A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than two authors) more naturally and accurately than ordinary graphs. Interestingly, many real-world systems modeled as hypergraphs contain edge-dependent node labels, i.e., node labels that vary depending on hyperedges. For example, on co-authorship datasets, the same author (i.e., a node) can be the primary author in a paper (i.e., a hyperedge) but the corresponding author in another paper (i.e., another hyperedge). In this work, we introduce a classification of edge-dependent node labels as a new problem. This problem can be used as a benchmark task for hypergraph neural networks, which recently have attracted great attention, and also the usefulness of edge-dependent node labels has been verified in various applications. To tackle this problem, we propose WHATsNet, a novel hypergraph neural network that represents the same node differently depending on the hyperedges it participates in by reflecting its varying importance in the hyperedges. To this end, WHATsNet models the relations between nodes within each hyperedge, using their relative centrality as positional encodings. In our experiments, we demonstrate that WHATsNet significantly and consistently outperforms ten competitors on six real-world hypergraphs, and we also show successful applications of WHATsNet to (a) ranking aggregation, (b) node clustering, and (c) product return prediction.

翻译：超图是一种由节点和超边构成的数据结构，其中每个超边是节点的任意大小子集。由于超边大小的灵活性，超图比普通图更自然、更准确地表示群体交互（例如，由两位以上作者合作的合著关系）。有趣的是，许多建模为超图的真实世界系统包含边依赖的节点标签，即标签随超边变化的节点。例如，在合著数据集中，同一作者（即一个节点）可能在一篇论文（即一个超边）中是第一作者，但在另一篇论文（即另一个超边）中是通讯作者。本文提出将边依赖节点标签分类作为一个新问题。该问题可作为近期备受关注的超图神经网络的基准任务，并且边依赖节点标签的有用性已在各种应用中得到验证。为解决此问题，我们提出了WHATsNet，一种新颖的超图神经网络，它通过反映节点在超边中不同重要性，使同一节点根据其参与的超边呈现不同表示。为此，WHATsNet利用节点在超边内的相对中心性作为位置编码，建模每个超边内节点间的关系。实验中，我们证明WHATsNet在六个真实世界超图上显著且一致地优于十种对比方法，并展示了WHATsNet在（a）排名聚合、（b）节点聚类和（c）产品退货预测中的成功应用。