Subspace clustering refers to the task of finding a multi-subspace
representation that best fits a collection of points taken from a
high-dimensional space. This paper introduces an algorithm inspired by sparse
subspace clustering (SSC) to cluster noisy data, and develops some novel
theory
demonstrating its correctness. In particular, the theory uses idea from
geometric functional analysis to show that the algorithm can accurately
recover
the underlying subspaces under minimal requirements on the orientation of the
subspaces, and on the number of samples per subspace. Synthetic as well as
real
data experiments complement our theoretical study, illustrating our approach
and
demonstrating its effectiveness.