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

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          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 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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          Most cited references23

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          Consensus and Cooperation in Networked Multi-Agent Systems

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            Atomic Decomposition by Basis Pursuit

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              $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

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                Author and article information

                Journal
                2014-12-25
                2015-08-17
                Article
                1412.7839
                e2a17a45-9036-4d24-a75b-d8b45dc2df27

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Accepted for Publication in IEEE Trans. Signal Processing (2015); 16 pages, 3 figures
                cs.LG cs.IT math.IT stat.ML

                Numerical methods,Information systems & theory,Machine learning,Artificial intelligence

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