Robust subspace recovery by Tyler's M-estimator

TL;DR

This paper demonstrates that Tyler's M-estimator can robustly recover a subspace from high-dimensional data with inliers, outperforming other methods in simulations and real data, under certain inlier percentage conditions.

Contribution

The paper introduces Tyler's M-estimator as a robust tool for subspace recovery, establishing theoretical guarantees and empirical performance advantages.

Findings

Tyler's M-estimator successfully recovers the subspace when inliers exceed a threshold.

The method performs favorably compared to convex algorithms in simulations.

Empirical results on real datasets validate the approach.

Abstract

This paper considers the problem of robust subspace recovery: given a set of $N$ points in $\mathbb{R}^D$, 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.