Developing tools to analyze signals defined over a graph is a research area that is attracting a significant amount of contributions because of its many applications. However, a graph representation does not capture the overall information about the data, as it implicitly takes into account only pairwise relations. The goal of this paper is to extend signal processing tools to signals defined over hypergraphs, which represent a formal framework to describe multi-way relations among the data. First, we suggest alternative ways to introduce a Fourier Transform (FT) for signals defined over hypergraphs and, in particular, for simplicial complexes. Then, building on the notion of Fourier Transform, we derive a sampling theorem aimed at identifying the minimum number of samples necessary to encode all information about band-limited hypergraph signals.

An introduction to hypergraph signal processing / BARBAROSSA, Sergio; Tsitsvero, Mikhail. - ELETTRONICO. - 2016-May(2016), pp. 6425-6429. ((Intervento presentato al convegno 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 tenutosi a Shanghai; China [10.1109/ICASSP.2016.7472914].

An introduction to hypergraph signal processing

BARBAROSSA, Sergio;
2016

Abstract

Developing tools to analyze signals defined over a graph is a research area that is attracting a significant amount of contributions because of its many applications. However, a graph representation does not capture the overall information about the data, as it implicitly takes into account only pairwise relations. The goal of this paper is to extend signal processing tools to signals defined over hypergraphs, which represent a formal framework to describe multi-way relations among the data. First, we suggest alternative ways to introduce a Fourier Transform (FT) for signals defined over hypergraphs and, in particular, for simplicial complexes. Then, building on the notion of Fourier Transform, we derive a sampling theorem aimed at identifying the minimum number of samples necessary to encode all information about band-limited hypergraph signals.
9781479999880
File allegati a questo prodotto
File Dimensione Formato  
Barbarossa_Hypergraph-signal-processing_2016.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 224.21 kB
Formato Adobe PDF
224.21 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/958760
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 23
social impact