l_p-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

Details l_p-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers l_p-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

2010-12-18

arxiv.org/abs/1012.4116v2

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Machine Learning

This is a revised version of the part of 1002.1994 that deals with recovery of the best l0 subspace. Version 1 extended unifor

Scientific paper

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric outliers. We study the recovery of the global l0 subspace (i.e., with largest number of points) by minimizing the lp-averaged distances of data points from d-dimensional subspaces of R^D, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 01 and there is more than one underlying subspace, then with overwhelming probability the global l0 subspace cannot be recovered and the generalized one cannot even be nearly recovered.

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