Abstract
This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast to some of the previous works on subspace representations, this paper focuses on the geometric structure of a union of subspaces (UoS). Specifically, it proposes a distributed algorithm, termed as cloud K-SVD, for learning a UoS structure underlying distributed data of interest. Cloud K-SVD accomplishes the goal of collaborative data-adaptive representations without requiring communication of individual data samples between different sites. The paper also provides a partial analysis of cloud K-SVD that gives insights into its convergence properties and deviations from a centralized solution in terms of properties of local data and topology of interconnections. Finally, it numerically illustrates the efficacy of cloud K-SVD.