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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

Abstract

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.

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Mahdi Soltanolkotabi. Ehsan Elhamifar. Emmanuel J. Candès. "Robust subspace clustering." Ann. Statist. 42 (2) 669 - 699, April 2014. https://doi.org/10.1214/13-AOS1199

Information

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

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

Subjects:
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

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Vol.42 • No. 2 • April 2014
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