Noisy subspace clustering via thresholding


Reinhard Heckel and Helmut Bölcskei


Proc. of IEEE International Symposium on Information Theory (ISIT), Istanbul, Turkey, pp. 1382-1386, July 2013

DOI: 10.1109/ISIT.2013.6620453

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We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm introduced recently in [1] shows that TSC succeeds in the noisy case, even when the subspaces intersect. Our results reveal an explicit tradeoff between the allowed noise level and the affinity of the subspaces. We furthermore find that the simple outlier detection scheme introduced in [1] provably succeeds in the noisy case.

The version posted here corrects a minor error in the version published in the proceedings. Specifically, the exponent -c n_l in the success probability of Theorem 1 and in the corresponding proof outline has been corrected to -c(n_l-1).

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