Skip to contents

Compute eigenvalues and eigenvectors

Source: R/pca_eig.R
pca_eigen.Rd

Return eigenvalues and eigenvectors of a matrix

Usage

pca_eigen(X)

pca_weighted_eigen(
  X,
  weighted_row = rep(1, nrow(X))/nrow(X),
  weighted_col = rep(1, ncol(X))
)

Arguments

X

X_active

weighted_row

row weights

weighted_col

column weights

Value

A list containing results of Single Value Decomposition (SVD).

Details

Standardization depends on what you need to perform factor analysis. We implemented two types:

  • pca_weighted_eigen: This is the default method in FactoMineR to compute eigvalues, eigvectors and U matrix.

  • pca_eigen: This is the standard method to compute eigenvalues, eigenvectors.

Examples

library(booklet)

iris[, -5] |>
  pca_standardize_norm() |>
  pca_eigen()
#> $values
#> [1] 434.856175 136.190540  21.866774   3.086511
#> 
#> $vectors
#>                   Dim.1       Dim.2      Dim.3      Dim.4
#> Sepal.Length  0.5210659 -0.37741762  0.7195664  0.2612863
#> Sepal.Width  -0.2693474 -0.92329566 -0.2443818 -0.1235096
#> Petal.Length  0.5804131 -0.02449161 -0.1421264 -0.8014492
#> Petal.Width   0.5648565 -0.06694199 -0.6342727  0.5235971
#> 
#> $U
#>             Dim.1         Dim.2        Dim.3        Dim.4
#> 1   -0.1082395313 -0.0409957970  0.027218646  0.013710648
#> 2   -0.0994577561  0.0575731483  0.050003401  0.058435855
#> 3   -0.1129963029  0.0292000319 -0.009420891  0.016098333
#> 4   -0.1098970995  0.0510193897 -0.019457133 -0.037416661
#> 5   -0.1142204597 -0.0552417975 -0.003354363 -0.020379051
#> 6   -0.0992030036 -0.1271804935 -0.005747892  0.003748828
#> 7   -0.1168102651 -0.0040689659 -0.071500545 -0.020862814
#> 8   -0.1067170177 -0.0190575546  0.018904131 -0.013962469
#> 9   -0.1115821423  0.0952525283 -0.030920984 -0.015237265
#> 10  -0.1043980945  0.0400552488  0.054086370 -0.022634909
#> 11  -0.1035369360 -0.0891344989  0.057265395  0.009491723
#> 12  -0.1111754327 -0.0113653128 -0.019983394 -0.075725286
#> 13  -0.1060289608  0.0622312605  0.049215308  0.001375727
#> 14  -0.1258467928  0.0821157306 -0.038534006 -0.010900993
#> 15  -0.1050869241 -0.1588547893  0.100791840  0.110471545
#> 16  -0.1081206062 -0.2294172328 -0.006506294  0.028667844
#> 17  -0.1055097633 -0.1267049550  0.001139014  0.107116335
#> 18  -0.1046858790 -0.0417483459  0.009423839  0.052810307
#> 19  -0.0907406226 -0.1199930706  0.079785722  0.034659809
#> 20  -0.1119993170 -0.0963219219 -0.028268219 -0.021419258
#> 21  -0.0914934282 -0.0349175769  0.089792273  0.006195658
#> 22  -0.1054822888 -0.0789229070 -0.034072915  0.033809630
#> 23  -0.1325974291 -0.0391440060 -0.070799052  0.011146576
#> 24  -0.0869217526 -0.0073069701 -0.007350733  0.085742453
#> 25  -0.1064453629 -0.0117219667 -0.025148574 -0.153250916
#> 26  -0.0932868238  0.0534298158  0.065142846  0.024712572
#> 27  -0.0980330233 -0.0206815371 -0.018407209  0.038394972
#> 28  -0.1036452889 -0.0450202449  0.044079818  0.005829242
#> 29  -0.1022586028 -0.0267497965  0.057791656  0.047800348
#> 30  -0.1082662331  0.0288433780 -0.014586072 -0.061427297
#> 31  -0.1022853047  0.0430893785  0.015986938 -0.027337597
#> 32  -0.0875395035 -0.0361849054  0.057646113  0.136078728
#> 33  -0.1249791972 -0.1531770786 -0.010066038 -0.130045793
#> 34  -0.1169129535 -0.1836789964  0.017619469 -0.027352078
#> 35  -0.1008444422  0.0393026999  0.036291563  0.016464749
#> 36  -0.1055203356  0.0176022268  0.048049532  0.095821620
#> 37  -0.0977460115 -0.0564991653  0.103271968  0.111394405
#> 38  -0.1207916644 -0.0505836854 -0.004142455 -0.077439180
#> 39  -0.1161222082  0.0772198492 -0.041189367 -0.005524618
#> 40  -0.1036994653 -0.0229631179  0.037487030  0.003998001
#> 41  -0.1092801213 -0.0377238980 -0.007437333  0.060691714
#> 42  -0.0888073715  0.1996226835  0.043529498  0.164440117
#> 43  -0.1220489602  0.0409167217 -0.065169588 -0.037783077
#> 44  -0.0938890947 -0.0403381986 -0.065986933  0.100465059
#> 45  -0.1021389050 -0.0975500093 -0.052949932 -0.085687106
#> 46  -0.0989216563  0.0607261627  0.013625695  0.079575044
#> 47  -0.1139762794 -0.0956882576 -0.012195139 -0.086360793
#> 48  -0.1144371654  0.0329867105 -0.029725517 -0.027704013
#> 49  -0.1065544885 -0.0852289357  0.038682496 -0.008468747
#> 50  -0.1053303317 -0.0007871062  0.032615968  0.028008637
#> 51   0.0526586881 -0.0737005873  0.145909396  0.019761239
#> 52   0.0349536459 -0.0507819874  0.020060649  0.002781831
#> 53   0.0593115438 -0.0526337785  0.118078347  0.005345903
#> 54   0.0194753038  0.1498316767  0.004923799  0.037310732
#> 55   0.0514013923  0.0177998198  0.084882263  0.059417342
#> 56   0.0185769784  0.0506683081 -0.026469588 -0.136623859
#> 57   0.0356797497 -0.0660183061 -0.031750621 -0.043891963
#> 58  -0.0232911731  0.1582033316 -0.053127198 -0.022987157
#> 59   0.0443482642 -0.0027522095  0.127064665 -0.016950735
#> 60   0.0005461049  0.0883084471 -0.114858419 -0.016146060
#> 61  -0.0052667368  0.2266662541  0.009972690  0.007806478
#> 62   0.0210625660  0.0054056103 -0.043708445  0.022763570
#> 63   0.0268654851  0.1507130709  0.163212825  0.025943335
#> 64   0.0343908442  0.0159041732  0.014633637 -0.093495303
#> 65  -0.0015941595  0.0374922694 -0.041547057  0.061863332
#> 66   0.0418393370 -0.0434756799  0.107315989  0.059534688
#> 67   0.0167399785  0.0167656461 -0.104622322 -0.108643470
#> 68   0.0075901902  0.0676474939  0.064374748 -0.116465628
#> 69   0.0585523010  0.1385447768  0.102795955  0.128153185
#> 70   0.0078821098  0.1112469683  0.036837818 -0.029344698
#> 71   0.0352569104 -0.0338684718 -0.131403446 -0.047247173
#> 72   0.0227637384  0.0356404784  0.056470641  0.064427405
#> 73   0.0589864852  0.0797089836  0.078521616 -0.005641540
#> 74   0.0302469157  0.0355608348  0.062213361 -0.155565391
#> 75   0.0335830895  0.0054155709  0.095064047  0.024653955
#> 76   0.0417851606 -0.0214185528  0.100723201  0.057703448
#> 77   0.0600537772  0.0065979096  0.154982313  0.022515340
#> 78   0.0649238094 -0.0282950706  0.055591320  0.037911633
#> 79   0.0317735642  0.0192949569 -0.018300615 -0.020672361
#> 80  -0.0019241258  0.0904179288  0.068112319  0.036754391
#> 81   0.0062512434  0.1334229800  0.031966756 -0.005334061
#> 82   0.0011209012  0.1342944135  0.051483289 -0.018591843
#> 83   0.0115441149  0.0663801654  0.032228588  0.013417442
#> 84   0.0507141081  0.0541322276 -0.022445561 -0.104365504
#> 85   0.0107048737  0.0245767726 -0.141788119 -0.144564410
#> 86   0.0205103365 -0.0722154109 -0.096045974 -0.062218849
#> 87   0.0501230591 -0.0445848827  0.084356003  0.021108717
#> 88   0.0499224830  0.1181116322  0.146700084  0.077626985
#> 89   0.0033259142  0.0187462824 -0.062145801 -0.083475281
#> 90   0.0135485518  0.1135285492 -0.019056421  0.005052273
#> 91   0.0133382833  0.0956539957 -0.020138632 -0.153544122
#> 92   0.0298507783 -0.0021285059  0.004365253 -0.083782656
#> 93   0.0160841808  0.0844128445  0.042496972  0.003704795
#> 94  -0.0173102447  0.1724493321 -0.022554188  0.011102543
#> 95   0.0137927321  0.0730820891 -0.027897197 -0.060929469
#> 96   0.0043665043  0.0154743834 -0.027489822 -0.130456346
#> 97   0.0108835326  0.0328733983 -0.033294519 -0.075227458
#> 98   0.0275479846  0.0132266974  0.057898249 -0.011266985
#> 99  -0.0213958618  0.1318447464 -0.040581137  0.113429843
#> 100  0.0122702186  0.0511438467 -0.019582682 -0.033256352
#> 101  0.0881595893 -0.0743367465 -0.214286328 -0.027939433
#> 102  0.0553399601  0.0596857075 -0.112995779 -0.022987468
#> 103  0.1053988377 -0.0479974810  0.043248148  0.033575257
#> 104  0.0688307676  0.0040128894 -0.034875332 -0.133752619
#> 105  0.0892704855 -0.0251977657 -0.084322325 -0.009246027
#> 106  0.1315234294 -0.0683574897  0.124110556 -0.057515529
#> 107  0.0175412961  0.1333573099 -0.210341675 -0.075521296
#> 108  0.1100431214 -0.0358749356  0.138901570 -0.135041056
#> 109  0.0959078612  0.0607591222  0.083973252 -0.049077575
#> 110  0.1080041231 -0.1640603917 -0.084732296  0.059475232
#> 111  0.0651995994 -0.0591636030 -0.060660846  0.061189334
#> 112  0.0765986545  0.0360145587 -0.004941839  0.033091599
#> 113  0.0900394207 -0.0358052527 -0.005613642  0.083061354
#> 114  0.0602261220  0.0992607340 -0.123671537  0.056252056
#> 115  0.0701448455  0.0377713992 -0.213959923  0.156381596
#> 116  0.0759963837 -0.0577534557 -0.136071618  0.108844086
#> 117  0.0703258066 -0.0218309163 -0.007977918 -0.088119032
#> 118  0.1159643160 -0.2183469966  0.027256038 -0.155331113
#> 119  0.1582318602 -0.0015185496  0.149899103  0.025635545
#> 120  0.0604006459  0.1457614800  0.057021524 -0.036977139
#> 121  0.0973909055 -0.0777568105 -0.050044030  0.095278929
#> 122  0.0467417517  0.0488304906 -0.176503041  0.015745775
#> 123  0.1384907715 -0.0353262612  0.182746756 -0.072238136
#> 124  0.0637206901  0.0411482094  0.001156975  0.079398977
#> 125  0.0812851201 -0.0865921500 -0.063610325 -0.034970557
#> 126  0.0934053712 -0.0860674097  0.089513520 -0.123863584
#> 127  0.0561630717  0.0270210935 -0.027694307  0.071151154
#> 128  0.0487954572 -0.0054953554 -0.071979154 -0.004909651
#> 129  0.0854726529  0.0160012432 -0.057686743  0.017636056
#> 130  0.0890714388 -0.0480214151  0.152526807 -0.118120689
#> 131  0.1164243223 -0.0221437147  0.155123226 -0.010167944
#> 132  0.1101620465 -0.2242963714  0.105176629 -0.120083860
#> 133  0.0890263052  0.0152486943 -0.075481550  0.056735715
#> 134  0.0532497371  0.0250165230  0.039107832 -0.105712982
#> 135  0.0574711817  0.0692889027  0.035108428 -0.277684505
#> 136  0.1337648367 -0.0731737275  0.115712475  0.167853641
#> 137  0.0753358013 -0.0912602228 -0.201594725  0.020199186
#> 138  0.0643448781 -0.0360769168 -0.038550928 -0.122208731
#> 139  0.0442012149 -0.0014709075 -0.088840326  0.002971755
#> 140  0.0885169072 -0.0577434950  0.002700873  0.110734472
#> 141  0.0962961390 -0.0524277845 -0.091292798  0.140428754
#> 142  0.0908941419 -0.0588919389 -0.027723560  0.266459419
#> 143  0.0553399601  0.0596857075 -0.112995779 -0.022987468
#> 144  0.0975267330 -0.0740890166 -0.072070383  0.025634706
#> 145  0.0954997292 -0.0896023456 -0.134789552  0.121428077
#> 146  0.0893991030 -0.0330481333 -0.054620974  0.220825832
#> 147  0.0747777843  0.0765799034  0.005620663  0.124915218
#> 148  0.0727030413 -0.0229793601 -0.038402352  0.067605916
#> 149  0.0656112167 -0.0863643414 -0.198939364  0.014822811
#> 150  0.0459137323  0.0020780018 -0.112588405 -0.092514345
#>