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}.

TGNE是一种创新方法，通过在潜在空间中使用高斯分布的分段线性轨迹将节点嵌入，捕捉结构信息和轨迹的不确定性。结果表明，TGNE在重新构建未观察到的边交互以及建模不确定性方面具有竞争力。

时序网络的高斯嵌入