mlsanityData to 7 Oct 2026

Riemannian CUR Decompositions for Robust Principal Component Analysis

arXiv 2206.09042 ↗First posted 17 Jun 2022stat.ML cs.LG cs.NAcited by 7

Not on the map. Why?

Abstract (arXiv)

Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper proposes a novel nonconvex Robust PCA algorithm, coined Riemannian CUR (RieCUR), which utilizes the ideas of Riemannian optimization and robust CUR decompositions. This algorithm has the same computational complexity as Iterated Robust CUR, which is currently state-of-the-art, but is more robust to outliers. RieCUR is also able to tolerate a significant amount of outliers, and is comparable to Accelerated Alternating Projections, which has high outlier tolerance but worse computational complexity than the proposed method. Thus, the proposed algorithm achieves state-of-the-art performance on Robust PCA both in terms of computational complexity and outlier tolerance.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 9 of its 28 references that are in the map. First posted on arXiv 17 Jun 2022.

Builds on

9 of 28 references.

References · 9

  1. 2014Non-convex Robust PCAcited by 41
  2. 2016Fast Algorithms for Robust PCA via Gradient Descentcited by 39
  3. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  4. 2017Accelerated Alternating Projections for Robust Principal Component Analysiscited by 25
  5. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
  6. 2016Guarantees of Riemannian Optimization for Low Rank Matrix Completioncited by 19
  7. 2020Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimationcited by 16
  8. 2022Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completioncited by 11
  9. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 5.

7 papers.

  1. 2022Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Samplingcited by 12
  2. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  3. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5
  4. 2024Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guaranteescited by 4
  5. 2024Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descentcited by 3
  6. 2024S3Attention: Improving Long Sequence Attention with Smoothed Skeleton Sketchingcited by 2
  7. 2024Structured Sampling for Robust Euclidean Distance Geometrycited by 2