mlsanityData to 7 Oct 2026

Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition

arXiv 2108.10448 ↗First posted 23 Aug 2021cs.LG cs.CV eess.IVcited by 8

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Abstract (arXiv)

We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm, coined Robust Tensor CUR (RTCUR), for large-scale TRPCA problems. RTCUR considers a framework of alternating projections and utilizes the recently developed tensor Fiber CUR decomposition to dramatically lower the computational complexity. The performance advantage of RTCUR is empirically verified against the state-of-the-arts on the synthetic datasets and is further demonstrated on the real-world application such as color video background subtraction.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 10 of its 35 references that are in the map. First posted on arXiv 23 Aug 2021.

Builds on

10 of 35 references.

References · 10

  1. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 110
  2. 2014Novel methods for multilinear data completion and de-noising based on tensor-SVDcited by 56
  3. 2014Non-convex Robust PCAcited by 41
  4. 2013Robust Low-rank Tensor Recovery: Models and Algorithmscited by 33
  5. 2017Accelerated Alternating Projections for Robust Principal Component Analysiscited by 25
  6. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
  7. 2020Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimationcited by 16
  8. 2021Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositionscited by 13
  9. 2019Robust Tensor Recovery with Fiber Outliers for Traffic Eventscited by 6
  10. 2015Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbationscited by 5

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 3; 2023: 1; 2024: 2; 2025: 1.

8 papers.

  1. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  2. 2022Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Samplingcited by 12
  3. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  4. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7
  5. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5
  6. 2022Error Analysis of Tensor-Train Cross Approximationcited by 1
  7. 2024Hyperspectral Band Selection based on Generalized 3DTV and Tensor CUR Decompositioncited by 0
  8. 2025Property Inheritance for Subtensors in Tensor Train Decompositionscited by 0