# Accelerated Alternating Projections for Robust Principal Component Analysis

arXiv: https://arxiv.org/abs/1711.05519 · HTML: https://mlsanity.com/paper/1711.05519/

## Key facts

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

## Built on by (most cited first, 25 of 25)

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- [Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions](https://mlsanity.com/paper/2103.11037/) (2021)
- [Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent](https://mlsanity.com/paper/2206.09109/) (2022)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition](https://mlsanity.com/paper/2108.10448/) (2021)
- [Riemannian CUR Decompositions for Robust Principal Component Analysis](https://mlsanity.com/paper/2206.09042/) (2022)
- [Robust Implementation of Foreground Extraction and Vessel Segmentation for X-ray Coronary Angiography Image Sequence](https://mlsanity.com/paper/2209.07237/) (2022)
- [On the Robustness of Cross-Concentrated Sampling for Matrix Completion](https://mlsanity.com/paper/2401.15566/) (2024)
- [Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guarantees](https://mlsanity.com/paper/2410.06376/) (2024)
- [Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery](https://mlsanity.com/paper/2410.16826/) (2024)
- [Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent](https://mlsanity.com/paper/2406.07409/) (2024)
- [rSVDdpd: A Robust Scalable Video Surveillance Background Modelling Algorithm](https://mlsanity.com/paper/2109.10680/) (2021)
- [Deep Unrolling for Nonconvex Robust Principal Component Analysis](https://mlsanity.com/paper/2307.05893/) (2023)
- [Structured Sampling for Robust Euclidean Distance Geometry](https://mlsanity.com/paper/2412.10664/) (2024)
- [Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functions](https://mlsanity.com/paper/2407.19446/) (2024)
- [A Dual Basis Approach for Structured Robust Euclidean Distance Geometry](https://mlsanity.com/paper/2505.18414/) (2025)
- [Robust Principal Component Analysis using Density Power Divergence](https://mlsanity.com/paper/2309.13531/) (2023)
- [Robust Anomaly Detection via Tensor Pseudoskeleton Decomposition](https://mlsanity.com/paper/2502.09926/) (2025)
- [RGNMR: A Gauss-Newton method for robust matrix completion with theoretical guarantees](https://mlsanity.com/paper/2505.12919/) (2025)
- [Mean-Shift PCA by Knockoff Mean](https://mlsanity.com/paper/2605.25460/) (2026)
- [Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling](https://mlsanity.com/paper/2608.03928/) (2026)

## 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.