On deterministic conditions for subspace clustering under missing data
This work addresses subspace clustering under missing data, which is an incremental contribution to the field of machine learning and data analysis.
The paper tackles the problem of subspace clustering with missing data by analyzing deterministic conditions for perfect clustering under a Union of Subspaces model, showing that accurate clustering does not guarantee accurate subspace identification and completion in missing data cases.
In this paper we present deterministic analysis of sufficient conditions for sparse subspace clustering under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. In this context we consider two cases, namely Case I when all the points are sampled at the same co-ordinates, and Case II when points are sampled at different locations. We show that results for Case I directly follow from several existing results in the literature, while results for Case II are not as straightforward and we provide a set of dual conditions under which, perfect clustering holds true. We provide extensive set of simulation results for clustering as well as completion of data under 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.