  This paper considers the problem of subspace clustering under noise.
Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when
either adversarial or random noise is added to the unlabelled input data
points, which are assumed to be in a union of low-dimensional subspaces. We
show that a modified version of SSC is \emph{provably effective} in correctly
identifying the underlying subspaces, even with noisy data. This extends
theoretical guarantee of this algorithm to more practical settings and provides
justification to the success of SSC in a class of real applications.
