ROBUST RECOVERY OF MULTIPLE SUBSPACES BY GEOMETRIC lp MINIMIZATION

• 成果类型: Article
• 署名作者: Lerman, Gilad; Zhang, Teng
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS914
• 发表日期: 2011
• 页码: 2686-2715
• 关键词: segmentation

摘要

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 < p <= 1, 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.