Optimal Transport for Unsupervised Graph Representation Learning
| Quand ? |
Le 19/04/2022, de 13:00 à 14:00 |
|---|---|
| Participants |
Cédric Vincent-Cuaz |
| Ajouter un événement au calendrier |
vCal
iCal
|
Title : Optimal Transport for Unsupervised Graph Representation Learning
Asbtract :
Dictionary learning on vectorial data is a key tool for representation learning, that explains the data as linear combination of few basic elements, while preserving as well as possible the data geometry within this « basis » using common distances (e.g euclidean distance). Yet, this analysis is not easily amenable in the context of graph learning, as graphs usually belong to different metric spaces, whose comparison can not be achieved using such distances. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), provides meaningful comparison between graphs seen as probability measures over specific spaces. In a previous work, we proposed a new Graph Dictionary Learning approach which efficiently leveraged GW’s properties and empirically demonstrated strong relevance for unsupervised representation learning. However, one potentially detrimental limitation highlighted by this work lies in the idea of conversation of mass at the core of OT thus of GW, which imposes a coupling between all the nodes from the two considered graphs. We then propose to 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.
More information : https://scholar.google.fr/citations?user=p0spNmMAAAAJ&hl=fr&oi=ao