mlsanityData to 7 Oct 2026

Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption

arXiv 2305.04080 ↗First posted 6 May 2023math.NA cs.LG cs.NAcited by 11

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Abstract (arXiv)

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse outlier component. This work proposes a fast algorithm, called Robust Tensor CUR Decompositions (RTCUR), for large-scale non-convex TRPCA problems under the Tucker rank setting. RTCUR is developed within a framework of alternating projections that projects between the set of low-rank tensors and the set of sparse tensors. We utilize the recently developed tensor CUR decomposition to substantially reduce the computational complexity in each projection. In addition, we develop four variants of RTCUR for different application settings. We demonstrate the effectiveness and computational advantages of RTCUR against state-of-the-art methods on both synthetic and real-world datasets.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 21 of its 63 references that are in the map. First posted on arXiv 6 May 2023.

Builds on

21 of 63 references.

References · 21

  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. 2017Introduction to Tensor Decompositions and their Applications in Machine Learningcited by 45
  4. 2014Non-convex Robust PCAcited by 41
  5. 2017Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimizationcited by 35
  6. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  7. 2013Tucker Tensor Regression and Neuroimaging Analysiscited by 26
  8. 2017Accelerated Alternating Projections for Robust Principal Component Analysiscited by 25
  9. 2021Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimizationcited by 24
  10. 2017Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entriescited by 23
  11. 2014Coauthorship and Citation Networks for Statisticianscited by 22
  12. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
9 more
  1. 2020Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimationcited by 16
  2. 2021Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositionscited by 13
  3. 2022Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completioncited by 11
  4. 2022Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descentcited by 11
  5. 2017Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decompositioncited by 8
  6. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8
  7. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7
  8. 2018Static and Dynamic Robust PCA and Matrix Completion: A Reviewcited by 6
  9. 2019Robust Tensor Recovery with Fiber Outliers for Traffic Eventscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 4; 2026: 1.

11 papers.

  1. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5
  2. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  3. 2024Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descentcited by 3
  4. 2024S3Attention: Improving Long Sequence Attention with Smoothed Skeleton Sketchingcited by 2
  5. 2024Robust Low-rank Tensor Train Recoverycited by 2
  6. 2025Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCAcited by 2
  7. 2024Variational Bayesian Inference for Tensor Robust Principal Component Analysiscited by 0
  8. 2025Robust Anomaly Detection via Tensor Pseudoskeleton Decompositioncited by 0
  9. 2025Property Inheritance for Subtensors in Tensor Train Decompositionscited by 0
  10. 2025Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentationcited by 0
  11. 2026Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Samplingcited by 0