.30 64.03 101.35 190.00 28.30 162.64 615.103.50 463.40 112.19 72.93 118.00 14.10 60.60 193.376.35 532.00 57.51 83.76 191.00 19.50 73.46 297.14 5.51 778.70 74.66 92.48 330.00 19.70 110.20 351.63 4.49 754.80 99.88 97.92 243.00 24.90 100.79 323.37 3.50 396.30 138.37 58.97 170.00 24.20 91.76 2893.47 5.51 687.80 85.52 72.85 201.00 19.00 103.20 403.27 4.29 526.00 55.31 81.43 93.00 19.90 100.65 369.80 4.29 449.10 67.22 51.64 315.00 15.70 106.97 294.69 6.56 852.70 72.59 158.67 311.00 21.20 124.24 377.14 16.58 459.00 94.79 47.17 1900.00 19.90 71.32 215.10 7.41 337.30 77.27 248.85 90.00 20.10 99.58 210.00 5.93 568.10 75.14 118.16 135.00 23.80 111.54 572.96 4.69 599.00 69.05 122.18 121.00 19.80 102.72 427.044.90 635.50 68.42 227.76 176.00 19.50 96.33 538.985.31 600.70 44.65 45.10 51.00 15.50 65.87 186.334.29 567.60 60.25 48.67 46.00 16.10 63.74 208.065.51 228.50 49.27 30.85 62.00 22.90 45.93 102.04 4.69 568.60 306.02 70.41 900.00 16.80 79.67 196.737.20 214.70 50.33 40.16 156.00 20.80 47.76 403.98 5.31 151.90 47.24 24.44 140.00 17.30 37.49 92.55 4.90 343.30 42.01 58.81 80.00 13.80 79.07 275.82 4.90 293.90 60.29 51.03 53.00 12.60 75.93 278.37 3.89 312.90 33.79 277.82 55.00 14.00 68.24 295.61 3.69 315.90 45.43 34.05 55.00 12.60 62.84 196.33 3.11 416.30 57.88 47.64 167.00 11.90 116.19 242.04 3.89 374.00 45.17 50.19 35.00 15.00 58.11 157.35 3.89 344.30 35.29 47.87 100.00 15.10 133.72 141.022.91 252.90 45.98 71.54 32.14 14.40 42.99 146.223.30 503.40 38.74 30.46 36.43 7.20 53.73 102.864.90 303.80 56.02 65.86 63.21 40.05 90.69 3760.82 4.09 127.00 27.58 23.99 30.00 11.93 57.47 85.61 2.91 265.00 35.66 29.39 24.64 9.23 60.54 122.962.72 278.90 43.43 32.61 64.29 9.90 53.40 135.713.11 751.20 53.11 53.80 27.86 10.46 60.27 155.00 3.30 361.30 47.54 52.28 25.71 9.11 113.46 218.27 3.30 488.00 51.18 34.55 37.50 10.80 54.62 125.926.14 227.00 42.15 67.04 49.29 16.31 34.28 82.963.69 347.40 37.76 19.97 26.79 10.01 54.41 221.224.49 136.00 36.56 23.07 21.43 14.96 34.19 78.98 3.11 327.10 25.98 23.73 25.71 9.79 63.81 138.06 8.06 113.10 52.40 20.81 65.36 19.69 29.56 62.24 3.69 270.50 33.12 57.85 25.71 13.50 62.04 118.16 3.69 160.30 38.29 26.08 25.71 14.29 40.13 82.86 3.50 305.50 39.50 30.86 31.07 14.74 61.89 148.88 2.72 70.90 19.45 9.12 15.007.09 22.73 32.861.77 119.80 15.32 13.34 8.57 6.19 26.31 47.762.53 468.80 37.04 32.03 45.00 12.15 65.25 178.983.69 150.70 59.61 19.00 34.29 24.98 38.47 89.08 6.14 100.30 37.49 20.23 34.29 14.85 29.29 61.94 10.99 109.80 56.07 69.06 58.93 20.70 38.87 63.27 6.35 91.80 36.12 16.91 36.43 12.49 27.01 47.76 30.13 743.90 49.03 26.18 27.86 17.66 72.76 182.04 3.89 416.80 37.04 23.78 22.50 11.48 54.45 105.00 2.91 369.80 36.34 52.48 22.507.99 42.02 84.08 1.96 194.00 18.08 16.17 26.79 6.98 40.27 94.69 6.98 50.10 41.02 14.25 17.14 13.39 26.57 40.92 2.91 198.80 28.21 19.24 13.93 9.56 47.81 94.80 5.93 886.60 42.69 28.12 43.93 21.15 94.64 163.27 5.93 128.90 47.52 16.31 12.86 17.66 33.51 91.73 7.41 114.30 48.34 21.45 35.36 16.54 35.83 63.88 4.29 232.90 29.17 40.02 1714.29 9.79 38.65 95.414.69 132.80 36.11 17.28 20.36 15.53 37.03 82.765.72 1619.80 43.48 15.50 20.36 15.41 30.99 57.556.77 282.50 41.97 52.80 27.86 18.34 49.10 104.90 4.49 180.60 37.23 18.70 27.86 11.93 36.45 63.98 3.11 386.60 35.93 26.38 24.64 12.26 60.00 157.24 2.91 345.00 40.46 152.21 23.57 15.53 58.05 170.71 4.29 95.60 22.49 17.15 85.71 10.13 27.97 67.24 7.63 87.10 45.83 14.83 30.00 14.63 29.25 48.78 5.93 203.00 35.97 16.88 15.00 14.51 45.83 89.49 2.34 353.00 24.53 12.70 11.79 9.00 58.80 89.08 2.91 233.20 24.92 21.62 85.71 8.33 45.20 100.10 5.72 174.30 33.83 29.45 20.36 13.05 42.10 71.43 2.34 87.60 18.46 9.73 13.93 8.89 24.43 43.37 6.56 245.60 36.73 61.30 55.71 14.18 47.24 114.29 4.69 167.90 33.15 18.96 60.00 15.98 33.46 55.71 6.35 111.40 28.82 59.17 206.79 11.70 28.02 61.53 5.10 94.60 77.92 20.34 23.57 28.69 25.92 58.47 4.69 111.60 24.57 12.09 31.07 8.55 27.12 43.883.50 85.50 26.33 24.88 36.43 11.36 26.77 64.084.69 169.50 39.11 22.51 25.71 15.98 39.53 82.96 4.49 138.00 34.52 35.54 50.36 12.60 25.45 52.45 3.30 131.40 35.97 11.29 43.93 11.03 30.06 61.94 2.91 41.00 41.77 12.50 17.14 17.10 19.68 78.374.09 129.70 26.83 10.12 40.71 7.76 28.84 68.165.72 148.00 36.73 14.21 52.50 12.60 27.15 57.86 4.90 108.10 22.729.40 35.36 8.89 32.39 69.39 4.90 132.50 79.52 18.67 42.86 27.68 28.30 92.245.93 88.80 52.41 15.30 10.71 19.91 28.62 63.88 2.91 206.70 17.46 12.02 31.07 5.51 53.79 79.18 2.72 121.80 19.98 7.71 24.648.10 27.30 57.96 2.34 231.10 36.48 12.80 37.50 17.66 29.02 96.532.53 128.60 21.75 9.10 30.00 9.56 22.77 58.063.89 126.80 50.01 12.74 53.57 18.68 29.40 69.90 2.34 79.70 74.36 27.49 9.64 45.45 21.22 87.65 2.34 294.10 42.68 12.27 79.29 15.53 83.44 99.491.96 238.30 19.71 25.22 19.29 6.64 66.24 142.862.72 109.30 18.52 12.55 19.29 9.79 26.06 61.433.11 69.40 22.93 7.56 26.79 7.65 22.09 53.06 3.50 155.70 33.30 12.08 42.86 11.36 28.05 51.53 2.72 109.30 19.83 14.54 19.29 9.45 34.56 47.55 1.77 205.50 173.34 27.81 41.79 74.03 55.71 229.80 3.50 53.20 35.15 7.91 20.36 11.14 24.90 34.39 2.53 40.00 19.08 2.29 15.00 7.88 24.15 54.29 9.17 82.80 63.88 24.85 11.79 31.50 21.68 76.537.41 222.40 31.10 38.50 142.50 8.66 128.60 133.98 5.72 164.80 49.44 27.98 126.43 13.61 37.64 76.12 8.06 194.00 41.79 31.43 213.21 13.61 45.52 127.35 5.72 310.10 56.40 37.11 138.21 16.43 59.63 154.49 8.72 1024.90 77.61 71.24 128.57 19.35 227.40 1389.39 6.77 492.80 37.86 35.61 142.50 13.39 114.13 118.98 6.56 202.30 33.28 37.67 1339.29 11.36 140.62 110.92 6.77 97.20 38.67 18.12 24.64 14.74 28.77 49.90 6.98 208.60 41.00 28.55 67.50 15.19 93.83 84.59 6.14 143.40 41.67 22.57 88.93 12.49 38.14 65.61 6.69 158.10 36.61 16.22 36.00 12.91 31.67 63.57 8.00 332.60 77.06 46.01 240.00 24.47 68.10 259.29 6.69 401.80 84.94 60.11 138.00 19.16 96.76 227.558.23 756.40 42.73 87.52 63.00 19.26 88.74 184.699.35 407.50 55.54 61.83 112.00 24.05 66.82 208.27 8.90 307.30 54.39 57.21 326.00 25.72 131.93 256.94 3.77 242.10 30.93 32.13 28.00 11.56 50.60 144.69 5.41 178.90 29.54 23.73 52.00 9.89 49.84 118.88 7.78 315.50 49.76 28.03 550.00 18.95 45.73 109.29 5.62 134.60 25.33 19.10 45.00 11.66 40.50 87.14 5.41 235.60 36.88 48.80 43.00 14.06 53.61 213.47 4.58 203.80 39.03 24.18 87.00 16.66 53.09 138.88 6.91 568.50 54.59 113.46 264.00 23.22 82.40 399.90 5.00 506.50 59.45 70.71 202.00 26.13 78.01 334.395.62 880.00 78.29 121.12 293.00 25.61 171.14 540.006.91 250.30 39.09 50.46 81.00 20.41 59.17 172.656.26 249.40 54.70 81.74 75.00 25.51 57.92 171.127.56 248.20 42.23 69.39 57.00 16.56 44.54 165.104.79 156.30 41.16 32.40 83.00 14.58 35.50 103.882.77 120.30 49.85 18.38 43.00 25.51 37.93 115.416.26 429.20 54.47 56.60 45.00 19.78 87.50 230.417.34 205.10 43.63 23.51 47.00 19.78 41.33 104.294.17 113.80 37.27 17.06 34.00 14.47 26.74 64.495.00 221.30 30.75 70.32 47.00 16.14 47.20 185.417.56 580.10 39.78 85.46 270.00 17.49 66.69 315.925.62 171.00 31.23 25.73 292.00 15.72 31.09 110.616.05 365.00 35.92 30.91 110.00 17.91 44.75 147.354.79 289.70 42.12 41.10 57.00 17.49 76.80 237.45 23.72 452.10 37.22 43.61 160.00 16.35 73.27 1635.926.47 847.60 53.17 59.00 96.00 19.05 68.82 186.534.17 310.70 40.70 42.64 58.00 14.99 115.59 177.765.00 317.50 42.46 30.96 162.00 17.81 59.94 221.944.17 357.50 38.78 43.89 14901.00 17.70 98.22 349.80 6.26 387.20 38.03 30.06 85.00 21.97 54.98 142.555.00 196.50 50.03 18.56 29.00 25.82 33.90 84.801.61 295.80 15.40 18.35 19.00 4.27 40.42 106.534.58 129.00 31.09 18.93 38.00 15.10 29.76 69.805.41 204.90 40.16 25.86 41.00 16.24 33.28 80.003.57 174.80 31.13 26.21 26.00 11.14 31.77 94.082.00 197.00 78.36 22.98 19.00 24.05 43.73 104.183.37 106.70 16.31 9.04 17.00 7.60 26.89 37.146.47 738.00 47.35 24.07 135.00 19.58 34.09 101.733.37 788.70 28.90 17.62 34.00 15.51 26.04 91.026.91 133.10 40.58 32.64 27.00 22.39 33.97 115.202.38 149.50 27.18 11.19 54.00 14.47 38.35 59.497.56 206.60 55.79 24.44 22.00 28.63 29.73 81.738.67 78.90 58.87 21.65 26.00 23.43 26.52 70.514.79 178.60 32.31 29.01 45.00 14.26 47.98 104.905.41 250.10 34.32 16.25 15.00 18.53 41.29 90.205.83 89.20 54.90 23.28 19.00 21.76 24.95 53.575.62 453.50 37.22 21.92 40.00 16.56 41.51 87.354.38 92.40 38.70 15.03 21.00 13.85 24.22 47.242.77 198.70 18.11 15.33 19.00 9.68 34.15 95.925.41 260.10 43.81 26.46 33.00 13.22 39.49 87.045.62 101.10 49.01 19.96 23.00 20.82 26.00 71.536.69 146.50 43.39 19.89 36.00 17.49 33.24 60.007.56 66.50 49.24 14.67 19.00 17.08 25.48 41.122.77 119.00 27.49 10.62 44.00 10.52 31.94 53.271.61 434.80 21.29 12.84 18.00 8.85 56.14 106.432.97 77.50 16.91 9.95 34.00 7.50 28.15 41.634.58 130.80 35.61 19.59 23.00 16.14 29.87 61.125.20 134.50 29.37 16.33 32.00 13.54 29.83 59.90 3.17 101.80 32.23 10.68 12.00 12.81 33.20 51.12 5.00 232.00 32.43 24.23 37.00 15.10 36.08 101.84 7.56 121.10 62.91 31.03 44.00 27.28 28.36 88.165.20 238.70 47.18 59.66 24.00 19.68 62.57 108.476.05 151.20 92.76 31.43 79.00 32.07 31.57 130.61 2.77 202.60 56.54 18.09 49.00 28.11 26.14 82.14 2.38 351.60 64.86 28.97 65.00 17.28 112.62 105.31 5.20 173.80 58.28 19.99 51.00 22.49 31.61 69.80 8.67 423.30 61.41 117.83 216.00 30.30 178.88 293.16 5.41 645.30 50.27 80.60 113.00 23.32 99.42 358.27 7.12 967.70 36.41 70.71 66.00 16.87 119.35 457.96 4.58 445.70 28.32 132.05 139.00 12.91 87.44 303.06 8.23 420.60 35.81 73.86 561.00 22.49 60.91 241.63 4.58 257.40 42.25 44.84 260.00 19.58 46.90 192.65 6.05 248.70 44.36 42.79 150.00 19.89 72.20 170.10 8.23 350.30 59.07 36.58 177.00 24.57 52.56 170.00 4.17 109.90 29.09 13.71 31.00 11.35 25.08 51.63 3.97 306.20 38.30 36.22 115.00 13.54 60.63 145.51 10.74 306.50 53.98 97.05 255.00 27.91 69.40 177.86 3.77 515.60 28.74 77.47 1801.00 15.10 70.18 178.57 10.27 175.90 57.88 37.50 65.00 26.97 45.34 100.415.20 417.80 35.71 47.58 801.00 16.03 94.93 204.086.47 368.20 44.22 65.70 91.00 18.33 76.88 247.04 6.47 393.00 35.82 70.17 135.00 18.53 72.96 254.80 8.90 117.50 32.54 20.51 41.00 14.47 41.45 56.33 3.37 379.10 32.13 37.81 49.00 13.74 70.37 208.37 6.69 320.30 87.90 66.99 78.00 21.90 123.60 230.11 4.17 613.40 50.34 149.26 133.00 16.60 110.20 447.83 8.23 220.50 61.48 41.96 84.00 22.40 58.37 153.274.38 229.30 32.69 60.40 64.00 13.70 62.62 204.815.20 334.30 47.05 40.37 76.00 18.40 61.03 211.47 5.20 284.30 40.47 44.73 349.00 16.00 119.46 184.61 5.41 230.10 41.65 35.71 57.00 16.90 43.91 118.70 5.00 551.10 71.75 71.23 74.00 22.30 111.62 209.50 9.58 201.00 39.11 25.26 125.00 10.70 99.35 90.07 3.17 203.80 26.57 24.29 23.00 11.90 41.69 94.34 3.77 355.20 26.25 32.87 14.00 9.60 59.22 117.87 9.13 133.70 52.99 22.10 26.00 24.80 37.73 95.48 7.34 95.60 47.85 19.51 14.00 20.80 28.52 57.68 5.62 352.60 44.57 58.98 51.00 13.30 69.95 531.454.79 556.20 50.87 143.31 92.00 19.10 180.05 388.695.20 113.70 41.85 20.73 12.00 19.00 31.87 57.273.37 240.50 28.04 22.63 261.00 11.70 35.74 92.467.34 120.30 54.19 21.90 27.00 23.00 29.63 81.013.57 514.10 42.34 47.67 13800.00 17.30 69.96 269.894.38 246.30 29.90 21.84 84.00 14.10 59.00 95.175.41 158.00 46.86 24.02 31.00 19.30 36.27 79.244.38 211.30 27.79 19.01 34.00 12.00 38.38 81.425.62 236.50 35.95 66.52 199.00 13.90 40.98 193.676.05 193.00 40.60 24.88 27.00 14.40 33.53 84.866.26 169.70 44.26 88.12 46.00 17.20 42.71 97.675.20 320.10 35.92 36.86 68.00 16.50 58.46 162.856.91 180.20 54.08 27.01 37.00 18.40 44.13 118.914.58 351.80 55.39 78.07 87.00 16.90 69.55 188.888.67 245.70 47.79 27.55 35.00 18.40 53.42 98.816.47 86.80 41.12 15.46 23.00 15.90 37.53 70.187.12 367.80 92.02 49.80 97.00 16.30 41.26 321.123.77 467.10 49.03 34.44 45.00 15.40 60.83 132.865.41 364.70 40.34 40.93 79.00 18.70 83.32 175.34 10.97 248.50 40.61 61.52 81.00 17.20 76.19 168.059.81 171.80 75.38 163.20 30.00 26.30 45.27 125.168.23 409.90 44.67 66.92 80.00 36.00 96.85 197.635.41 302.50 34.22 27.60 408.00 14.80 68.70 218.242.77 236.20 42.67 16.35 62.00 9.40 41.88 149.527.78 114.50 56.38 26.96 36.00 22.40 31.24 75.916.47 165.20 73.40 42.73 40.00 19.70 84.13 95.695.62 380.40 46.63 28.31 48.00 14.60 83.82 155.983.77 398.40 29.57 18.64 60.00 10.50 113.84 172.533.57 268.60 28.11 23.20 64.00 12.20 54.52 101.004.38 126.50 28.57 20.57 19.00 12.10 25.17 53.106.91 290.30 47.87 28.90 34.00 14.80 44.26 94.967.12 228.40 40.29 25.15 37.00 15.30 40.10 83.194.38 305.50 52.44 22.92 13.00 19.10 45.21 109.333.97 407.60 35.65 22.33 11.00 18.60 60.36 121.628.00 96.60 19.42 11.26 12.00 7.50 27.54 47.383.57 185.50 23.15 13.42 34.00 9.50 29.49 92.363.37 288.70 26.12 15.10 18.00 10.30 30.14 63.833.17 90.40 16.20 8.30 32.00 7.00 44.31 44.672.97 285.40 26.86 15.00 65.00 13.30 38.63 68.207.12 100.00 46.15 19.43 14.00 23.00 22.01 65.705.62 306.90 42.02 25.21 40.00 19.20 36.99 141.505.83 319.50 43.32 25.89 54.00 15.80 40.98 83.403.97 100.10 21.69 11.96 40.00 7.90 42.79 69.243.17 218.60 39.51 15.26 34.00 10.50 50.98 84.242.77 239.80 26.06 15.82 35.00 10.20 41.43 80.903.17 156.80 19.73 8.34 42.00 7.60 39.21 71.012.97 281.10 28.56 11.42 48.00 12.60 37.95 81.013.17 142.50 36.75 9.93 43.00 13.30 32.61 61.641.80 195.50 28.53 7.32 36.00 9.70 37.41 50.923.17 153.90 20.90 8.21 37.00 7.60 31.37 38.213.77 104.20 30.34 12.34 24.00 11.80 39.31 57.164.79 72.10 65.54 11.55 35.00 19.80 26.04 47.583.57 190.80 31.33 10.67 65.00 15.70 51.56 94.026.47 282.90 52.68 20.34 25.00 22.90 32.53 103.507.34 149.00 44.22 20.14 33.00 16.00 35.43 147.758.23 121.30 43.29 31.63 86.00 11.40 33.21 46.8610.74 479.20 96.28 29.23 98.00 25.30 80.36 112.3511.68 870.50 70.84 35.17 302.00 29.10 78.15 435.447.34 279.00 51.25 27.95 44.00 22.50 51.20 117.666.05 162.00 36.22 17.91 35.00 14.20 36.41 61.025.41 907.00 43.08 36.48 10.00 14.50 41.02 121.206.26 132.90 42.59 16.58 27.00 16.20 35.52 63.316.47 197.00 38.18 21.09 64.00 18.60 40.18 168.056.47 100.70 36.19 13.31 42.00 11.50 34.34 56.234.79 119.10 35.76 19.71 44.00 9.90 39.66 67.067.56 63.50 33.65 21.90 60.00 12.50 41.29 60.509.35 156.00 57.36 31.06 59.00 25.80 51.03 95.90]; %8种重金属元素的浓度原始数据>> bjz=[3.61303113.23512.33169]'; %8种重金属元素的背景值的均值>>[n,m]=size(data1);>> for i=1:m %求污染程度数据矩阵data2(:,i)=data1(:,i)./bjz(:,i);end>>data3=zscore(data2); %将污染程度数据矩阵中心化标准化>> R3=data3'*data3./n %求污染程度矩阵的相关系数矩阵R3 =0.9969 0.2539 0.1884 0.1592 0.0642 0.3156 0.2890 0.24610.2539 0.9969 0.3513 0.3955 0.2639 0.3283 0.6583 0.42980.1884 0.3513 0.9969 0.5299 0.1029 0.7135 0.3816 0.42300.1592 0.3955 0.5299 0.9969 0.4154 0.4930 0.5184 0.38610.0642 0.2639 0.1029 0.4154 0.9969 0.1026 0.2972 0.19520.3156 0.3283 0.7135 0.4930 0.1026 0.9969 0.3058 0.43500.2890 0.6583 0.3816 0.5184 0.2972 0.3058 0.9969 0.49210.2461 0.4298 0.4230 0.3861 0.1952 0.4350 0.4921 0.9969 >> [P,score,egenvalue,t2]=princomp(data3) %对标准化污染程度数据做主成分分析P =-0.2256 0.1861 -0.6932 0.6286 -0.0346 0.0990 -0.0130 0.1659 -0.3767 -0.2624 -0.2875 -0.3676 -0.3346 -0.4944 0.4024 0.2305 -0.3895 0.4140 0.3089 -0.0527 -0.1442 -0.1494 -0.5203 0.5146 -0.4009 -0.1162 0.3718 0.1569 -0.2034 0.6210 0.4560 0.1674 -0.2165 -0.6279 0.3028 0.5121 0.2027 -0.3585 -0.1862 -0.0236 -0.3831 0.4798 0.1932 0.1561 -0.0183 -0.3038 0.2180 -0.6490 -0.4049 -0.2930 -0.2415 -0.2828 -0.2074 0.3297 -0.5166 -0.4396 -0.3704 0.0349 -0.1254 -0.2750 0.8604 0.0909 0.1005 0.1079score =0.5456 0.4760 -0.2385 0.9238 0.0347 0.0562 -0.0448 -0.00680.7236 0.3890 0.1517 0.4457 0.0965 0.0977 -0.0533 -0.04400.1029 -0.6786 -0.3148 -0.6068 -0.1762 0.0955 0.2073 0.26030.5289 -0.0888 0.0282 0.7029 0.1653 -0.1864 0.0361 0.1829-2.2377 -0.8590 -0.8366 -1.0018 0.5103 0.4119 -0.4269 -0.6101 -7.0283 -2.3626 -4.0263 -1.6355 -1.1503 1.6389 -1.4879 -2.1198 -0.3681 0.5809 -0.5586 0.6635 -0.1787 0.0705 -0.4055 0.3925 -15.5620 -6.6945 5.7248 3.5181 -1.3891 6.1650 2.6337 1.0367 -6.0371 -6.9258 1.2082 2.9402 1.8860 -4.2464 -1.0592 -0.2348 -0.0015 0.7581 -0.4581 0.8739 -0.1659 -0.2192 0.1137 0.09280.6954 0.1341 0.0674 0.3664 0.0591 0.0268 -0.0202 0.1885-0.2674 0.3478 -0.8345 0.7230 0.0449 0.1003 0.0674 -0.06300.1822 0.5162 0.2579 0.2336 -0.1541 -0.0185 -0.3874 -0.1035-2.1906 0.7026 0.6746 -1.3487 0.8725 0.3109 -1.5612 1.6705 -1.5324 -0.2124 -0.3571 -0.9523 0.0396 -0.0076 -0.2709 -0.0697 -6.0460 -2.4069 -3.9522 -2.5619 -2.0637 1.4629 -2.7735 -2.3424 -1.3424 -0.2013 -0.2190 -0.5147 -0.1666 0.4430 -0.0608 0.0551 -0.6321 0.1785 -0.4933 0.2850 0.0627 0.1584 0.1581 0.0416 -1.2540 0.6515 -0.1718 -0.1308 -0.0092 0.0480 -0.8613 0.6978 -7.5796 3.7551 1.3460 -1.7726 -0.6913 -0.9056 -5.5039 3.41100.0944 -0.2025 -0.2070 -0.2764 0.0309 0.3363 -0.4892 -0.0266 -17.4212 8.9703 5.9221 -0.0944 -1.4722 -1.2894 0.8421 0.1725 -2.1046 1.4921 -0.2319 0.4977 0.0202 -0.1274 -0.6136 0.04220.6397 -0.3411 0.4288 -0.5322 0.1214 0.3348 -0.3583 0.12191.4171 0.0243 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-1.2052 -2.7072 -2.4707 1.1227 -0.0943 -0.1468 -0.1098 -0.4295 -0.6749 -0.9341 -0.4303 -0.6773 0.0528 -0.2342 -0.1111-0.1933 -1.0926 -0.4721 0.2073 -0.2135 0.6730 -1.1701 -0.5717 1.0010 0.4069 -0.0233 0.7211 0.0926 0.2576 -0.0931 0.1129 0.1729 -0.0758 -0.4896 0.2159 -0.2704 0.4691 -0.5391 -0.3240 0.9282 0.1422 0.0027 0.4359 0.0325 0.2666 -0.1663 0.2209 0.9517 0.2118 -0.1487 0.5521 0.0370 0.1945 -0.0411 0.2519 -0.7175 0.5932 -0.4110 0.4186 -0.0085 -0.2246 -0.0397 -0.1848 -0.7932 0.0804 -0.3808 -0.2108 -0.3324 -0.0177 -0.3394 -0.0270 -1.2166 -0.4314 -1.2681 -0.3538 -0.9096 -0.6028 0.7595 0.1899。
根据主成分分析的方法，分析 ……的数据。
步骤如下：Step 1为了消除不同变量的量纲的影响，首先需要对变量进行标准化，设检测数据样本共有n 个，指标共有p 个，分别设X 「X 2,X p ，令X j (i=1,2,…,n ;j=1,2,…,p) 为第i 个样本第j 个指标的值。
作变换Step 2:在标准化数据矩阵Y =(V j )np 的基础上计算p 个原始指标相关系数矩阵得到标准化数据矩阵Y X j -E(X j ) j_Var(X j )(j=l,2,…,p)X ij_X jS j1 i其中X j ― X j n i 二n2 1 2 ,S j (X j -X j )nR - (r ij ) p p「11|r-12「r ipr 2pr p2其中，「jn7 (X ki -X i )( kA n、(X kik =1X kj -X j ) --------- n(i,j=1,2,…,p)-X i )S (X kj -X j )2k =1Step 3:求相关系数矩阵R 的特征值并排序「一二-，p - 0,再求出R 的特征值相应的正则化特征向量e i =(和&2,e jp )，则第i 个主成分表示为各指标X k 的p组合乙八.e i k X k 。
i吕Step 4：计算累积贡献率确定主成分的数目。
主成分乙的贡献率为w i(i =1,2, ,p)累计贡献率为i二.叫k =1 p ■---k(i =1,2, ,p)pZk W一般取累计贡献率达85%~95%的特征值「，-，…，窃所对应的第1、第2,…, 第m (m W p )个主成分。
Step 5:计算主成分载荷，确定综合得分。
当主成分之间不相关时，主成分载荷 是主成分和各指标的相关系数，相关系数越大，说明主成分对该指标变量的代表 性就越好，计算公式为l j 二 P (Z i ，xJ 「*(门=1,2, ,P )Step 6:各主成分的得分，确定综合评分函数。
精品文档主成分分析主成分分析的主要目的是希望用较少的变量去解释原来资料中的大部分变量，通常是将我们手中许多相关性很高的变量转化成彼此相互独立或不相关的变量。
即所谓主成能解释大部分资料中的变异的几个新变量，选出比原始变量个数少，分，并用以解释资料的综合性指标。
、主成分分析的应用1）我国各地区普通高等教育发展水平综合评价。
（1 ）投资效益的分析和排序等。
（2、主成分分析法的步骤2①对原始数据进行标准化处理xx,,x,a表示第n个，用表示主成分分析指标的m个变量，评价对象有m12ij aa，转化为标准化指标i个评价对象对应于第j个指标的取值。
将每个指标值ijij即??a jij)mj?1,2,,,(i?1,2,,na?;ij sj??2??，式中：)??a?s(a jjijjij1?nn1?ii?1相应地，标准化指标变量为 nn11??x jj)m1,2,,(x?,j?j sj②计算相关系数矩阵RR?(r)mmij?n??aa kjki1k?,(ir?,j?1,2,,m)ij n?1r?1,r?rr是第i个指标和第j其中：指标之间的相关系数。
，ijjiiiij③计算相关系数矩阵的特征值与特征向量精品文档．精品文档?????0???,(i?1,2,,m)?0?I?R再求解特征方程得到特征值，；m2i1?T),m?u(i1,2,，其中的特征向量出相对应的特征值由特,,,uuu)?(u,iijmjj21j m征向量组成的个新的指标变量为xuux??y?ux??m21m112111 ?xx??uy?ux?u?m2m2212122???x?uux??yux??m2mmmm1m21m yyy 为第1主成分，?，其中：主成分为第1主成分，为第m12）（≤④选择pp个主成分，计算综合评价值。
m?),m(j?1,2, 1）计算特征值的信息贡献率和累积贡献率（j y b用的信息贡献率，则有表示主成分ij?j )?1,2,?b,m(jjm??k1?k y,,y,ay用的累积贡献率，则有表示主成分p12pp??k1?k?apm??k1k?—aa个指标变量85%的范围为）时，则用前95%若接近于1（一般p pp m yy,,,y 个主成分进个主成分，代替原来个指标变量，再对作为pp p12行综合分析。
