hosvd: (Truncated-)Higher-order SVD

In rikenbit/DelayedTensor: R package for sparse and out-of-core arithmetic and decomposition of Tensor

(Truncated-)Higher-order SVD

Description

Higher-order SVD of a K-Tensor. Write the K-Tensor as a (m-mode) product of a core Tensor (possibly smaller modes) and K orthogonal factor matrices. Truncations can be specified via ranks (making them smaller than the original modes of the K-Tensor will result in a truncation). For the mathematical details on HOSVD, consult Lathauwer et. al. (2000).

Usage

hosvd(darr, ranks=NULL)

## S4 method for signature 'DelayedArray'
hosvd(darr, ranks)

Arguments

darr	Tensor with K modes
ranks	a vector of desired modes in the output core tensor, default is darr@modes

Details

This function is an extension of the hosvd by DelayedArray.

A progress bar is included to help monitor operations on large tensors.

Value

a list containing the following:

Z

core tensor with modes speficied by ranks

U

a list of orthogonal matrices, one for each mode

est

estimate of darr after compression

fnorm_resid

the Frobenius norm of the error fnorm(est-darr) - if there was no truncation, then this is on the order of mach_eps * fnorm.

Note

The length of ranks must match darr@num_modes.

References

L. Lathauwer, B.Moor, J. Vanderwalle "A multilinear singular value decomposition". Journal of Matrix Analysis and Applications 2000.

See Also

tucker

Examples

library("DelayedRandomArray")
darr <- RandomUnifArray(c(3,4,5))
hosvd(darr, ranks=c(2,1,3))

rikenbit/DelayedTensor documentation built on Jan. 30, 2023, 6:15 p.m.