mlsanityData to 14 Oct 2026

Accelerated Alternating Projections for Robust Principal Component Analysis

arXiv 1711.05519 ↗First posted 15 Nov 2017cs.IT cs.LG cs.NAcited by 25

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Abstract (arXiv)

We study robust PCA for the fully observed setting, which is about separating a low rank matrix boldsymbolL and a sparse matrix boldsymbolS from their sum boldsymbolD=boldsymbolL+boldsymbolS. In this paper, a new algorithm, dubbed accelerated alternating projections, is introduced for robust PCA which significantly improves the computational efficiency of the existing alternating projections proposed in [Netrapalli, Praneeth, et al., 2014] when updating the low rank factor. The acceleration is achieved by first projecting a matrix onto some low dimensional subspace before obtaining a new estimate of the low rank matrix via truncated SVD. Exact recovery guarantee has been established which shows linear convergence of the proposed algorithm. Empirical performance evaluations establish the advantage of our algorithm over other state-of-the-art algorithms for robust PCA.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Nov 2017.

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Citing papers per year: 2021: 7; 2022: 3; 2023: 3; 2024: 6; 2025: 4; 2026: 2.

25 papers.

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  1. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  2. 2025Time-o1: Time-Series Forecasting Needs Transformed Label Alignmentcited by 22
  3. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
  4. 2021abess: A Fast Best Subset Selection Library in Python and Rcited by 16
  5. 2021Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approachcited by 14
  6. 2021Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositionscited by 13
  7. 2022Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descentcited by 11
  8. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  9. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8
  10. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7
  11. 2022Robust Implementation of Foreground Extraction and Vessel Segmentation for X-ray Coronary Angiography Image Sequencecited by 5
  12. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5
13 more
  1. 2024Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guaranteescited by 4
  2. 2024Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recoverycited by 4
  3. 2024Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descentcited by 3
  4. 2021rSVDdpd: A Robust Scalable Video Surveillance Background Modelling Algorithmcited by 2
  5. 2023Deep Unrolling for Nonconvex Robust Principal Component Analysiscited by 2
  6. 2024Structured Sampling for Robust Euclidean Distance Geometrycited by 2
  7. 2024Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functionscited by 1
  8. 2025A Dual Basis Approach for Structured Robust Euclidean Distance Geometrycited by 1
  9. 2023Robust Principal Component Analysis using Density Power Divergencecited by 0
  10. 2025Robust Anomaly Detection via Tensor Pseudoskeleton Decompositioncited by 0
  11. 2025RGNMR: A Gauss-Newton method for robust matrix completion with theoretical guaranteescited by 0
  12. 2026Mean-Shift PCA by Knockoff Meancited by 0
  13. 2026Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Samplingcited by 0