Robust Adaptive Machine Learning Algorithms for Distributed Signal Processing

Distributed networks comprising a large number of nodes, e.g., Wireless Sensor Networks, Personal Computers (PC?s laptops, smart phones, etc., which cooperate with each other in order to reach a common goal, constitute a promising technology for several applications. Typical examples include: distributed environmental monitoring, acoustic source localization, power spectrum estimation, etc. Sophisticated cooperation mechanisms can significantly benefit the learning process, through which the nodes achieve their common objective. In this dissertation, the problem of adaptive learning in distributed networks is studied, focusing on the task of distributed estimation. A set of nodes sense information related to certain parameters and the estimation of these parameters constitutes the goal. Towards this direction, nodes exploit locally sensed measurements as well as information springing from interactions with other nodes of the network. Throughout this dissertation, the cooperation among the nodes follows the diffusion optimization rationale and the developed algorithms belong to the APSM algorithmic family. First, robust APSM?based techniques are proposed. The goal is to ?harmonize? the spatial information, received from the neighborhood, with the locally sensed one. This ?harmonization? is achieved by projecting the information of the neighborhood onto a convex set, constructed via the locally sensed measurements. Next, the scenario, in which a subset of the node set is malfunctioning and produces measurements heavily corrupted with noise, is considered. This problem is attacked by employing the Huber cost function, which is resilient to the presence of outliers. In the sequel, we study the issue of sparsity?aware adaptive distributed learning. The nodes of the network seek for an unknown sparse vector, which consists of a small number of non?zero coefficients. Weighted $\ell_1$?norm constraints are embedded, together with sparsity?promoting variable metric projections. Finally, we propose algorithms, which lead to a reduction of the communication demands, by forcing the estimates to lie within lower dimensional Krylov subspaces. The derived schemes serve a good trade-off between complexity/bandwidth demands and achieved performance.