On Generalizing Static Node Embedding to Dynamic Settings

ABSTRACTTemporal graph embedding has been widely studied thanks to its superiority in tasks such as prediction and recommendation. Despite the advances in algorithms and novel frameworks such as deep learning, there has been relatively little work on systematically studying the properties of temporal network models and their cornerstones, the graph time-series representations that are used in these approaches. This paper aims to fill this gap by introducing a general framework that extends an arbitrary existing static embedding approach to handle dynamic tasks, and conducting a systematic study of seven base static embedding methods and six temporal network models. Our framework generalizes static node embeddings derived from the time-series representation of stream data to the dynamic setting by modeling the temporal dependencies with classic models such as the reachability graph. While previous works on dynamic modeling and embedding have focused on representing a stream of timestamped edges using a time-series of graphs based on a specific time-scale (\eg, 1 month), we introduce the notion of an ε-graph time-series that uses a fixed number of edges for each graph, and show its superiority in practical settings over the standard solution. From the 42 methods that our framework subsumes, we find that leveraging the new ε-graph time-series representation and capturing temporal dependencies with the proposed reachability or summary graph tend to perform well. Furthermore, the new dynamic embedding methods based on our framework perform comparably and on average better than the state-of-the-art embedding methods designed specifically for temporal graphs in link prediction tasks.