Learning from signals defined over simplicity complexes

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.