Generalized CP Decomposition

Fits a CP model by minimizing the sum of an arbitrary elementwise loss f(x, m) between the data and the model with L-BFGS-B, mirroring the dense/deterministic mode of the MATLAB Tensor Toolbox gcp_opt.

Usage

gcp_opt(
  X,
  R,
  type = "gaussian",
  init = "random",
  maxiters = 500L,
  factr = 1e+07,
  printitn = 0L
)

Arguments

X

A Tensor or array-like object.

R

Target CP rank.

type

Loss name: one of "gaussian" (alias "normal"), "poisson" (alias "count"), "poisson-log", "bernoulli-odds", "bernoulli-logit", "rayleigh", "gamma", "huber". Alternatively a list with elements f(x, m), g(x, m) (the derivative in m), and lower (factor lower bound, -Inf if unconstrained) for a custom loss.

init

"random", "nvecs", or a list of initial factor matrices.

maxiters

Maximum optimizer iterations (default 500).

factr

optim L-BFGS-B factr convergence parameter.

printitn

If positive, print the optimizer trace.

Value

A list with elements K (the fitted KTensor) and objective (the final loss value).

References

Hong, D., Kolda, T. G., and Duersch, J. A. (2020). Generalized canonical polyadic tensor decomposition. SIAM Review 62(1).

Examples

set.seed(1)
X <- tensor(array(rpois(24, 3), dim = c(2, 3, 4)))
res <- gcp_opt(X, R = 2, type = "poisson", maxiters = 100)