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 |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Xuezhong surname: Wang fullname: Wang, Xuezhong email: xuezhongwang77@126.com organization: School of Mathematics, Hexi University, Zhangye, 734000, People’s Republic of China – sequence: 2 givenname: Kai surname: Wang fullname: Wang, Kai email: wangkai@fudan-js.org.cn organization: Jiashan Fudan Institute, Jiaxing, 314100, People’s Republic of China – sequence: 3 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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| Cites_doi | 10.1016/j.patcog.2023.110207 10.1016/j.laa.2010.09.020 10.1137/19M1261043 10.1016/j.laa.2010.05.025 10.1109/TSP.2018.2853137 10.1007/s10444-025-10232-0 10.1137/090771806 10.1137/090752286 10.1137/110841229 10.1109/34.927464 10.1007/BF02310791 10.1137/110837711 10.1007/s10589-020-00167-1 10.1137/23M1594066 10.1137/17M1159932 10.1137/130938700 10.1137/19M1237016 10.1137/07070111X 10.1002/nla.2179 10.1016/j.patcog.2023.109545 10.1137/S0895479896305696 10.1016/j.laa.2019.12.035 10.1016/j.patcog.2022.109169 10.1016/j.patcog.2011.03.021 10.1007/s10915-022-01956-y 10.1109/CVPR.2016.567 10.1137/080736417 10.1137/090764189 10.1007/s10444-018-9622-8 10.1145/2842602 10.1007/s10444-020-09816-9 10.1007/s42967-019-00055-4 10.1016/j.aml.2024.109198 10.1007/s10915-023-02411-2 |
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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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| 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 |
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