| sparse.svd {InspectChangepoint} | R Documentation |
Computing the sparse leading left singular vector of a matrix
Description
Estimating the sparse left leading singular vector by first computing a maximiser Mhat of the convex problem
<Z, M> - \lambda |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), max.iter = 1000, tolerance = 1e-05)
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. |
max.iter |
maximum iteration for ADMM, only used if schatten=1 |
tolerance |
tolerance level for convergence checking, only used if schatten=1 |
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)