Distributed Adaptive Learning of Graph Signals

Over the last few years, there was a surge of interest in the development of processing tools for the analysis of signals defined over a graph, or graph signals for short, in view of the many potential applications spanning from sensor networks, social media, vehicular networks, big data or biological networks [1]-[3]. Graph signal processing (GSP) considers signals defined over a discrete domain having a very general structure, represented by a graph, and subsumes classical discrete-time signal processing as a very simple case. Several processing methods for signals defined over a graph were proposed in [2], [4]-[6], and one of the most interesting aspects is that these analysis tools come to depend on the graph topology. A fundamental role in GSP is of course played by spectral analysis, which passes through the definition of the Graph Fourier Transform (GFT). Two main approaches for GFT have been proposed in the literature, based on the projection of the signal onto the eigenvectors of either the graph Laplacian, see, e.g., [1], [7], [8], or of the adjacency matrix, see, e.g.