  In this paper we present deterministic conditions for success of sparse
subspace clustering (SSC) under missing data, when data is assumed to come from
a Union of Subspaces (UoS) model. We consider two algorithms, which are
variants of SSC with entry-wise zero-filling that differ in terms of the
optimization problems used to find affinity matrix for spectral clustering. For
both the algorithms, we provide deterministic conditions for any pattern of
missing data such that perfect clustering can be achieved. We provide extensive
sets of simulation results for clustering as well as completion of data at
missing entries, under the UoS model. Our experimental results indicate that in
contrast to the full data case, accurate clustering does not imply accurate
subspace identification and completion, indicating the natural order of
relative hardness of these problems.
