This paper is part of a line of research devoted to developing a compositional and geometric theory of Group Equivariant Non-Expansive Operators (GENEOs) for Geometric Deep Learning. It has two objectives. The first objective is to generalize the notions of permutants and permutant measures, originally defined for the identity of a single “perception pair”, to a map between two such pairs. The second and main objective is to extend the application domain of the whole theory, which arose in the set-theoretical and topological environments, to graphs. This is performed using classical methods of mathematical definitions and arguments. The theoretical outcome is that, both in the case of vertex-weighted and edge-weighted graphs, a coherent theory is developed. Several simple examples show what may be hoped from GENEOs and permutants in graph theory and how they can be built. Rather than being a competitor to other methods in Geometric Deep Learning, this theory is proposed as an approach that can be integrated with such methods

Generalized Permutants and Graph GENEOs / Ahmad F.; Ferri M.; Frosini P.. - In: MACHINE LEARNING AND KNOWLEDGE EXTRACTION. - ISSN 2504-4990. - ELETTRONICO. - 5:4(2023), pp. 1905-1920. [10.3390/make5040092]

Generalized Permutants and Graph GENEOs

Ahmad F.;Frosini P.
2023

Abstract

This paper is part of a line of research devoted to developing a compositional and geometric theory of Group Equivariant Non-Expansive Operators (GENEOs) for Geometric Deep Learning. It has two objectives. The first objective is to generalize the notions of permutants and permutant measures, originally defined for the identity of a single “perception pair”, to a map between two such pairs. The second and main objective is to extend the application domain of the whole theory, which arose in the set-theoretical and topological environments, to graphs. This is performed using classical methods of mathematical definitions and arguments. The theoretical outcome is that, both in the case of vertex-weighted and edge-weighted graphs, a coherent theory is developed. Several simple examples show what may be hoped from GENEOs and permutants in graph theory and how they can be built. Rather than being a competitor to other methods in Geometric Deep Learning, this theory is proposed as an approach that can be integrated with such methods
2023
Generalized Permutants and Graph GENEOs / Ahmad F.; Ferri M.; Frosini P.. - In: MACHINE LEARNING AND KNOWLEDGE EXTRACTION. - ISSN 2504-4990. - ELETTRONICO. - 5:4(2023), pp. 1905-1920. [10.3390/make5040092]
Ahmad F.; Ferri M.; Frosini P.
File in questo prodotto:
File Dimensione Formato  
make-05-00092-v3 (1).pdf

accesso aperto

Descrizione: articolo
Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 731.37 kB
Formato Adobe PDF
731.37 kB Adobe PDF Visualizza/Apri

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: https://hdl.handle.net/11585/955319
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact