Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:1206.309

Distributed Adaptive Learning of Graph Signals

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

Adaptive diffusion schemes for heterogeneous networks

In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or step size. Although such heterogeneous networks have been considered from the first works on diffusion networks, obtaining practical and robust schemes to adaptively adjust the combiners in different scenarios is still an open problem. In this paper, we study a diffusion strategy specially designed and suited to heterogeneous networks. Our approach is based on two key ingredients: 1) the adaptation and combination phases are completely decoupled, so that network nodes keep purely local estimations at all times and 2) combiners are adapted to minimize estimates of the network mean-square-error. Our scheme is compared with the standard adapt-Then-combine scheme and theoretically analyzed using energy conservation arguments. Several experiments involving networks with heterogeneous nodes show that the proposed decoupled adapt-Then-combine approach with adaptive combiners outperforms other state-of-The-Art techniques, becoming a competitive approach in these scenarios