Robust subspace clustering

Mahdi Soltanolkotabi, Ehsan Elhamifar, Emmanuel J. Candès

The Annals of Statistics · 2014 · Volume 42 · Issue 2

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.

Keywords

$\ell_{1}$ minimization, 62-07, Dantzig selector, geometric functional analysis, Lasso, multiple hypothesis testing, nonasymptotic random matrix theory, spectral clustering, Subspace clustering, true and false discoveries

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