Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes can be used to improve our understanding of the structure resulting from higher-order interactions. We consider the problem of community detection in hypergraphs and develop a principled model that combines higher-order interactions and node attributes to better represent the observed interactions and to detect communities more accurately than using either of these types of information alone. The method learns automatically from the input data the extent to which structure and attributes contribute to explain the data, down weighing or discarding attributes if not informative. Our algorithmic implementation is efficient and scales to large hypergraphs and interactions of large numbers of units. We apply our method to a variety of systems, showing strong performance in hyperedge prediction tasks and in selecting community divisions that correlate with attributes when these are informative, but discarding them otherwise. Our approach illustrates the advantage of using informative node attributes when available with higher-order data.

翻译：许多用超图编码的、涉及两个或更多单元成组交互的网络数据集，往往伴随有关于节点的额外信息，例如个体在工作场所中的角色。本文展示了如何利用这些节点属性来增进我们对高阶交互所产生结构的理解。我们考虑了超图中的社区检测问题，并开发了一个原理性模型，该模型结合了高阶交互与节点属性，能够比单独使用其中任一类型信息更准确地表示观察到的交互，并检测出社区。该方法能从输入数据中自动学习结构和属性对解释数据的贡献程度，若属性无信息价值则降低其权重或予以舍弃。我们的算法实现高效，可扩展至大型超图及大量单元的交互。我们将该方法应用于多种系统，在超边预测任务以及选择与属性相关的社区划分时（当属性具有信息价值时）表现出色，而在属性无用时则舍弃它们。我们的方法阐明了当高阶数据附带可用信息性节点属性时利用这些属性的优势。