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Generalized Permutants and Graph GENEOs
- 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