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
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ISSN:0031-3203
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Abstract 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.
AbstractList 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.
ArticleNumber 112066
Author Wang, Xuezhong
Wang, Kai
Mo, Changxin
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  surname: Wang
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  givenname: Kai
  surname: Wang
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  email: wangkai@fudan-js.org.cn
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  givenname: Changxin
  surname: Mo
  fullname: Mo, Changxin
  email: cxmo16@cqnu.edu.cn
  organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, People’s Republic of China
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Keywords t-SVD
Randomized t-SVD
Tensor-tensor product
Probabilistic error
Subspace-orbit t-SVD
Deterministic error
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Snippet 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...
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StartPage 112066
SubjectTerms Deterministic error
Probabilistic error
Randomized t-SVD
Subspace-orbit t-SVD
t-SVD
Tensor-tensor product
Title Subspace-orbit randomized algorithms for low rank approximations of third-order tensors in t-product format
URI https://dx.doi.org/10.1016/j.patcog.2025.112066
Volume 170
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