# An Overview of Robust Subspace Recovery

arXiv: https://arxiv.org/abs/1803.01013 · HTML: https://mlsanity.com/paper/1803.01013/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

## Built on by (most cited first, 29 of 29)

- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion](https://mlsanity.com/paper/2404.11590/) (2024)
- [Probabilistic Robust Autoencoders for Outlier Detection](https://mlsanity.com/paper/2110.00494/) (2021)
- [Unveiling Multiple Descents in Unsupervised Autoencoders](https://mlsanity.com/paper/2406.11703/) (2024)
- [Robust Vector Quantized-Variational Autoencoder](https://mlsanity.com/paper/2202.01987/) (2022)
- [Stochastic and Private Nonconvex Outlier-Robust PCA](https://mlsanity.com/paper/2203.09276/) (2022)
- [A Riemannian ADMM](https://mlsanity.com/paper/2211.02163/) (2022)
- [Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator](https://mlsanity.com/paper/2403.18658/) (2024)
- [Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization](https://mlsanity.com/paper/2511.02329/) (2025)
- [SLA2P: Self-supervised Anomaly Detection with Adversarial Perturbation](https://mlsanity.com/paper/2111.12896/) (2021)
- [Nested subspace learning with flags](https://mlsanity.com/paper/2502.06022/) (2025)
- [Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery](https://mlsanity.com/paper/2512.16875/) (2025)
- [Low-Degree Method Fails to Predict Robust Subspace Recovery](https://mlsanity.com/paper/2603.02594/) (2026)
- [Decentralized Weakly Convex Optimization Over the Stiefel Manifold](https://mlsanity.com/paper/2303.17779/) (2023)
- [A Robust Autoencoder Ensemble-Based Approach for Anomaly Detection in Text](https://mlsanity.com/paper/2405.13031/) (2024)
- [Error-Robust Multi-View Clustering: Progress, Challenges and Opportunities](https://mlsanity.com/paper/2105.03058/) (2021)
- [Boosting RANSAC via Dual Principal Component Pursuit](https://mlsanity.com/paper/2110.02918/) (2021)
- [Implicit Bias of Projected Subgradient Method Gives Provable Robust Recovery of Subspaces of Unknown Codimension](https://mlsanity.com/paper/2201.09079/) (2022)
- [Local Linear Convergence of Gradient Methods for Subspace Optimization via Strict Complementarity](https://mlsanity.com/paper/2202.04020/) (2022)
- [A Combinatorial Approach to Robust PCA](https://mlsanity.com/paper/2311.16416/) (2023)
- [AdaContour: Adaptive Contour Descriptor with Hierarchical Representation](https://mlsanity.com/paper/2404.08292/) (2024)
- [RANSAC Revisited: An Improved Algorithm for Robust Subspace Recovery under Adversarial and Noisy Corruptions](https://mlsanity.com/paper/2504.09648/) (2025)
- [T-Rex: Fitting a Robust Factor Model via Expectation-Maximization](https://mlsanity.com/paper/2505.12117/) (2025)
- [Rethinking PCA Through Duality](https://mlsanity.com/paper/2510.18130/) (2025)
- [Unsupervised Feature Selection via Robust Autoencoder and Adaptive Graph Learning](https://mlsanity.com/paper/2512.18720/) (2025)
- [A Robust Optimization Approach to Sparse Principal Component Analysis](https://mlsanity.com/paper/2606.03553/) (2026)
- [The Sharp Phase Transition of Tyler's M-Estimator for Robust Subspace Recovery](https://mlsanity.com/paper/2606.06782/) (2026)

## 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.