An Overview of Robust Subspace Recovery

Abstract

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.

31 pages, 5 figures, 3 tables

References in corpus (8)

• Optimal Algorithms for $L_1$-subspace Signal Processing
• Regularized $M$-estimators of scatter matrix
• Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms
• Static and Dynamic Robust PCA and Matrix Completion: A Review
• Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling
• Reliable Eigenspectra for New Generation Surveys
• Robust PCA in High-dimension: A Deterministic Approach
• RANSAC Algorithms for Subspace Recovery and Subspace Clustering

Cited by in corpus (31)

• Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
• Static and Dynamic Robust PCA and Matrix Completion: A Review
• TDOA-based localization with NLOS mitigation via robust model transformation and neurodynamic optimization
• Parseval Proximal Neural Networks
• From Symmetry to Geometry: Tractable Nonconvex Problems
• Structured and Unstructured Outlier Identification for Robust PCA: A Non iterative, Parameter free Algorithm
• Robust Subspace Recovery Layer for Unsupervised Anomaly Detection
• HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise
• Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods
• A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing
• A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
• Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications
• Robust Subspace Recovery with Adversarial Outliers
• A robust principal component analysis for outlier identification in messy microcalorimeter data
• SLA${}^2$P: Self-supervised Anomaly Detection with Adversarial Perturbation
• Spectrally Constrained Optimization
• Fast and Exact Outlier Detection in Metric Spaces: A Proximity Graph-based Approach
• Novelty Detection via Robust Variational Autoencoding
• Robust PCA via Regularized REAPER with a Matrix-Free Proximal Algorithm
• Dual Principal Component Pursuit: Probability Analysis and Efficient Algorithms
• Manifold Proximal Point Algorithms for Dual Principal Component Pursuit and Orthogonal Dictionary Learning
• Outlier Detection and Data Clustering via Innovation Search
• Fast, Parameter free Outlier Identification for Robust PCA
• The Virtual Goniometer: A new method for measuring angles on 3D models of fragmentary bone and lithics
• Geometrical and statistical properties of M-estimates of scatter on Grassmann manifolds
• Linear Convergence of a Proximal Alternating Minimization Method with Extrapolation for ${\ell }_1$-Norm Principal Component Analysis
• Boosting RANSAC via Dual Principal Component Pursuit
• Depth Descent Synchronization in $\mathrm{SO}(D)$
• Modal Principal Component Analysis
• Error-Robust Multi-View Clustering: Progress, Challenges and Opportunities
• On the Dynamical System of Principal Curves in ${\mathbb{R}}^d$