Ellipsoidal embeddings of graphs

Fanuel, Michaël; Aspeel, Antoine; Schaub, Michael T.; Delvenne, Jean-Charles

Type de document :

Pré-publication ou Document de travail

Titre :

Ellipsoidal embeddings of graphs

Auteur(s) :

Fanuel, Michaël [Auteur correspondant]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Centre National de la Recherche Scientifique [CNRS]
Aspeel, Antoine [Auteur]
University of Michigan [Ann Arbor]
Schaub, Michael T. [Auteur]
RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen [RWTH Aachen]
Delvenne, Jean-Charles [Auteur]
Université Catholique de Louvain = Catholic University of Louvain [UCL]

Date de publication :

2024-03-22

Discipline(s) HAL :

Informatique [cs]

Résumé en anglais : [en]

Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many ...
Lire la suite >Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are based on the algebraic representation of graphs via matrices such as the graph Laplacian, or on associated graph embeddings. Such embeddings associate to each node a set of coordinates in a vector space, a representation which can then be employed for learning tasks such as the classification or alignment of the nodes of the graph. As the geometric picture provided by embedding methods enables the use of a multitude of methods developed for vector space data, embeddings have thus gained interest both from a theoretical as well as a practical perspective. Inspired by trace-optimization problems, often encountered in the analysis of graph-based data, here we present a method to derive ellipsoidal embeddings of the nodes of a graph, in which each node is assigned a set of coordinates on the surface of a hyperellipsoid. Our method may be seen as an alternative to popular spectral embedding techniques, to which it shares certain similarities we discuss. To illustrate the utility of the embedding we conduct a case study in which we analyse synthetic and real world networks with modular structure, and compare the results obtained with known methods in the literature.Lire moins >

Langue :

Anglais

Projet Européen :

Fast Monte Carlo integration with repulsive processes

Commentaire :

29 pages, 6 figures

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

Fichiers

2403.15023
Accès libre
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Ellipsoidal embeddings of graphs

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