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Higher-Order Singular Value Decomposition

Source: R/tucker_decomposition.R
hosvd.Rd

Computes the (truncated) higher-order SVD of a tensor, returning a Tucker representation whose factor matrices span the leading left singular spaces of the mode-n unfoldings. Mirrors the MATLAB Tensor Toolbox hosvd.

Usage

hosvd(
  X,
  ranks = NULL,
  tol = NULL,
  dimorder = NULL,
  sequential = TRUE,
  verbosity = 0L
)

Arguments

X

A Tensor or array-like object.

ranks

Optional integer vector of per-mode truncation ranks. Scalar inputs are replicated across modes.

tol

Relative truncation tolerance. Ignored when ranks is supplied. Per-mode truncation keeps enough singular vectors to ensure the dropped energy is below tol^2 / ndims(X) of fnorm(X)^2.

dimorder

Order in which modes are processed (matters only for sequential = TRUE).

sequential

Logical; if TRUE (default) the ST-HOSVD variant is used, progressively contracting the core, which is typically more accurate and cheaper than the classical HOSVD.

verbosity

Non-negative integer controlling diagnostic messages.

Value

A TTensor.

Examples

X <- tensor(array(runif(60), dim = c(3, 4, 5)))
T <- hosvd(X, ranks = c(2, 3, 4))