Hyperbolic Temporal Network Embedding

Temporal networks arise in various real-world scenarios, including social networks, user-item networks, traffic networks, financial transaction networks, etc. Modeling the dynamics of temporal networks is of importance as it describes how the networks evolve, which helps to understand and predict the behavior of the systems. There has been a lot of research on temporal network representation learning so far. Nonetheless, most of them are based on euclidean geometry, which fails to encode the underlying hierarchical layout or scale-free property of the real-world temporal network. Encouragingly, hyperbolic geometry excels in preserving both node similarity and network hierarchies. In the preliminary work, we proposed a hyperbolic temporal graph network (HTGN) on the Poincaré ball model, taking advantage of the exponential capacity and hierarchical awareness of hyperbolic geometry. HTGN moves the temporal network embedding into hyperbolic space and employs the hyperbolic graph neural network and hyperbolic gated recurrent neural network to capture spatial and temporal dynamics, respectively. In addition, two modules were further put forward to advance the performance: (1) hyperbolic temporal contextual self-attention to watch historical states and (2) hyperbolic temporal consistency to enforce the embeddings changing gradually. In this work, we further design a lightweight and efficient hyperbolic graph convolutional module that enables HTGN to scale to large-size graphs easily and flexibly handle datasets with different densities. Moreover, we investigate the hyperbolic temporal network embedding in the Lorentz model of hyperbolic geometry with regard to its numerical stability and optimization advantages. Extensive experiments demonstrate the effectiveness of the proposals as they consistently outperform the competing baselines on small-, medium-, and large-scale datasets.