Multitask Diffusion Adaptation over Networks

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. The stability and convergence of the algorithm in the mean and in the mean-square sense is analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to spectral sensing, target localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio

Adaptive regularized diffusion adaptation over multitask networks

The focus of this paper is on multitask learning over adaptive networks where different clusters of nodes have different objectives. We propose an adaptive regularized diffusion strategy using Gaussian kernel regularization to enable the agents to learn about the objectives of their neighbors and to ignore misleading information. In this way, the nodes will be able to meet their objectives more accurately and improve the performance of the network. Simulation results are provided to illustrate the performance of the proposed adaptive regularization procedure in comparison with other implementations

Adaptation and learning over networks for nonlinear system modeling

In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.Comment: To be published as a chapter in `Adaptive Learning Methods for Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C. Principe (2018

A Multitask Diffusion Strategy with Optimized Inter-Cluster Cooperation

We consider a multitask estimation problem where nodes in a network are divided into several connected clusters, with each cluster performing a least-mean-squares estimation of a different random parameter vector. Inspired by the adapt-then-combine diffusion strategy, we propose a multitask diffusion strategy whose mean stability can be ensured whenever individual nodes are stable in the mean, regardless of the inter-cluster cooperation weights. In addition, the proposed strategy is able to achieve an asymptotically unbiased estimation, when the parameters have same mean. We also develop an inter-cluster cooperation weights selection scheme that allows each node in the network to locally optimize its inter-cluster cooperation weights. Numerical results demonstrate that our approach leads to a lower average steady-state network mean-square deviation, compared with using weights selected by various other commonly adopted methods in the literature.Comment: 30 pages, 8 figures, submitted to IEEE Journal of Selected Topics in Signal Processin

Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of $\ell_1$-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy

Diffusion LMS for clustered multitask networks

Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that there are multiple parameter vectors that need to be inferred simultaneously. In this paper, we employ diffusion strategies to develop distributed algorithms that address clustered multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. Some results on the mean-square stability and convergence of the algorithm are also provided. Simulations are conducted to illustrate the theoretical findings.Comment: 5 pages, 6 figures, submitted to ICASSP 201

Distributed Unmixing of Hyperspectral Data With Sparsity Constraint

Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L 1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.Comment: 6 pages, conference pape