6 research outputs found
Neighborhood Selection for Thresholding-based Subspace Clustering
Subspace clustering refers to the problem of clustering high-dimensional data
points into a union of low-dimensional linear subspaces, where the number of
subspaces, their dimensions and orientations are all unknown. In this paper, we
propose a variation of the recently introduced thresholding-based subspace
clustering (TSC) algorithm, which applies spectral clustering to an adjacency
matrix constructed from the nearest neighbors of each data point with respect
to the spherical distance measure. The new element resides in an individual and
data-driven choice of the number of nearest neighbors. Previous performance
results for TSC, as well as for other subspace clustering algorithms based on
spectral clustering, come in terms of an intermediate performance measure,
which does not address the clustering error directly. Our main analytical
contribution is a performance analysis of the modified TSC algorithm (as well
as the original TSC algorithm) in terms of the clustering error directly.Comment: ICASSP 201
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