A hyperbolic neural network outperforms a Euclidean model in spatiotemporal link prediction for location-based social networks

Link prediction is a fundamental task for understanding user interactions in location-based social networks (LBSNs), where check-ins and spatial media data exhibit hierarchical structures. This paper proposes a Hyperbolic Neural Network (HNN) model that integrates spatiotemporal user features with friendship relations and compares it to a classical multi-layer perceptron (MLP) in Euclidean space. Experiments on the Brightkite and Gowalla datasets show that the hyperbolic model achieves substantial gains over the MLP, with up to 13.1% higher F1-score and 23.8% higher Recall for class 1 on Brightkite, and 7.2% and 9.9% improvements on Gowalla. Moreover, the hyperbolic network demonstrates faster convergence to optimal configurations in large-scale settings despite higher per iteration complexity. These results highlight the advantage of hyperbolic geometry for modeling hierarchical relationships in LBSNs.