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CP Decomposition via Randomized (Sampled) ALS

Source: R/cp_variants.R
cp_arls.Rd

Alternating least squares in which each subproblem is solved from a uniform sample of tensor fibers rather than the full unfolding, in the spirit of the MATLAB Tensor Toolbox cp_arls. Unlike cp_arls, no FFT-based mixing is applied before sampling (a documented divergence); sampling is plain uniform with replacement.

Usage

cp_arls(
  X,
  R,
  tol = 1e-04,
  maxiters = 50L,
  nsamples = NULL,
  ridge = 1e-10,
  init = "random",
  printitn = 0L
)

Arguments

X

A Tensor or array-like object.

R

Target CP rank.

tol

Convergence tolerance on change in (exact) fit.

maxiters

Maximum number of sweeps (default 50).

nsamples

Number of sampled fibers per solve. Defaults to max(ceiling(10 * R * log2(R + 1)), 4 * R) capped at the full count.

ridge

Tikhonov regularizer added to the sampled normal equations (default 1e-10).

init

"random" or a list of initial factor matrices.

printitn

Print fit every printitn iterations.

Value

A KTensor.

Examples

set.seed(1)
X <- tensor(array(rnorm(60), dim = c(3, 4, 5)))
K <- cp_arls(X, R = 2, maxiters = 20)