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Optimal Transport for structured data with application on graphs

Abstract : This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Fréchet means or barycenters of graphs are illustrated and discussed in a clustering context.
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Contributor : Nicolas Courty <>
Submitted on : Friday, July 5, 2019 - 9:16:50 AM
Last modification on : Tuesday, May 26, 2020 - 6:50:43 PM

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  • HAL Id : hal-02174322, version 1
  • ARXIV : 1805.09114


Titouan Vayer, Laetitia Chapel, Rémi Flamary, Romain Tavenard, Nicolas Courty. Optimal Transport for structured data with application on graphs. ICML 2019 - 36th International Conference on Machine Learning, Jun 2019, Long Beach, United States. pp.1-16. ⟨hal-02174322⟩



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