Exploiting Edge Features in Graph-based Learning with Fused Network Gromov-Wasserstein Distance

Pairwise comparison of graphs is key to many applications in Machine Learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on informative representations of these structured objects such as bag of substructures or other graph embeddings. A recently popular solution consists in representing graphs as metric measure spaces, allowing to successfully leverage Optimal Transport, which provides meaningful distances allowing to compare them, namely the Gromov-Wasserstein distance and its variant the Fused Gromov-Wasserstein that applies on node attributed graphs. However, this family of distances overlooks edge attributes, which are essential for many structured objects. In this work, we introduce an extension of the Fused Gromov-Wasserstein distance for comparing graphs whose both nodes and edges have features. We propose novel algorithms for distance and barycenter computation. We present a range of studies that illustrate the properties of the proposed distance and empirically demonstrate its effectiveness in supervised graph prediction tasks.