A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917577223045120 |
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| author | Zhang, Yuanwei Zhu, Ya-Nan Zhang, Xiaoqun |
| author_facet | Zhang, Yuanwei Zhu, Ya-Nan Zhang, Xiaoqun |
| contents | This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix tangent space projection in Riemannian gradient descent and sequentially truncated high-order singular value decomposition (ST-HOSVD), SM-QRGD achieves a much faster convergence speed than existing state-of-the-art algorithms. Theoretically, we establish the convergence of SM-QRGD through the Tensor Restricted Isometry Property (TRIP) and the geometry of the fixed-rank matrix manifold. Numerically, extensive experiments are conducted, affirming the accuracy and efficacy of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery Zhang, Yuanwei Zhu, Ya-Nan Zhang, Xiaoqun Optimization and Control This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix tangent space projection in Riemannian gradient descent and sequentially truncated high-order singular value decomposition (ST-HOSVD), SM-QRGD achieves a much faster convergence speed than existing state-of-the-art algorithms. Theoretically, we establish the convergence of SM-QRGD through the Tensor Restricted Isometry Property (TRIP) and the geometry of the fixed-rank matrix manifold. Numerically, extensive experiments are conducted, affirming the accuracy and efficacy of the proposed algorithm. |
| title | A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.15925 |