Noisy Sparse Subspace Clustering

This paper considers the problem of subspace clustering {\em under noise}. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabeled input data points that are assumed to lie 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 previous guarantees of this algorithm in the noiseless case to the practical setting and provides justification to the success of SSC in a class of real applications.