mlsanityData to 7 Oct 2026

An Overview of Robust Subspace Recovery

arXiv 1803.01013 ↗First posted 2 Mar 2018cs.LG stat.MLcited by 29

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Abstract (arXiv)

This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due to its underlying nonconvexity. This work emphasizes advantages and disadvantages of proposed approaches and unsolved problems in the area.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Mar 2018.

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Cited by year (2026 to 7 Oct)

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

29 papers.

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  1. 2024Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributionscited by 53
  2. 2022ARCS: Accurate Rotation and Correspondence Searchcited by 15
  3. 2026Advances in Global Solvers for 3D Visioncited by 12
  4. 2021Probabilistic Robust Autoencoders for Outlier Detectioncited by 7
  5. 2024A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motioncited by 7
  6. 2022Robust Vector Quantized-Variational Autoencodercited by 4
  7. 2022Stochastic and Private Nonconvex Outlier-Robust PCAcited by 4
  8. 2024Theoretical Guarantees for the Subspace-Constrained Tyler's Estimatorcited by 3
  9. 2024Unveiling Multiple Descents in Unsupervised Autoencoderscited by 3
  10. 2025Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronizationcited by 3
  11. 2021SLA2P: Self-supervised Anomaly Detection with Adversarial Perturbationcited by 2
  12. 2022A Riemannian ADMMcited by 2
17 more
  1. 2025Nested subspace learning with flagscited by 2
  2. 2025Learning Confidence Ellipsoids and Applications to Robust Subspace Recoverycited by 2
  3. 2023Decentralized Weakly Convex Optimization Over the Stiefel Manifoldcited by 1
  4. 2024A Robust Autoencoder Ensemble-Based Approach for Anomaly Detection in Textcited by 1
  5. 2021Error-Robust Multi-View Clustering: Progress, Challenges and Opportunitiescited by 0
  6. 2021Boosting RANSAC via Dual Principal Component Pursuitcited by 0
  7. 2022Implicit Bias of Projected Subgradient Method Gives Provable Robust Recovery of Subspaces of Unknown Codimensioncited by 0
  8. 2022Local Linear Convergence of Gradient Methods for Subspace Optimization via Strict Complementaritycited by 0
  9. 2023A Combinatorial Approach to Robust PCAcited by 0
  10. 2024AdaContour: Adaptive Contour Descriptor with Hierarchical Representationcited by 0
  11. 2025RANSAC Revisited: An Improved Algorithm for Robust Subspace Recovery under Adversarial and Noisy Corruptionscited by 0
  12. 2025T-Rex: Fitting a Robust Factor Model via Expectation-Maximizationcited by 0
  13. 2025Rethinking PCA Through Dualitycited by 0
  14. 2025Unsupervised Feature Selection via Robust Autoencoder and Adaptive Graph Learningcited by 0
  15. 2026Low-Degree Method Fails to Predict Robust Subspace Recoverycited by 0
  16. 2026A Robust Optimization Approach to Sparse Principal Component Analysiscited by 0
  17. 2026The Sharp Phase Transition of Tyler's M-Estimator for Robust Subspace Recoverycited by 0