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The choice of good distances and similarity measures between objects isimportant for many machine learning methods. Therefore, many metric learningalgorithms have been developed in recent years, mainly for Euclidean data inorder to improve performance of classification or clustering methods. However,due to difficulties in establishing computable, efficient and differentiabledistances between attributed graphs, few metric learning algorithms adapted tographs have been developed despite the strong interest of the community. Inthis paper, we address this issue by proposing a new Simple Graph MetricLearning - SGML - model with few trainable parameters based on Simple GraphConvolutional Neural Networks - SGCN - and elements of Optimal Transporttheory. This model allows us to build an appropriate distance from a databaseof labeled (attributed) graphs to improve the performance of simpleclassification algorithms such as $k$-NN. This distance can be quickly trainedwhile maintaining good performances as illustrated by the experimental studypresented in this paper.

A Simple Way to Learn Metrics Between Attributed Graphs