Distributed Adaptive Learning of Graph Signals

TL;DR

This paper introduces distributed adaptive algorithms for reconstructing and tracking bandlimited signals over graphs using limited samples, with theoretical guarantees and strategies for sampling set selection.

Contribution

It proposes novel distributed adaptive learning methods for graph signals, including sampling strategies and performance analysis, advancing the field of graph signal processing.

Findings

The methods guarantee mean-square error performance.

Sampling strategy significantly affects reconstruction accuracy.

Numerical results validate theoretical analysis and effectiveness.

Abstract

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.