Learning from signals defined over simplicity complexes
04 Pubblicazione in atti di convegno
Barbarossa S., Sardellitti S., Ceci E.
In the last years, several new tools have been devised to analyze signals defined over the vertices of a graph, i.e., over a discrete domain whose structure is described by pairwise relations. In this paper, we expand these tools to the analysis of signals defined on simplicial complexes, whose domain has a structure specified by various multi-way relations. Within this framework, we show how to filter signals and how to reconstruct edge and vertex signals from a subset of observations. Finally, we propose two alternative algorithms to infer the structure of the simplicial complex from the observations.