Optimal Transport for structured data with application on graphs

23 May 2018  ·  Titouan Vayer, Laetitia Chapel, Rémi Flamary, Romain Tavenard, Nicolas Courty ·

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 Fr\'echet means or barycenters of graphs are illustrated and discussed in a clustering context. read more

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification ENZYMES FGW sp Accuracy 71.00% # 2
Graph Classification MUTAG FGW wl h=2 sp Accuracy 86.42% # 39
Graph Classification MUTAG FGW raw sp Accuracy 83.26% # 52
Graph Classification MUTAG FGW wl h=4 sp Accuracy 88.42% # 27
Graph Classification NCI1 FGW wl h=2 sp Accuracy 85.82% # 5
Graph Classification NCI1 FGW raw sp Accuracy 72.82% # 38
Graph Classification NCI1 FGW wl h=4 sp Accuracy 86.42% # 2
Graph Classification PROTEINS FGW sp Accuracy 74.55% # 49


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