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

2023/01/14 by Chen, Zhuo-Ran, Vong, Seak-Weng, Xie, Ze-Jia
#15A69 #65F99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2301.05937

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.

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