sparse.svd: Computing the sparse leading left singular vector of a matrix

In Tveten/capacc: Collective and point anomalies in cross-correlated data

Description

Estimating the sparse left leading singular vector by first computing a maximiser Mhat of the convex problem

<Z, M> - λ |M|_1

subject to the Schatten norm constraint |M|_schatten <= 1 using alternating direction method of multipliers (ADMM). Then the leading left singular vector of Mhat is returned.

Usage

sparse.svd(Z, lambda, schatten = c(1, 2), tolerance = 1e-05, max.iter = 10000)

Arguments

Z	Input matrix whose left leading singular vector is to be estimated.
lambda	Regularisation parameter
schatten	Schatten norm constraint to be used. Default uses Schatten-2-norm, i.e. the Frobenius norm. Also possible to use Schatten-1-norm, the nuclear norm.
tolerance	Tolerance criterion for convergence of the ADMM algorithm. Not used when shatten=2.
max.iter	Maximum number of iteration in the ADMM algorithm. Not used when shatten=2.

Details

In case of schatten = 2, a closed-form solution for Mhat using matrix soft thresholding is possible. We use the closed-form solution instead of the ADMM algorithm to speed up the computation.

Value

A vector that has the same length as nrow(Z) is returned.

Examples

Z <- matrix(rnorm(20),4,5)
lambda <- 0.5
sparse.svd(Z, lambda)

Tveten/capacc documentation built on Sept. 29, 2021, 5:31 a.m.