Graph Neural Networks (GNNs) have exhibited remarkable efficacy in diverse graph learning tasks, particularly on static homophilic graphs. Recent attention has pivoted towards more intricate structures, encompassing (1) static heterophilic graphs encountering the edge heterophily issue in the spatial domain and (2) event-based continuous graphs in the temporal domain. State-of-the-art (SOTA) has been concurrently addressing these two lines of work but tends to overlook the presence of heterophily in the temporal domain, constituting the temporal heterophily issue. Furthermore, we highlight that the edge heterophily issue and the temporal heterophily issue often co-exist in event-based continuous graphs, giving rise to the temporal edge heterophily challenge. To tackle this challenge, this paper first introduces the temporal edge heterophily measurement. Subsequently, we propose the Temporal Heterophilic Graph Convolutional Network (THeGCN), an innovative model that incorporates the low/high-pass graph signal filtering technique to accurately capture both edge (spatial) heterophily and temporal heterophily. Specifically, the THeGCN model consists of two key components: a sampler and an aggregator. The sampler selects events relevant to a node at a given moment. Then, the aggregator executes message-passing, encoding temporal information, node attributes, and edge attributes into node embeddings. Extensive experiments conducted on 5 real-world datasets validate the efficacy of THeGCN.

翻译：图神经网络（GNNs）在各类图学习任务中展现出卓越性能，尤其在静态同质图上表现突出。近期研究焦点已转向更复杂的图结构，主要包括：（1）在空间域面临边异质性问题的静态异质图，以及（2）时间域中基于事件的连续图。当前前沿研究虽同时关注这两个方向，却往往忽视时间域中存在的异质性现象，即时序异质性问题。进一步地，我们指出边异质性问题与时序异质性问题常共存于基于事件的连续图中，从而形成时序边异质性挑战。为应对这一挑战，本文首先提出时序边异质性度量方法。随后，我们提出时序异质图卷积网络（THeGCN）——一种创新模型，该模型融合低通/高通图信号滤波技术，以精准捕捉边（空间）异质性与时序异质性。具体而言，THeGCN模型包含两个核心组件：采样器与聚合器。采样器负责在给定时刻选取与节点相关的事件；聚合器则执行消息传递，将时序信息、节点属性及边属性编码为节点嵌入。在5个真实世界数据集上的大量实验验证了THeGCN的有效性。