approxloads: Low Rank Approximation LL' of a Square Symmetrix Matrix R

In cds: Constrained Dual Scaling for Detecting Response Styles

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))

cds documentation built on April 16, 2025, 1:10 a.m.