5 research outputs found
Noisy Subspace Clustering via Thresholding
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.Comment: Presented at the IEEE Int. Symp. Inf. Theory (ISIT) 2013, Istanbul,
Turkey. The version posted here corrects a minor error in the published
version. 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