## The Annals of Statistics

### Robust subspace clustering

#### 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.

#### Article information

Source
Ann. Statist., Volume 42, Number 2 (2014), 669-699.

Dates
First available in Project Euclid: 20 May 2014

https://projecteuclid.org/euclid.aos/1400592174

Digital Object Identifier
doi:10.1214/13-AOS1199

Mathematical Reviews number (MathSciNet)
MR3210983

Zentralblatt MATH identifier
1360.62353

Subjects
Primary: 62-07: Data analysis

#### Citation

Soltanolkotabi, Mahdi; Elhamifar, Ehsan; Candès, Emmanuel J. Robust subspace clustering. Ann. Statist. 42 (2014), no. 2, 669--699. doi:10.1214/13-AOS1199. https://projecteuclid.org/euclid.aos/1400592174

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