An Overview of Robust Subspace Recovery
arXiv:1803.01013 · doi:10.1109/JPROC.2018.2853141
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.
arXiv comment31 pages, 5 figures, 3 tables
References in corpus (30)
- Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation
- Rank-Sparsity Incoherence for Matrix Decomposition
- A geometric analysis of subspace clustering with outliers
- Geometric median and robust estimation in Banach spaces
- Optimal Algorithms for -subspace Signal Processing
- Median K-flats for hybrid linear modeling with many outliers
- Hybrid Linear Modeling via Local Best-fit Flats
- Fast Algorithms for Robust PCA via Gradient Descent
- Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis
- Regularized -estimators of scatter matrix
- Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models
- Online Robust Subspace Tracking from Partial Information
- Two Proposals for Robust PCA using Semidefinite Programming
- Spectral clustering based on local linear approximations
- Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms
- Robust computation of linear models by convex relaxation
- Static and Dynamic Robust PCA and Matrix Completion: A Review
- Innovation Pursuit: A New Approach to Subspace Clustering
- Robust recovery of multiple subspaces by geometric l_p minimization
- Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling
- Fast, Robust and Non-convex Subspace Recovery
- Finding a sparse vector in a subspace: Linear sparsity using alternating directions
- A cautionary note on robust covariance plug-in methods
- A Well-Tempered Landscape for Non-convex Robust Subspace Recovery
- On the Complexity of Robust PCA and -norm Low-Rank Matrix Approximation
- Algorithms and Hardness for Robust Subspace Recovery
- Reliable Eigenspectra for New Generation Surveys
- Robust PCA in High-dimension: A Deterministic Approach
- lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers
- RANSAC Algorithms for Subspace Recovery and Subspace Clustering
Cited by in corpus (33)
- 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
- A Well-Tempered Landscape for Non-convex Robust Subspace Recovery
- 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 with Applications to Target Localization in Hyperspectral Imaging
- A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing
- 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
- SLAP: Self-supervised Anomaly Detection with Adversarial Perturbation
- Novelty Detection via Robust Variational Autoencoding
- Fast and Exact Outlier Detection in Metric Spaces: A Proximity Graph-based Approach
- Spectrally Constrained Optimization
- Robust PCA via Regularized REAPER with a Matrix-Free Proximal Algorithm
- Outlier Detection and Data Clustering via Innovation Search
- Manifold Proximal Point Algorithms for Dual Principal Component Pursuit and Orthogonal Dictionary Learning
- Dual Principal Component Pursuit: Probability Analysis and Efficient Algorithms
- Distributed Robust Subspace Recovery
- Geometrical and statistical properties of M-estimates of scatter on Grassmann manifolds
- The Virtual Goniometer: A new method for measuring angles on 3D models of fragmentary bone and lithics
- Fast, Parameter free Outlier Identification for Robust PCA
- Error-Robust Multi-View Clustering: Progress, Challenges and Opportunities
- Depth Descent Synchronization in
- Modal Principal Component Analysis
- Linear Convergence of a Proximal Alternating Minimization Method with Extrapolation for -Norm Principal Component Analysis
- Boosting RANSAC via Dual Principal Component Pursuit
- On the Dynamical System of Principal Curves in