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Cloud K-SVD: A Collaborative Dictionary Learning Algorithm for Big,
Distributed Data
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 with 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.

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