Kernel-based Inference of Functions over Graphs

TL;DR

This paper introduces a flexible kernel-based framework for inferring functions over network nodes, unifying and extending existing graph signal reconstruction methods in both static and dynamic scenarios.

Contribution

It proposes a novel kernel-based approach that generalizes recent graph signal reconstruction techniques, applicable to static and dynamic network settings.

Findings

Effective in static and dynamic network inference

Outperforms state-of-the-art methods in numerical tests

Provides a versatile modeling framework

Abstract

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.