Open Access
Translator Disclaimer
April 2014 Robust subspace clustering
Mahdi Soltanolkotabi, Ehsan Elhamifar, Emmanuel J. Candès
Ann. Statist. 42(2): 669-699 (April 2014). DOI: 10.1214/13-AOS1199


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.


Download Citation

Mahdi Soltanolkotabi. Ehsan Elhamifar. Emmanuel J. Candès. "Robust subspace clustering." Ann. Statist. 42 (2) 669 - 699, April 2014.


Published: April 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1360.62353
MathSciNet: MR3210983
Digital Object Identifier: 10.1214/13-AOS1199

Primary: 62-07

Keywords: $\ell_{1}$ minimization , Dantzig selector , geometric functional analysis , Lasso , multiple hypothesis testing , nonasymptotic random matrix theory , spectral clustering , Subspace clustering , true and false discoveries

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 2 • April 2014
Back to Top