  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.
