This paper focuses on the development of novel greedy techniques fordistributed learning under sparsity constraints. Greedy techniques have widelybeen used in centralized systems due to their low computational requirementsand at the same time their relatively good performance in estimating sparseparameter vectors/signals. The paper reports two new algorithms in the contextof sparsity--aware learning. In both cases, the goal is first to identify thesupport set of the unknown signal and then to estimate the non--zero valuesrestricted to the active support set. First, an iterative greedy multi--stepprocedure is developed, based on a neighborhood cooperation strategy, usingbatch processing on the observed data. Next, an extension of the algorithm tothe online setting, based on the diffusion LMS rationale for adaptivity, isderived. Theoretical analysis of the algorithms is provided, where it is shownthat the batch algorithm converges to the unknown vector if a RestrictedIsometry Property (RIP) holds. Moreover, the online version converges in themean to the solution vector under some general assumptions. Finally, theproposed schemes are tested against recently developed sparsity--promotingalgorithms and their enhanced performance is verified via simulation examples.
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