mlsanityData to 7 Oct 2026

On the Robustness of Cross-Concentrated Sampling for Matrix Completion

arXiv 2401.15566 ↗First posted 28 Jan 2024stat.ML cs.IT cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS model against sparse outliers remains unclear in the existing studies. In this paper, we aim to answer this question by exploring a novel Robust CCS Completion problem. A highly efficient non-convex iterative algorithm, dubbed Robust CUR Completion (RCURC), is proposed. The empirical performance of the proposed algorithm, in terms of both efficiency and robustness, is verified in synthetic and real datasets.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 14 of its 32 references that are in the map. First posted on arXiv 28 Jan 2024.

Builds on

14 of 32 references.

References · 14

  1. 2020Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descentcited by 70
  2. 2014Non-convex Robust PCAcited by 41
  3. 2016Fast Algorithms for Robust PCA via Gradient Descentcited by 39
  4. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  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. 2013Robust Spectral Compressed Sensing via Structured Matrix Completioncited by 13
  9. 2017Robust PCA by Manifold Optimizationcited by 13
  10. 2022Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Samplingcited by 12
  11. 2022Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completioncited by 11
  12. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
2 more
  1. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8
  2. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 1.

5 papers.

  1. 2024Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descentcited by 3
  2. 2024S3Attention: Improving Long Sequence Attention with Smoothed Skeleton Sketchingcited by 2
  3. 2024Structured Sampling for Robust Euclidean Distance Geometrycited by 2
  4. 2025Robust Anomaly Detection via Tensor Pseudoskeleton Decompositioncited by 0
  5. 2026Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Samplingcited by 0