Subspace clustering via thresholding and spectral clustering

Authors

Reinhard Heckel and Helmut Bölcskei

Reference

Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, pp. 3263-3267, May 2013.

DOI: 10.1109/ICASSP.2013.6638261

[BibTeX, LaTeX, and HTML Reference]

Abstract

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data points followed by spectral clustering. A probabilistic performance analysis shows that this algorithm succeeds even when the subspaces intersect, and when the dimensions of the subspaces scale (up to a log-factor) linearly in the ambient dimension. Moreover, we prove that the algorithm also succeeds for data points that are subject to erasures with the number of erasures scaling (up to a log-factor) linearly in the ambient dimension. Finally, we propose a simple scheme that provably detects outliers.

Comments

Relative to the version published in the proceedings, the version posted here corrects "direct sum" to "set sum" in footnote 1.

Download this document:

 

Copyright Notice: © 2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.