Cross-network alignment aims at identifying users who participate in different social networks, which benefits a variety of downstream social applications such as precise content delivery, fraud detection, and content/user recommender systems. Recent advances in network representations and graph neural networks have spurred various network structure-based methods for capturing underlying node similarities across social networks, thereby addressing the network alignment problem. However, most of the existing solutions rely on embedding methods that compute node similarity in Euclidean space, resulting in severe distortion or semantic loss when representing real-world social networks, which are usually scale free and with hierarchical structures. We address these issues by presenting a novel model: Hyperbolic Graph Embedding for Network Alignment (HGENA), which learns the structural semantics more efficiently by embedding nodes in hyperbolic space instead of Euclidean. HGENA overcomes the scalability issue since it requires far fewer dimensions in Riemannian manifolds and increases the capability of learning hierarchical structures, while enabling smaller distortion for tree-liked networks to facilitate node alignment. We also introduce alternative network mapping functions to compute node similarity across-network based on its distance on the Poincare ball. Experimental evaluations conducted on real world datasets demonstrate that HGENA achieves superior performance on social network alignment, especially for more tree-liked networks.
