mlsanityData to 7 Oct 2026

Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection

arXiv 2110.05649 ↗First posted 11 Oct 2021cs.LG cs.CV cs.ITcited by 34

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Abstract (arXiv)

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for high-dimensional RPCA problems, which we call Learned Robust PCA (LRPCA). LRPCA is highly efficient, and its free parameters can be effectively learned to optimize via deep unfolding. Moreover, we extend deep unfolding from finite iterations to infinite iterations via a novel feedforward-recurrent-mixed neural network model. We establish the recovery guarantee of LRPCA under mild assumptions for RPCA. Numerical experiments show that LRPCA outperforms the state-of-the-art RPCA algorithms, such as ScaledGD and AltProj, on both synthetic datasets and real-world applications.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). Builds on 20 of its 49 references that are in the map. First posted on arXiv 11 Oct 2021.

Builds on

20 of 49 references.

References · 20

  1. 2016Learning to learn by gradient descent by gradient descentcited by 616
  2. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 411
  3. 2017Learned Primal-dual Reconstructioncited by 251
  4. 2017Learned Optimizers that Scale and Generalizecited by 109
  5. 2018Understanding and correcting pathologies in the training of learned optimizerscited by 97
  6. 2018Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholdscited by 83
  7. 2020Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descentcited by 70
  8. 2017Learned D-AMP: Principled Neural Network based Compressive Image Recoverycited by 65
  9. 2018Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasoundcited by 43
  10. 2014Non-convex Robust PCAcited by 41
  11. 2016Fast Algorithms for Robust PCA via Gradient Descentcited by 39
  12. 2020Training Stronger Baselines for Learning to Optimizecited by 31
8 more
  1. 2016Maximal Sparsity with Deep Networks?cited by 29
  2. 2017Accelerated Alternating Projections for Robust Principal Component Analysiscited by 25
  3. 2021Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimizationcited by 24
  4. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
  5. 2020Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimationcited by 16
  6. 2016Nearly-optimal Robust Matrix Completioncited by 13
  7. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8
  8. 2020A Deep-Unfolded Reference-Based RPCA Network For Video Foreground-Background Separationcited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 8; 2023: 5; 2024: 8; 2025: 7; 2026: 5.

34 papers.

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  1. 2022ADBench: Anomaly Detection Benchmarkcited by 230
  2. 2023LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuningcited by 92
  3. 2023RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detectioncited by 43
  4. 2021Hyperparameter Tuning is All You Need for LISTAcited by 22
  5. 2023Towards Constituting Mathematical Structures for Learning to Optimizecited by 13
  6. 2022Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descentcited by 11
  7. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  8. 2025RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentationcited by 11
  9. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7
  10. 2022Deep Unfolded Tensor Robust PCA with Self-supervised Learningcited by 7
  11. 2025Deep Unfolding: Recent Developments, Theory, and Design Guidelinescited by 7
  12. 2022LR-CSNet: Low-Rank Deep Unfolding Network for Image Compressive Sensingcited by 6
22 more
  1. 2024Specularity Factorization for Low-Light Enhancementcited by 6
  2. 2022A Comprehensive Review of Trends, Applications and Challenges In Out-of-Distribution Detectioncited by 5
  3. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5
  4. 2024Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recoverycited by 4
  5. 2025Efficient Over-parameterized Matrix Sensing from Noisy Measurements via Alternating Preconditioned Gradient Descentcited by 4
  6. 2024Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architecturescited by 3
  7. 2024Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descentcited by 3
  8. 2023Deep Unrolling for Nonconvex Robust Principal Component Analysiscited by 2
  9. 2024Structured Sampling for Robust Euclidean Distance Geometrycited by 2
  10. 2025Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCAcited by 2
  11. 2022Working memory inspired hierarchical video decomposition with transformative representationscited by 1
  12. 2025FedRPCA: Enhancing Federated LoRA Aggregation Using Robust PCAcited by 1
  13. 2022A Deep-Unfolded Spatiotemporal RPCA Network For L+S Decompositioncited by 0
  14. 2024Generative Principal Component Regression via Variational Inferencecited by 0
  15. 2024Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrollingcited by 0
  16. 2025Nuclear Diffusion Models for Low-Rank Background Suppression in Videoscited by 0
  17. 2025Factor Decorrelation Enhanced Data Removal from Deep Predictive Modelscited by 0
  18. 2026Robust Principal Component Completioncited by 0
  19. 2026Mean-Shift PCA by Knockoff Meancited by 0
  20. 2026Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filtercited by 0
  21. 2026LCPNet: Latent Consistent Proximal Unfolding Network for Infrared Small Target Detectioncited by 0
  22. 2026Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Samplingcited by 0