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Semi-relaxed Gromov Wasserstein divergence with applications on graphs

Cédric Vincent-Cuaz 1, 2 Rémi Flamary 3 Marco Corneli 2 Titouan Vayer 4 Nicolas Courty 5
2 MAASAI - Modèles et algorithmes pour l’intelligence artificielle
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SPARKS - Scalable and Pervasive softwARe and Knowledge Systems, UNS - Université Nice Sophia Antipolis (... - 2019), JAD - Laboratoire Jean Alexandre Dieudonné
4 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
5 OBELIX - Observation de l’environnement par imagerie complexe
Abstract : Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific nature of the associated objects. More specifically, through the nodes connectivity relations, GW operates on graphs, seen as probability measures over specific spaces. At the core of OT is the idea of conservation of mass, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary or partition learning, and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. Aside from immediate computational benefits, we discuss its properties, and show that it can lead to an efficient graph dictionary learning algorithm. We empirically demonstrate its relevance for complex tasks on graphs such as partitioning, clustering and completion.
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Preprints, Working Papers, ...
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Contributor : Cédric Vincent-Cuaz Connect in order to contact the contributor
Submitted on : Wednesday, October 13, 2021 - 6:16:39 PM
Last modification on : Tuesday, October 19, 2021 - 11:04:45 AM

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  • HAL Id : hal-03376923, version 1
  • ARXIV : 2110.02753


Cédric Vincent-Cuaz, Rémi Flamary, Marco Corneli, Titouan Vayer, Nicolas Courty. Semi-relaxed Gromov Wasserstein divergence with applications on graphs. 2021. ⟨hal-03376923⟩



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