Principal Components Analysis (PR#8320)
Please do RTFM: ?princomp says
Note:
The signs of the columns of the loadings and scores are arbitrary,
and so may differ between different programs for PCA, and even
between different builds of R.
and ?prcomp has a similar comment. Equally, the signs of eigenvectors are
arbitrary, and ?eigen says
Recall that the eigenvectors are only defined up to a
constant: even when the length is specified they are still
only defined up to a scalar of modulus one (the sign for real
matrices).
If you don't know why these are true, please ask your advisors for help.
On Thu, 17 Nov 2005 sarkar at mail.utexas.edu wrote:
Full_Name: Sahotra Sarkar Version: 2.2.0 OS: Windows XP Professional Submission from: (NULL) (146.6.130.180) The following two commands should give the same results for the eigenvectors but do not (there is a sign reversal for the first one):
summary(princomp(bumpus),loading = TRUE)
Importance of components:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
Standard deviation 6.2801653 2.4285636 1.13995042 0.560733747 0.03458915
Proportion of Variance 0.8399662 0.1256084 0.02767525 0.006696272 0.00002548
Cumulative Proportion 0.8399662 0.9655746 0.99324988 0.999946156 0.99997164
Comp.6 Comp.7 Comp.8 Comp.9
Standard deviation 3.025628e-02 1.405339e-02 1.147326e-02 9.339938e-03
Proportion of Variance 1.949623e-05 4.206121e-06 2.803451e-06 1.857837e-06
Cumulative Proportion 9.999911e-01 9.999953e-01 9.999981e-01 1.000000e+00
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
V1 0.497 0.851 0.171
V2 0.853 -0.515
V3 0.149 0.103 -0.965 0.189
V4 -0.180 -0.981
V5 -0.288 0.568 0.327 0.693
V6 -0.399 0.565 0.154 -0.705
V7 -0.867 -0.475 -0.107
V8 0.352 -0.926 0.118
V9 0.994
eigen(cov(bumpus))
$values
[1] 3.973263e+01 5.941610e+00 1.309113e+00 3.167514e-01 1.205271e-03
9.222233e-04
[7] 1.989606e-04 1.326107e-04 8.788062e-05
$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.496897319 0.8505093640 0.171388489 0.018744742 -0.0002708851
[2,] -0.852790441 -0.5152155401 0.081515933 0.025301353 0.0031275939
[3,] -0.149011771 0.1032588064 -0.965116017 0.188813583 0.0029039523
[4,] -0.059981091 0.0228574697 -0.180065518 -0.981007482 0.0301789269
[5,] -0.002474454 -0.0009781164 -0.003402721 -0.011404980 -0.2884751568
[6,] -0.002255070 -0.0003234929 -0.002776659 -0.014386855 -0.3990284747
[7,] -0.003505091 -0.0005603692 -0.006526439 -0.022328724 -0.8671382015
[8,] -0.001124313 0.0005858447 -0.003031985 -0.006957916 -0.0674635788
[9,] -0.003810707 0.0004531193 -0.006127501 -0.009908937 -0.0122192249
[,6] [,7] [,8] [,9]
[1,] -0.001028476 1.638253e-06 0.0004887328 -0.0003561342
[2,] -0.002350593 -8.313864e-04 -0.0003929312 0.0005026715
[3,] -0.004636198 8.031165e-05 0.0015963693 0.0010649875
[4,] -0.011239114 -5.568762e-03 0.0035062479 0.0003785351
[5,] 0.083901242 5.675807e-01 0.3265320650 -0.6934139460
[6,] 0.032231827 5.646388e-01 0.1541661011 0.7049350072
[7,] -0.058318858 -4.748060e-01 -0.1070487286 -0.0849487969
[8,] 0.014813290 3.516922e-01 -0.9260185177 -0.1182046449
[9,] 0.994055719 -9.937481e-02 -0.0249932592 0.0324567705
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Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595