In this paper, a sparsity promoting adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. In addition, sparsity is also imposed by employing variable metric projections onto weighted balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme compared to other algorithms, which have been developed in the context of sparse adaptive learning.
Bibliographical noteFunding Information:
Manuscript received November 08, 2011; revised March 17, 2012 and May 28, 2012; accepted May 30, 2012. Date of publication June 15, 2012; date of current version September 11, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Huaiyu Dai. This work was supported by the European Union (European Social Fund—ESF) and by the Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund.
- Adaptive distributed learning
- Diffusion networks