robustbase: classPC – R documentation

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classPC

Compute Classical Principal Components via SVD or Eigen

Description

Compute classical principal components (PC) via SVD (svd or eigenvalue decomposition (eigen) with non-trivial rank determination.

Usage

classPC(x, scale = FALSE, center = TRUE, signflip = TRUE,
        via.svd = n > p, scores = FALSE)

Arguments

`x`	a numeric `matrix`.
`scale`	logical indicating if the matrix should be scaled; it is mean centered in any case (via `scale(*, scale=scale)`c
`center`	logical or numeric vector for “centering” the matrix.
`signflip`	logical indicating if the sign(.) of the loadings should be determined should flipped such that the absolutely largest value is always positive.
`via.svd`	logical indicating if the computation is via SVD or Eigen decomposition; the latter makes sense typically only for n <= p.
`scores`	logical indicating

Value

a list with components

`rank`	the (numerical) matrix rank of `x`; an integer number, say k, from `0:min(dim(x))`. In the n > p case, it is `rankMM(x)`.
`eigenvalues`	the k eigenvalues, in the n > p case, proportional to the variances.
`loadings`	the loadings, a p k* matrix.
`scores`	if the `scores` argument was true, the n k* matrix of scores, where k is the `rank` above.
`center`	a numeric p-vector of means, unless the `center` argument was false.
`scale`	if the `scale` argument was not false, the `scale` used, a p-vector.

Author(s)

Valentin Todorov; efficiency tweaks by Martin Maechler

Examples

set.seed(17)
x <- matrix(rnorm(120), 10, 12) # n < p {the unusual case}
pcx  <- classPC(x)
(k <- pcx$rank) # = 9  [after centering!]
pc2  <- classPC(x, scores=TRUE)
pcS  <- classPC(x, via.svd=TRUE)
all.equal(pcx, pcS, tol = 1e-8)
## TRUE: eigen() & svd() based PC are close here
pc0 <- classPC(x, center=FALSE, scale=TRUE)
pc0$rank # = 10  here *no* centering (as E[.] = 0)

## Loadings are orthnormal:
zapsmall( crossprod( pcx$loadings ) )

## PC Scores are roughly orthogonal:
S.S <- crossprod(pc2$scores)
print.table(signif(zapsmall(S.S), 3), zero.print=".")
stopifnot(all.equal(pcx$eigenvalues, diag(S.S)/k))

## the usual n > p case :
pc.x <- classPC(t(x))
pc.x$rank # = 10, full rank in the n > p case

cpc1 <- classPC(cbind(1:3)) # 1-D matrix
stopifnot(cpc1$rank == 1,
          all.equal(cpc1$eigenvalues, 1),
          all.equal(cpc1$loadings, 1))

robustbase

Basic Robust Statistics

v0.93-7

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian)

Initial release

2021-01-04