Question

Possible Duplicate:
Comparing svd and princomp in R

How to perform PCA using 2 methods (princomp() and svd of correlation matrix ) in R

I have a data set like:

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

So I am doing this:

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. 

For the second method suppose I have the correlation matrix of “C:\data_25_1000.txt”
which is:

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

I have also computed svd of this correlation matrix and got:

> 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

My question is, how can I use $d, $u and $v to get principal components
Could I use prcomp() ?? If, so how?

Answer 1

Try this one

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

For cor matrix, all princomp, svd, and eigen produces same results.