Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917263504834560 |
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| author | Lopez-Moreno, Susana Lee, June-Ho Kim, Taehyeong |
| author_facet | Lopez-Moreno, Susana Lee, June-Ho Kim, Taehyeong |
| contents | The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends the notion of matrix multiplication to higher order tensors, and which is a generalization of the T-product. Under this framework, we introduce the tensor CUR decomposition, show its performance in video foreground-background separation for different linear maps and compare it to a robust matrix CUR decomposition, another tensor approximation and the slice-based singular value decomposition (SS-SVD). We also provide a theoretical analysis of our tensor CUR decomposition, extending classical matrix results to establish exactness conditions and perturbation bounds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_09539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication Lopez-Moreno, Susana Lee, June-Ho Kim, Taehyeong Numerical Analysis 15A69, 94A08 The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends the notion of matrix multiplication to higher order tensors, and which is a generalization of the T-product. Under this framework, we introduce the tensor CUR decomposition, show its performance in video foreground-background separation for different linear maps and compare it to a robust matrix CUR decomposition, another tensor approximation and the slice-based singular value decomposition (SS-SVD). We also provide a theoretical analysis of our tensor CUR decomposition, extending classical matrix results to establish exactness conditions and perturbation bounds. |
| title | Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication |
| topic | Numerical Analysis 15A69, 94A08 |
| url | https://arxiv.org/abs/2602.09539 |