Robust subspace recovery by Tyler’s M-estimator

Teng Zhang
Mar 28 2013 - 3:00pm
Event type: 
102A McDonnell Hall

We show that Tyler’s M-estimator has a nice property for robust subspace recovery (though it was mainly used for robust covariance estimation). Specifically, when inliers are sampled from a subspace and the percentage of inliers is larger than some threshold, then the underlying subspace can be exactly recovered by Tyler’s M-estimator. The main tools for the proof are the geodesic convexity of the objective function and the majorization-minimization property of the associated algorithm. Besides, we will also discuss the stability of Tyler’s M-estimator, and show similar convexity to other maximum-likelihood estimation of covariance matrix.