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.

Learning from signals defined over simplicity complexes / Barbarossa, S.; Sardellitti, S.; Ceci, E.. - (2018), pp. 51-55. ((Intervento presentato al convegno 2018 IEEE Data Science Workshop, DSW 2018 tenutosi a Lausanne; Switzerland [10.1109/DSW.2018.8439885].

Learning from signals defined over simplicity complexes

Barbarossa S.;Sardellitti S.;Ceci E.
2018

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/1291223
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