DHGAT: Hyperbolic representation learning on dynamic graphs via attention networks

Hao Li, Hao Jiang, Dongsheng Ye, Qiang Wang, Liang Du, Yuanyuan Zeng, Liu Yuan, Yingxue Wang, Cheng Chen

Abstract: Hyperbolic graph embedding has garnered significant attention in a wide range of downstream applications. This is because hyperbolic geometry provides a valuable mapping tool, whereby the scale-free or hierarchical properties of complex networks can be naturally reflected as hyperbolic metric properties. Despite this, most advancements have focused on learning hyperbolic representations of static graphs, the potential advantages of hyperbolic metrics in dynamic graphs embedding have not been fully exploited. To fully harness the properties of hyperbolic space, we propose DHGAT1, a dynamic hyperbolic graph attention network with a novel architecture that designs a spatiotemporal self-attention mechanism based on hyperbolic distance. DHGAT maps dynamic graphs into the hyperbolic space, generates spatiotemporal self-attention of nodes, and directly aggregates weighted node representations without the tangent space. This is achieved by using the Einstein gyromidpoints, which reduces distortions and preserves manifold properties. The results of experiments on real-world datasets demonstrate that DHGAT performs exceptionally well in multi-step link prediction tasks, particularly in predicting new links compared to the baselines.