ROBUST SUBSPACE CLUSTERING

• 成果类型: Article
• 署名作者: Soltanolkotabi, Mahdi; Elhamifar, Ehsan; Candes, Emmanuel J.
• 署名单位: Stanford University; University of California System; University of California Berkeley; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1199
• 发表日期: 2014
• 页码: 669-699
• 关键词: high-dimensional regression; switched arx systems; RECOVERY; segmentation; algorithm; graphs

摘要

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-2797] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its effectiveness.