Distributed dictionary learning for sparse representation in sensor networks

This paper develops a distributed dictionary learning algorithm for sparse representation of the data distributed across nodes of sensor networks, where the sensitive or private data are stored or there is no fusion center or there exists a big data application. The main contributions of this paper are: 1) we decouple the combined dictionary atom update and nonzero coefficient revision procedure into two-stage operations to facilitate distributed computations, first updating the dictionary atom in terms of the eigenvalue decomposition of the sum of the residual (correlation) matrices across the nodes then implementing a local projection operation to obtain the related representation coefficients for each node; 2) we cast the aforementioned atom update problem as a set of decentralized optimization subproblems with consensus constraints. Then, we simplify the multiplier update for the symmetry undirected graphs in sensor networks and minimize the separable subproblems to attain the consistent estimates iteratively; and 3) dictionary atoms are typically constrained to be of unit norm in order to avoid the scaling ambiguity. We efficiently solve the resultant hidden convex subproblems by determining the optimal Lagrange multiplier. Some experiments are given to show that the proposed algorithm is an alternative distributed dictionary learning approach, and is suitable for the sensor network environment.