Subspace clustering via thresholding and spectral clustering


Reinhard Heckel and Helmut Bölcskei


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

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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.

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

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