Cloud K-SVD: A Collaborative Dictionary Learning Algorithm for Big, Distributed Data
This addresses the challenge of collaborative dictionary learning for geographically-distributed sites with massive local data, where privacy or volume concerns discourage raw data sharing, though it appears incremental as it builds on existing subspace-based methods.
The paper tackles the problem of learning data-adaptive representations for big, distributed data by proposing cloud K-SVD, a distributed algorithm that collaboratively learns a union of subspaces structure without exchanging raw data between sites, and it demonstrates efficacy on real and synthetic data.
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 previous works on subspace-based data representations, this paper focuses on the geometric structure of a union of subspaces (UoS). In this regard, it proposes a distributed algorithm---termed cloud K-SVD---for collaborative learning of a UoS structure underlying distributed data of interest. The goal of cloud K-SVD is to learn a common overcomplete dictionary at each individual site such that every sample in the distributed data can be represented through a small number of atoms of the learned dictionary. Cloud K-SVD accomplishes this goal without requiring exchange of individual samples between sites. This makes it suitable for applications where sharing of raw data is discouraged due to either privacy concerns or large volumes of data. This paper also provides an analysis of cloud K-SVD that gives insights into its properties as well as deviations of the dictionaries learned at individual sites from a centralized solution in terms of different measures of local/global data and topology of interconnections. Finally, the paper numerically illustrates the efficacy of cloud K-SVD on real and synthetic distributed data.