Some Tucker-like approximations based on the modal semi-tensor product

TL;DR

This paper introduces novel Tucker-like tensor approximation methods based on the modal semi-tensor product, including new SVD and HOSVD algorithms, with theoretical analysis and numerical validation.

Contribution

It presents new Tucker-like tensor decompositions utilizing the modal semi-tensor product, along with algorithms and theoretical insights.

Findings

New SVD and HOSVD algorithms derived

Numerical examples validate theoretical results

Applicable in various fields like signal processing and chemometrics

Abstract

Approximating higher-order tensors by the Tucker format has been applied in many fields such as psychometrics, chemometrics, signal processing, pattern classification, and so on. In this paper, we propose some new Tucker-like approximations based on the modal semi-tensor product (STP), especially, a new singular value decomposition (SVD) and a new higher-order SVD (HOSVD) are derived. Algorithms for computing new decompositions are provided. We also give some numerical examples to illustrate our theoretical results.