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.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). This chapter surveys recent work on kernel-based inference
of functions over graphs including arXiv:1612.03615 and arXiv:1605.07174 and
arXiv:1711.0930
