Distributed dictionary learning via projections onto convex sets
We study a problem in which the nodes of a network, each with different data, are interested in computing a common dictionary that is suitable for the efficient sparse coding of all their data. To this end, distributed processing is employed, that is, the nodes merge local and neighboring information. We formulate this as a convex feasibility problem, and propose a suitable distributed algorithm for obtaining a solution that employs projections onto convex sets. A fast method for computing the involved projection operations is also given. The proposed approach allows the associated convex sets to be updated at every iteration of the algorithm, thus resulting into a faster agreement of the nodes in a common dictionary. Simulation results are provided that demonstrate the effectiveness of the proposed scheme in computing a common dictionary, in a scenario where the data of the nodes are significantly different and a second scenario, in which the nodes have the same data.