Robust recovery of multiple subspaces by geometric l_p minimization

Gilad Lerman; Teng Zhang

doi:10.1214/11-aos914

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arXiv · 1104.3770

Robust recovery of multiple subspaces by geometric l_p minimization

Gilad Lerman·Teng Zhang

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Abstract

We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l_p-averaged distances of the sampled data points from any K subspaces. Under some conditions, we show that if $0 1 and p>1, then the underlying subspaces cannot be recovered or even nearly recovered by l_p minimization. The results of this paper partially explain the successes and failures of the basic approach of l_p energy minimization for modeling data by multiple subspaces.

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Gilad Lerman, Teng Zhang. 2011-04-19. Robust recovery of multiple subspaces by geometric l_p minimization. https://doi.org/10.1214/11-aos914

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