Robust recovery of multiple subspaces by geometric l_p minimization
arXiv:1104.3770 · doi:10.1214/11-AOS914
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 , then all underlying subspaces can be precisely recovered by l_p minimization with overwhelming probability. On the other hand, if K>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.
Published in at http://dx.doi.org/10.1214/11-AOS914 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (3)
Cited by in corpus (13)
- A geometric analysis of subspace clustering with outliers
- Robust subspace clustering
- Hybrid Linear Modeling via Local Best-fit Flats
- Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis
- An Overview of Robust Subspace Recovery
- Robust computation of linear models by convex relaxation
- Randomized Robust Subspace Recovery for High Dimensional Data Matrices
- Fast, Robust and Non-convex Subspace Recovery
- A New Approach To Two-View Motion Segmentation Using Global Dimension Minimization
- lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers
- Closed-Form, Provable, and Robust PCA via Leverage Statistics and Innovation Search
- Low Rank Matrix Recovery with Simultaneous Presence of Outliers and Sparse Corruption
- Inference and Mixture Modeling with the Elliptical Gamma Distribution