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.
@article{arxiv.2301.05937,
title = {A tensor SVD-like decomposition based on the semi-tensor product of tensors},
author = {Zhuo-Ran Chen and Seak-Weng Vong and Ze-Jia Xie},
journal= {arXiv preprint arXiv:2301.05937},
year = {2023}
}