Robust subspace recovery by Tyler's M-estimator
This addresses robust subspace estimation for data analysis, but it is incremental as it applies an existing estimator to a known problem.
The paper tackles robust subspace recovery by showing that Tyler's M-estimator can recover a d-dimensional subspace from N points in R^D when the inlier percentage exceeds d/D and points are in general position, with empirical results favoring it over other convex algorithms in simulations and real data.
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.