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

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 character...

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Bibliographic Details
Published inarXiv.org
Main Authors Chen, Zhuo-Ran, Seak-Weng Vong, Ze-Jia Xie
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.01.2023
Subjects
Algorithms
Data compression
Decomposition
Mathematical analysis
Tensors
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Summary: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.
ISSN:2331-8422