A survey on sparse subspace clustering

Sparse subspace clustering (SSC) is a newly developed spectral clustering-based framework for data clustering. High-dimensional data usually lie in a union of several low-dimensional subspaces, which allows sparse representation of high-dimensional data with an appropriate dictionary. Sparse subspace clustering methods pursue a sparse representation of high-dimensional data and use it to build the affinity matrix. The subspace clustering result of the data is finally obtained by means of spectral clustering. The key to sparse subspace clustering is to design a good representation model which can reveal the real subspace structure of high-dimensional data. More importantly, the obtained representation coefficient and the affinity matrix are more beneficial to accurate subspace clustering. Sparse subspace clustering has been successfully applied to different research fields, including machine learning, computer vision, image processing, system identification and others, but there is still a vast space to develop. In this paper, the fundamental models, algorithms and applications of sparse subspace clustering are reviewed in detail. Limitations existing in available methods are analyzed. Problems for further research on sparse subspace clustering are discussed. Copyright © 2015 Acta Autornatica. All rights reserved.