Embedding and trajectories of temporal networks

TL;DR

This paper introduces a novel method for embedding temporal networks into low-dimensional trajectories using landmark multidimensional scaling and tie-decay frameworks, enabling continuous analysis of complex evolving systems.

Contribution

It presents a new approach to generate low-dimensional trajectories of temporal networks from event data, combining landmark MDS with tie-decay models for continuous-time embedding.

Findings

Successfully embedded social contact data into low-dimensional trajectories.

Revealed temporal organization and contact loss patterns over days.

Demonstrated the method's ability to analyze complex temporal dynamics.

Abstract

Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to coarse grain temporal network data into a numeric trajectory embedded in a low-dimensional space. We refer to such a procedure as temporal network embedding, which is distinct from procedures that aim at embedding individual nodes. Temporal network embedding is a challenging task because we often have access only to discrete time-stamped events between node pairs, and, in general, the events occur with irregular intervals, making the construction of the network at a given time a nontrivial question already. We propose a method to generate trajectories of temporal networks embedded in a low-dimensional space given a sequence of time-stamped events as input. We realize this goal by combining the landmark multidimensional scaling, which is an out-of-sample extension of the well-known multidimensional scaling method, and the framework of tie-decay temporal networks. This combination enables us to obtain a continuous-time trajectory describing the evolution of temporal networks. We then study mathematical properties of the proposed temporal network embedding framework. Finally, we showcase the method with empirical data of social contacts to find temporal organization of contact events and loss of them over a single day and across different days.