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arXiv · 2602.09539

Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication

Susana Lopez-Moreno·June-Ho Lee·Taehyeong Kim
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Abstract

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.

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Susana Lopez-Moreno, June-Ho Lee, Taehyeong Kim. 2026-02-10. Tensor CUR Decomposition under the Linear-Map-Based Tensor-Tensor Multiplication. https://doi.org/10.1109/lsp.2026.3711540

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