tensorregress (version 5.1)

hosvd: (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(tnsr, ranks = NULL)

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 tnsr after compression

fnorm_resid

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

Arguments

tnsr

Tensor with K modes

ranks

a vector of desired modes in the output core tensor, default is tnsr@modes

Details

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

References

L. Lathauwer, B.Moor, J. Vandewalle, "A multilinear singular value decomposition". Journal of Matrix Analysis and Applications 2000, Vol. 21, No. 4, pp. 1253–1278.

See Also

tucker

Examples

tnsr <- rand_tensor(c(6,7,8))
hosvdD <-hosvd(tnsr)
hosvdD$fnorm_resid
hosvdD2 <-hosvd(tnsr,ranks=c(3,3,4))
hosvdD2$fnorm_resid