Low-Rank Tensor Decomposition over Finite Fields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913317941936128 |
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| author | Yang, Jason |
| author_facet | Yang, Jason |
| contents | We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$, over a fixed finite field can be done in polynomial time. However, if some cells in the tensor are allowed to have arbitrary values, then rank-2 is NP-hard over the integers modulo 2. We also explore rank-1 decomposition of a 3D tensor and of a matrix where some cells are allowed to have arbitrary values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low-Rank Tensor Decomposition over Finite Fields Yang, Jason Computational Complexity We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$, over a fixed finite field can be done in polynomial time. However, if some cells in the tensor are allowed to have arbitrary values, then rank-2 is NP-hard over the integers modulo 2. We also explore rank-1 decomposition of a 3D tensor and of a matrix where some cells are allowed to have arbitrary values. |
| title | Low-Rank Tensor Decomposition over Finite Fields |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2401.06857 |