Robust subspace recovery by Tyler's M-estimator

2012/06/07 by Teng Zhang, Zhang, Teng
Engineering · Mathematics · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Computer science #Estimator #FOS: Computer and information sciences #Geometry #Machine Learning (stat.ML) #Mathematical analysis #Mathematics #Random subspace method #Regular polygon #Set (abstract data type) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics #Subspace topology #stat.ML

paper · pdf · doi:10.48550/arxiv.1206.1386

openalex publication_date 2012/06/07 · arxiv created 2021/04/29 · arxiv updated 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the problem of robust subspace recovery: given a set of N points in ℝ^D, if many lie in a d-dimensional subspace, then can we recover the underlying subspace? We show that Tyler's M-estimator can be used to recover the underlying subspace, if the percentage of the inliers is larger than d/D and the data points lie in general position. Empirically, Tyler's M-estimator compares favorably with other convex subspace recovery algorithms in both simulations and experiments on real data sets.

Citations

• A Distribution-Free M-Estimator of Multivariate Scatter
• A Tutorial on MM Algorithms
• Trace inequalities and quantum entropy: an introductory course
• Fundamentals of Differential Geometry
• Convex Functions and Their Applications

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• Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
• Algorithms and Hardness for Robust Subspace Recovery
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• Robust Subspace Recovery with Adversarial Outliers
• Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization