title: Semi-relaxed Gromov-Wasserstein divergence and applications on graphs
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.
authors: Cédric Vincent-Cuaz Rémi Flamary Marco Corneli Titouan Vayer Nicolas Courty
hIndex: Nicolas Courty 29