Robust recovery of multiple subspaces by geometric l_p minimization

By Gilad Lerman, Teng Zhang. 2011

86 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0a829bbc820dd21ce3145f7ab0f38c9e270795db

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Citations in the corpus

Robust Subspace Clustering (2013, background): “The work in [30] formulates the robust subspace clustering problem as a nonconvex geometric minimization problem over the Grassmanian.”
Robust Computation of Linear Models by Convex Relaxation (2012, methodology): “LAD has also been considered as a method for hybrid linear modeling in [48,81].”
A Geometric Analysis of Subspace Clustering with Outliers (2011, background): “(9)The result of [25] is a bit more general in that the points on each subspace can be sampled from a single distribution obeying certain regularity conditions, other than the uniform measure.”