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

Subspace Clustering via Thresholding and Spectral Clustering