pca en R avec princomp() et en utilisant SVD()

Question

de Possible en double:
Comparing svd and princomp in R

Comment effectuer l'APC en utilisant 2 méthodes (princomp() et SVD de la matrice de corrélation) dans R

I ont un ensemble de données comme:

438,498,3625,3645,5000,2918,5000,2351,2332,2643,1698,1687,1698,1717,1744,593,502,493,504,445,431,444,440,429,10 
438,498,3625,3648,5000,2918,5000,2637,2332,2649,1695,1687,1695,1720,1744,592,502,493,504,449,431,444,443,429,10 
438,498,3625,3629,5000,2918,5000,2637,2334,2643,1696,1687,1695,1717,1744,593,502,493,504,449,431,444,446,429,10 
437,501,3625,3626,5000,2918,5000,2353,2334,2642,1730,1687,1695,1717,1744,593,502,493,504,449,431,444,444,429,10 
438,498,3626,3629,5000,2918,5000,2640,2334,2639,1696,1687,1695,1717,1744,592,502,493,504,449,431,444,441,429,10 
439,498,3626,3629,5000,2918,5000,2633,2334,2645,1705,1686,1694,1719,1744,589,502,493,504,446,431,444,444,430,10 
440,5000,3627,3628,5000,2919,3028,2346,2330,2638,1727,1684,1692,1714,1745,588,501,492,504,451,433,446,444,432,10 
444,5021,3631,3634,5000,2919,5000,2626,2327,2638,1698,1680,1688,1709,1740,595,500,491,503,453,436,448,444,436,10 
451,5025,3635,3639,5000,2920,3027,2620,2323,2632,1706,1673,1681,1703,753,595,499,491,502,457,440,453,454,442,20 
458,5022,3640,3644,5000,2922,5000,2346,2321,2628,1688,1666,1674,1696,744,590,496,490,498,462,444,458,461,449,20 
465,525,3646,3670,5000,2923,5000,2611,2315,2631,1674,1658,1666,1688,735,593,495,488,497,467,449,462,469,457,20 
473,533,3652,3676,5000,2925,5000,2607,2310,2623,1669,1651,1659,1684,729,578,496,487,498,469,454,467,476,465,20 
481,544,3658,3678,5000,2926,5000,2606,2303,2619,1668,1643,1651,1275,723,581,495,486,497,477,459,472,484,472,20 
484,544,3661,3665,5000,2928,5000,2321,2304,5022,1647,1639,1646,1270,757,623,493,484,495,480,461,474,485,476,20 
484,532,3669,3662,2945,2926,5000,2326,2306,2620,1648,1639,1646,1270,760,533,493,483,494,507,461,473,486,476,20 
482,520,3685,3664,2952,2927,5000,2981,2307,2329,1650,1640,1644,1268,757,533,492,482,492,513,459,474,485,474,20 
481,522,3682,3661,2955,2927,2957,2984,1700,2622,1651,1641,1645,1272,761,530,492,482,492,513,462,486,483,473,20 
480,525,3694,3664,2948,2926,2950,2995,1697,2619,1651,1642,1646,1269,762,530,493,482,492,516,462,486,483,473,20 
481,515,5018,3664,2956,2927,2947,2993,1697,2622,1651,1641,1645,1269,765,592,489,482,495,531,462,499,483,473,20 
479,5000,3696,3661,2953,2927,2944,2993,1702,2622,1649,1642,1645,1269,812,588,489,481,491,510,462,481,483,473,20 
480,506,5019,3665,2941,2929,2945,2981,1700,2616,1652,1642,1645,1271,814,643,491,480,493,524,461,469,484,473,20 
479,5000,5019,3661,2943,2930,2942,2996,1698,2312,1653,1642,1644,1274,811,617,491,479,491,575,461,465,484,473,20 
479,5000,5020,3662,2945,2931,2942,2997,1700,2313,1654,1642,1644,1270,908,616,490,478,489,503,460,460,478,473,10 
481,508,5021,3660,2954,2936,2946,2966,1705,2313,1654,1643,1643,1270,1689,678,493,477,483,497,467,459,476,473,10 
486,510,522,3662,2958,2938,2939,2627,1707,2314,1659,1643,1639,1665,1702,696,516,476,477,547,465,457,470,474,10 
479,521,520,3663,2954,2938,2941,2957,1712,2314,1660,1643,1638,1660,1758,688,534,475,475,489,461,456,465,474,10 
480,554,521,3664,2954,2938,2941,2632,1715,2313,1660,1643,1637,1656,1761,687,553,475,474,558,462,453,465,476,10 
481,511,5023,3665,2954,2937,2941,2627,1707,2312,1660,1641,1636,1655,1756,687,545,475,475,504,463,458,470,477,10 
482,528,524,3665,2953,2937,2940,2629,1706,2312,1657,1640,1635,1654,1756,566,549,475,476,505,464,459,468,477,10 

Je fais ceci:

x <- read.csv("C:\\data_25_1000.txt",header=F,row.names=NULL) 
p1 <- princomp(x, cor = TRUE) ## using correlation matrix 
p1 
Call: 
princomp(x = x, cor = TRUE) 

    Standard deviations: 
     Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 
    1.9800328 1.8321498 1.4147367 1.3045541 1.2016116 1.1708212 1.1424120 1.0134829 1.0045317 0.9078734 0.8442308 0.8093044 0.7977656 0.7661921 0.7370972 0.7075442 
     Comp.17 Comp.18 Comp.19 Comp.20 Comp.21 Comp.22 Comp.23 Comp.24 Comp.25 
    0.7011462 0.6779179 0.6671614 0.6407627 0.6077336 0.5767217 0.5659030 0.5526520 0.5191375 

    25 variables and 1000 observations. 

Pour la deuxième méthode suppose que j'ai la matrice de corrélation de "C: \ data_25_1000.txt" qui est:

1.0  0.3045 0.1448 -0.0714 -0.038 -0.0838 -0.1433 -0.1071 -0.1988 -0.1076 -0.0313 -0.157 -0.1032 -0.137 -0.0802 0.1244 0.0701 0.0457 -0.0634 0.0401 0.1643 0.3056 0.3956 0.4533 0.1557 
0.3045 0.9999 0.3197 0.1328 0.093 -0.0846 -0.132 0.0046 -0.004 -0.0197 -0.1469 -0.1143 -0.2016 -0.1 -0.0316 0.0044 -0.0589 -0.0589 0.0277 0.0314 0.078 0.0104 0.0692 0.1858 0.0217 
0.1448 0.3197 1  0.3487 0.2811 0.0786 -0.1421 -0.1326 -0.2056 -0.1109 0.0385 -0.1993 -0.1975 -0.1858 -0.1546 -0.0297 -0.0629 -0.0997 -0.0624 -0.0583 0.0316 0.0594 0.0941 0.0813 -0.1211 
-0.0714 0.1328 0.3487 1  0.6033 0.2866 -0.246 -0.1201 -0.1975 -0.0929 -0.1071 -0.212 -0.3018 -0.3432 -0.2562 0.0277 -0.1363 -0.2218 -0.1443 -0.0322 -0.012 0.1741 -0.0725 -0.0528 -0.0937 
-0.038 0.093 0.2811 0.6033 1  0.4613 0.016 0.0655 -0.1094 0.0026 -0.1152 -0.1692 -0.2047 -0.2508 -0.319 -0.0528 -0.1839 -0.2758 -0.2657 -0.1136 -0.0699 0.1433 -0.0136 -0.0409 -0.1538 
-0.0838 -0.0846 0.0786 0.2866 0.4613 0.9999 0.2615 0.2449 0.1471 0.0042 -0.1496 -0.2025 -0.1669 -0.142 -0.1746 -0.1984 -0.2197 -0.2631 -0.2675 -0.1999 -0.1315 0.0469 0.0003 -0.1113 -0.1217 
-0.1433 -0.132 -0.1421 -0.246 0.016 0.2615 1  0.3979 0.3108 0.1622 -0.0539 0.0231 0.1801 0.2129 0.1331 -0.1325 -0.0669 -0.0922 -0.1236 -0.1463 -0.1452 -0.2422 -0.0768 -0.1457 0.036 
-0.1071 0.0046 -0.1326 -0.1201 0.0655 0.2449 0.3979 1  0.4244 0.3821 0.119 -0.0666 0.0163 0.0963 -0.0078 -0.1202 -0.204 -0.2257 -0.2569 -0.2334 -0.234 -0.2004 -0.138 -0.0735 -0.1442 
-0.1988 -0.004 -0.2056 -0.1975 -0.1094 0.1471 0.3108 0.4244 0.9999 0.5459 0.0498 -0.052 0.0987 0.186 0.2576 -0.052 -0.1921 -0.2222 -0.1792 -0.0154 -0.058 -0.1868 -0.2232 -0.3118 0.0186 
-0.1076 -0.0197 -0.1109 -0.0929 0.0026 0.0042 0.1622 0.3821 0.5459 0.9999 0.2416 0.0183 0.063 0.0252 0.186 0.0519 -0.1943 -0.2241 -0.2635 -0.0498 -0.0799 -0.0553 -0.1567 -0.2281 -0.0263 
-0.0313 -0.1469 0.0385 -0.1071 -0.1152 -0.1496 -0.0539 0.119 0.0498 0.2416 1  0.2601 0.1625 -0.0091 -0.0633 0.0355 0.0397 -0.0288 -0.0768 -0.2144 -0.2581 0.1062 0.0469 -0.0608 -0.0578 
-0.157 -0.1143 -0.1993 -0.212 -0.1692 -0.2025 0.0231 -0.0666 -0.052 0.0183 0.2601 0.9999 0.3685 0.3059 0.1269 -0.0302 0.1417 0.1678 0.2219 -0.0392 -0.2391 -0.2504 -0.2743 -0.1827 -0.0496 
-0.1032 -0.2016 -0.1975 -0.3018 -0.2047 -0.1669 0.1801 0.0163 0.0987 0.063 0.1625 0.3685 1  0.6136 0.2301 -0.1158 0.0366 0.0965 0.1334 -0.0449 -0.1923 -0.2321 -0.1848 -0.1109 0.1007 
-0.137 -0.1 -0.1858 -0.3432 -0.2508 -0.142 0.2129 0.0963 0.186 0.0252 -0.0091 0.3059 0.6136 1  0.4078 -0.0615 0.0607 0.1223 0.1379 0.0072 -0.1377 -0.3633 -0.2905 -0.1867 0.0277 
-0.0802 -0.0316 -0.1546 -0.2562 -0.319 -0.1746 0.1331 -0.0078 0.2576 0.186 -0.0633 0.1269 0.2301 0.4078 1  0.0521 -0.0345 0.0444 0.0778 0.0925 0.0596 -0.2551 -0.1499 -0.2211 0.244 
0.1244 0.0044 -0.0297 0.0277 -0.0528 -0.1984 -0.1325 -0.1202 -0.052 0.0519 0.0355 -0.0302 -0.1158 -0.0615 0.0521 1  0.295 0.2421 -0.06 0.0921 0.243 0.0953 0.0886 0.0518 -0.0032 
0.0701 -0.0589 -0.0629 -0.1363 -0.1839 -0.2197 -0.0669 -0.204 -0.1921 -0.1943 0.0397 0.1417 0.0366 0.0607 -0.0345 0.295 0.9999 0.4832 0.2772 0.0012 0.1198 0.0411 0.1213 0.1409 0.0368 
0.0457 -0.0589 -0.0997 -0.2218 -0.2758 -0.2631 -0.0922 -0.2257 -0.2222 -0.2241 -0.0288 0.1678 0.0965 0.1223 0.0444 0.2421 0.4832 1  0.2632 0.0576 0.0965 -0.0043 0.0818 0.102 0.0915 
-0.0634 0.0277 -0.0624 -0.1443 -0.2657 -0.2675 -0.1236 -0.2569 -0.1792 -0.2635 -0.0768 0.2219 0.1334 0.1379 0.0778 -0.06 0.2772 0.2632 1  0.2036 -0.0452 -0.142 -0.0696 -0.0367 0.3039 
0.0401 0.0314 -0.0583 -0.0322 -0.1136 -0.1999 -0.1463 -0.2334 -0.0154 -0.0498 -0.2144 -0.0392 -0.0449 0.0072 0.0925 0.0921 0.0012 0.0576 0.2036 0.9999 0.2198 0.1268 0.0294 0.0261 0.3231 
0.1643 0.078 0.0316 -0.012 -0.0699 -0.1315 -0.1452 -0.234 -0.058 -0.0799 -0.2581 -0.2391 -0.1923 -0.1377 0.0596 0.243 0.1198 0.0965 -0.0452 0.2198 1  0.2667 0.2833 0.2467 0.0288 
0.3056 0.0104 0.0594 0.1741 0.1433 0.0469 -0.2422 -0.2004 -0.1868 -0.0553 0.1062 -0.2504 -0.2321 -0.3633 -0.2551 0.0953 0.0411 -0.0043 -0.142 0.1268 0.2667 1  0.4872 0.3134 0.1663 
0.3956 0.0692 0.0941 -0.0725 -0.0136 0.0003 -0.0768 -0.138 -0.2232 -0.1567 0.0469 -0.2743 -0.1848 -0.2905 -0.1499 0.0886 0.1213 0.0818 -0.0696 0.0294 0.2833 0.4872 0.9999 0.4208 0.1317 
0.4533 0.1858 0.0813 -0.0528 -0.0409 -0.1113 -0.1457 -0.0735 -0.3118 -0.2281 -0.0608 -0.1827 -0.1109 -0.1867 -0.2211 0.0518 0.1409 0.102 -0.0367 0.0261 0.2467 0.3134 0.4208 1  0.0592 
0.1557 0.0217 -0.1211 -0.0937 -0.1538 -0.1217 0.036 -0.1442 0.0186 -0.0263 -0.0578 -0.0496 0.1007 0.0277 0.244 -0.0032 0.0368 0.0915 0.3039 0.3231 0.0288 0.1663 0.1317 0.0592 0.9999 

J'ai également calculé SVD de cette matrice de corrélation et obtenu:

> s = svd(Correlation_25_1000) 
$d 
[1] 3.9205298 3.3567729 2.0014799 1.7018614 1.4438704 1.3708223 1.3051053 1.0271475 1.0090840 0.8242341 0.7127256 0.6549736 0.6364299 0.5870503 0.5433123 0.5006188 0.4916060 
[18] 0.4595726 0.4451043 0.4105769 0.3693401 0.3326079 0.3202462 0.3054243 0.2695037 

$u 

matrix 

$v 

matrix 

Ma question est, comment puis-je utiliser $ d, u $ et $ v pour obtenir des composants principaux Puis-je utiliser prcomp() ?? Si c'est le cas, comment?

Answer 1

Essayez celui

princomp

princomp(USArrests, cor = TRUE)$loadings 
Loadings: 
     Comp.1 Comp.2 Comp.3 Comp.4 
Murder -0.536 0.418 -0.341 0.649 
Assault -0.583 0.188 -0.268 -0.743 
UrbanPop -0.278 -0.873 -0.378 0.134 
Rape  -0.543 -0.167 0.818  

SVD

svd(cor(USArrests))$u 
     [,1]  [,2]  [,3]  [,4] 
[1,] -0.5358995 0.4181809 -0.3412327 0.64922780 
[2,] -0.5831836 0.1879856 -0.2681484 -0.74340748 
[3,] -0.2781909 -0.8728062 -0.3780158 0.13387773 
[4,] -0.5434321 -0.1673186 0.8177779 0.08902432 

eigen

eigen(cor(USArrests))$vectors 
      [,1]  [,2]  [,3]  [,4] 
[1,] -0.5358995 0.4181809 -0.3412327 0.64922780 
[2,] -0.5831836 0.1879856 -0.2681484 -0.74340748 
[3,] -0.2781909 -0.8728062 -0.3780158 0.13387773 
[4,] -0.5434321 -0.1673186 0.8177779 0.08902432 

Pour la matrice cor, tous princomp, svd, et eigen produit les mêmes résultats.