Low-Rank Tensor Recovery via Theta Nuclear p-Norm
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917982881447936 |
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| author | Röhrich, Felix Zhou, Yuhuai |
| author_facet | Röhrich, Felix Zhou, Yuhuai |
| contents | We investigate the low-rank tensor recovery problem using a relaxation of the nuclear p-norm by theta bodies.
We provide algebraic descriptions of the norms and compute their Gröbner bases.
Moreover, we develop geometric properties of these bodies.
Finally, our numerical results suggest that for
$n\times\cdots\times n$ tensors,
$m\geq O(n)$ measurements should be sufficient to recover low-rank tensors via theta body relaxation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-Rank Tensor Recovery via Theta Nuclear p-Norm Röhrich, Felix Zhou, Yuhuai Optimization and Control Algebraic Geometry 13A50, 13P10, 14L30, 14P05, 15A29, 15A69, 52A41, 60G15, 90C22, 94A20 We investigate the low-rank tensor recovery problem using a relaxation of the nuclear p-norm by theta bodies. We provide algebraic descriptions of the norms and compute their Gröbner bases. Moreover, we develop geometric properties of these bodies. Finally, our numerical results suggest that for $n\times\cdots\times n$ tensors, $m\geq O(n)$ measurements should be sufficient to recover low-rank tensors via theta body relaxation. |
| title | Low-Rank Tensor Recovery via Theta Nuclear p-Norm |
| topic | Optimization and Control Algebraic Geometry 13A50, 13P10, 14L30, 14P05, 15A29, 15A69, 52A41, 60G15, 90C22, 94A20 |
| url | https://arxiv.org/abs/2504.08911 |