On Deterministic Conditions for Subspace Clustering under Missing Data
This work addresses subspace clustering under missing data, which is incremental as it extends existing sparse subspace clustering methods to handle missing entries with theoretical guarantees.
The paper tackles the problem of subspace clustering with missing data by providing deterministic conditions for perfect clustering using two variants of sparse subspace clustering with entry-wise zero-filling, and shows through simulations that accurate clustering does not guarantee accurate subspace identification or data completion.
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.