approxloads {cds}

Low Rank Approximation LL' of a Square Symmetrix Matrix R

Description

Uses the eigendecomposition of a square, symmetrix matrix R to obtain the loadings matrix L such that R is approximated by LL', with L restricted to have r columns. Hence LL' is a rank r approximation of R. The eigendecomposition of R is used to obtain L from the first r eigenvectors and eigenvalues. In case procr.target is not NULL, L is further rotated through orthogonal Procrustes analysis to match as closely as possible the matrix procr.target through orthprocr.

Usage

approxloads(R, r = 3, procr.target = NULL, refl.target = NULL)

Arguments

R

Square, symmetric matrix R to be approximated

r

The required rank of the approximation

procr.target

Optional; the target matrix for L in the orthogonal Procrustes analysis

refl.target

Optional; the matrix to check against for possible reflections of the loading vectors.

Examples

R <- rcormat(10, r = 3)
all.equal(R$L, approxloads(R$R, r = 3, procr.target = R$L))