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 unlabeled input data points that are assumed to lie in a union of lowdimensional subspaces. We show that a modified version of SSC is 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.
Reference REF considers the problem of subspace clustering under noise.
Noisy Sparse Subspace Clustering
ICML
Mathematics Computer Science