Subspace-orbit randomized algorithms for low rank approximations of third-order tensors in t-product format

This paper focuses on computing low rank approximations of third-order tensors in the t-product format using random techniques. Given a truncated term K, we derive randomized algorithms for approximating the K-term t-SVD, which is called as the subspace-orbit randomized t-SVD (sort-SVD). Additionall...

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Vydáno v:	Pattern recognition Ročník 170; s. 112066
Hlavní autoři:	Wang, Xuezhong, Wang, Kai, Mo, Changxin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.02.2026
Témata:	Deterministic error Probabilistic error Randomized t-SVD Subspace-orbit t-SVD t-SVD Tensor-tensor product t-SVD Randomized t-SVD Tensor-tensor product Probabilistic error Subspace-orbit t-SVD Deterministic error
ISSN:	0031-3203
On-line přístup:	Získat plný text
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Popis
Shrnutí:	This paper focuses on computing low rank approximations of third-order tensors in the t-product format using random techniques. Given a truncated term K, we derive randomized algorithms for approximating the K-term t-SVD, which is called as the subspace-orbit randomized t-SVD (sort-SVD). Additionally, we conduct an analysis of the deterministic and probabilistic error bounds of the proposed algorithm, subject to certain assumptions. We integrate the present algorithm with the power method to enhance the accuracy of the approximate the K-term t-SVD. Furthermore, we demonstrate the effectiveness of our algorithms through numerous numerical examples. Lastly, the proposed algorithms are employed to compress data tensors from various image databases.
ISSN:	0031-3203
DOI:	10.1016/j.patcog.2025.112066