Optimal transport for structured data

Date(s) : 08/03/2019   iCal
14 h 00 min - 15 h 00 min

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.


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