Gaussian Embedding of Temporal Networks

Abstract: Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions introduces unique challenges due to its sparsity. Merely embedding nodes as trajectories in the latent space overlooks this sparsity, emphasizing the need to quantify uncertainty around the latent positions. In this paper, we propose TGNE (\textbf{T}emporal \textbf{G}aussian \textbf{N}etwork \textbf{E}mbedding), an innovative method that bridges two distinct strands of literature: the statistical analysis of networks via Latent Space Models (LSM)\cite{Hoff2002} and temporal graph machine learning. TGNE embeds nodes as piece-wise linear trajectories of Gaussian distributions in the latent space, capturing both structural information and uncertainty around the trajectories. We evaluate TGNE's effectiveness in reconstructing the original graph and modelling uncertainty. The results demonstrate that TGNE generates competitive time-varying embedding locations compared to common baselines for reconstructing unobserved edge interactions based on observed edges. Furthermore, the uncertainty estimates align with the time-varying degree distribution in the network, providing valuable insights into the temporal dynamics of the graph. To facilitate reproducibility, we provide an open-source implementation of TGNE at \url{https://github.com/aida-ugent/tgne}.