A tensor SVD-like decomposition based on the semi-tensor product of tensors

TL;DR

This paper introduces a new tensor decomposition method based on semi-tensor product, enabling data compression and generalizing tensor SVD, with numerical results demonstrating its advantages.

Contribution

It proposes a novel tensor decomposition strategy using semi-tensor product, extending tensor SVD and facilitating data compression.

Findings

Effective data compression achieved

Numerical comparisons show advantages over existing methods

Generalizes tensor SVD with semi-tensor product

Abstract

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the tensor SVD based on semi-tensor product. Due to the characteristic of semi-tensor product for compressing the data scale, we can therefore achieve data compression in this way. Numerical comparisons are given to show the advantages of this decomposition.