Continuous Latent Position Models for Instantaneous Interactions

TL;DR

This paper introduces a continuous-time latent position model for analyzing instantaneous interactions like emails and calls, capturing how entities move in a latent space to explain interaction timing and frequency.

Contribution

It extends latent position network models by incorporating continuous trajectories for entities, enabling dynamic analysis of interaction data over time.

Findings

Effective inference of individual trajectories from interaction data

Application to both artificial and real-world datasets

Demonstrates the model's ability to capture interaction dynamics

Abstract

We create a framework to analyse the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays, and easily available. Examples of instantaneous interactions include email networks, phone call networks and some common types of technological and transportation networks. Our framework relies on a novel extension of the latent position network model: we assume that the entities are embedded in a latent Euclidean space, and that they move along individual trajectories which are continuous over time. These trajectories are used to characterize the timing and frequency of the pairwise interactions. We discuss an inferential framework where we estimate the individual trajectories from the observed interaction data, and propose applications on artificial and real data.