  State-of-the-art algorithms for sparse subspace clustering perform spectral
clustering on a similarity matrix typically obtained by representing each data
point as a sparse combination of other points using either basis pursuit (BP)
or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in
practice while the performance of OMP-based schemes are unsatisfactory,
especially in settings where data points are highly similar. In this paper, we
propose a novel algorithm that exploits an accelerated variant of orthogonal
least-squares to efficiently find the underlying subspaces. We show that under
certain conditions the proposed algorithm returns a subspace-preserving
solution. Simulation results illustrate that the proposed method compares
favorably with BP-based method in terms of running time while being
significantly more accurate than OMP-based schemes.
