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

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.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-02-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2602.09539
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• On the computation of tensor functions under tensor-tensor multiplications with linear maps

  2025cited by this paper
• Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representations

  2024cited by this paper
• Tensor BM‐Decomposition for Compression and Analysis of Video Data

  2023cited by this paper
• Tensor CUR Decomposition under T-Product and Its Perturbation

  2022cited by this paper
• Robust CUR Decomposition: Theory and Imaging Applications

  2021cited by this paper
• Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation

  2020cited by this paper
• Perturbations of CUR Decompositions

  2019cited by this paper
• SVD-Based Tensor-Completion Technique for Background Initialization

  2018cited by this paper
• Towards Benchmarking Scene Background Initialization

  2015cited by this paper
• Tensor-Tensor Products with Invertible Linear Transforms

  2015cited by this paper
• A New Selection Operator for the Discrete Empirical Interpolation Method - Improved A Priori Error Bound and Extensions

  2015cited by this paper
• CDnet 2014: An Expanded Change Detection Benchmark Dataset

  2014cited by this paper
• Factorization strategies for third-order tensors

  2011cited by this paper

• No citing papers are available for this paper.