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: the Gromov-Wasserstein distances. However, this family of distances overlooks edge attributes, which are essential for many structured objects. In this work, we introduce an extension of Gromov-Wasserstein distance for comparing graphs whose both nodes and edges have features. We propose novel algorithms for distance and barycenter computation. We empirically show the effectiveness of the novel distance in learning tasks where graphs occur in either input space or output space, such as classification and graph prediction.

翻译：图的两两比较是机器学习中许多应用的关键，涵盖从聚类、基于核的分类/回归到最近受监督的图预测等领域。图之间的距离通常依赖于这些结构化对象的有效表示，例如子结构包或其他图嵌入。近期一种流行的解决方案是将图表示为度量度量空间，从而能够成功利用最优传输理论，提供有意义的距离（即格罗莫夫-瓦瑟斯坦距离）用于比较。然而，这类距离忽略了边属性，而边属性对许多结构化对象至关重要。在本工作中，我们引入了格罗莫夫-瓦瑟斯坦距离的一种扩展，用于比较节点和边均具有特征的图。我们提出了用于距离计算和重心计算的新算法。实验表明，在输入空间或输出空间中涉及图的学习任务（如分类和图预测）中，这一新距离的有效性。