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Generalized Permutants and Graph GENEOs

Authors :
Faraz Ahmad
Massimo Ferri
Patrizio Frosini
Source :
Machine Learning and Knowledge Extraction, Vol 5, Iss 4, Pp 1905-1920 (2023)
Publication Year :
2023
Publisher :
MDPI AG, 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.

Details

Language :
English
ISSN :
25044990
Volume :
5
Issue :
4
Database :
Directory of Open Access Journals
Journal :
Machine Learning and Knowledge Extraction
Publication Type :
Academic Journal
Accession number :
edsdoj.55c31ce5fab94e558e2bf0a94cfcfa68
Document Type :
article
Full Text :
https://doi.org/10.3390/make5040092