Distributed dictionary learning via projections onto convex sets

Abstract

Abstract-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.

Potential Games for Distributed Constrained Consensus

“…In can be formulated in various ways, such as finding a common point of closed and convex sets, finding a common fixed-point of nonexpansive operators, finding a common minimum of convex functionals or solving a system of variational inequalities [17]. Likewise, the problem has found numerous and diverse applications, in particular in solving inverse image reconstruction problems [17], [18], in image restoration [19] but also in source localization [20] and node/network positioning problems [21], [22] and in distributed dictionary learning [23]. On the other hand, various centralized optimization algorithms have been studied for the solution of convex feasibility problems.…”