Corso breve Roma 2018: Programma didattico
From graph theory to signal processing on graphs
Relatore:Prof. Sergio Barbarossa Università degli Studi di Roma “La Sapienza”.
Abstract:
Network science has emerged as a major catalyst for understanding the behavior of complex systems. In such systems, the
interactionamong simple constituents is what gives rise to a complex behavior. The set of all the interactions can be described by a
graph, whichcan be associated to either a real network, like a telecommunication network or a smart grid or the set of links in the
world wide web(www) or in a social network, or it can be just an abstract representation of similarities of elements in a set. In many
machinelearning algorithms, graph representations are the basic tools for unsupervised and semi-supervised learning. In this short
course, wereview the basic tools of algebraic graph theory. We introduce the concept of signal defined over a graph and the
fundamental toolsfor analyzing signals on graphs, like the Graph Fourier Transform, sampling theory and graph filters. Then, we
tackle the problem ofinferring the topology of a graph from data. Finally, we enlarge the perspective by generalizing graph
representations to morecomplex structures, like simplicial complexes and hypergraphs. Finally, we show a number of applications,
from the inference of the brain functionality map from electrocorticography (ECoG) seizure data, the reconstruction of the
electromagnetic field map from sparse measurements to the analysis of vehicular network and data traffic over the Internet.