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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Optimal transport for structured data




Date(s) : 08/03/2019   iCal
14h00 - 15h00

In this work, we consider 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. which minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. After introducing Wasserstein and 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), we will present our new distance which exploits jointly both information, and consequently being called Fused Gromov-Wasserstein (FGW). We will discuss 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.

https://tvayer.github.io

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