Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs.

中文翻译：

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单纯复形上的（超）图内核

在处理测量图之间的相似性时，图核是主流方法之一，特别是对于模式识别和机器学习任务。反过来，图形因其对从生物信息学到社交网络分析的几种现实世界现象的建模能力而获得了很多关注。然而，最近的注意力已经转移到超图，可以考虑多向关系（除了成对关系）的普通图的泛化。在本文中，提出了四个（超）图内核，并以双重方式比较了它们的效率和有效性。首先，通过推断底层图顶部的单纯复形，并将 18 个基准数据集与最先进的方法进行比较；其次，通过面对现实世界的案例研究（即，代谢途径分类），其中输入数据由超图本机表示。通过这项工作，我们旨在促进图内核向超图的扩展，更一般地说，弥合结构模式识别和超图领域之间的差距。