Ed Davis

Contact & Links

Email: edward.davis[at]bristol.ac.uk

Office: School of Mathematics University of Bristol, Fry Building, GA.06 Woodland Road Bristol, BS8 1UG.

Twitter: EdD8ta

PhD supervised by Prof. Patrick Rubin-Delanchy and Dr Daniel Lawson.

Research Outline

My work focuses on dynamic network embedding. Dynamic networks encode both spatial and temporal relations between nodes, which are desirable for many applications from cyber security to neuroscience. By representing the nodes of the network as a vector space, it allows us to detect spatial and temporal patterns through clustering. Methods that I have developed during my PhD have been used by Microsoft and LV, and I have presented these methods at the Institute of Mathematics Big Data Conference and the COMPASS conference in 2022. I am interested in progressing dynamic embedding methods and applying them to a diverse range of problems.

Papers

A Simple but Powerful Framework for Dynamic Graph Embedding

In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of single-graph embedding is wide and established, the field of dynamic graph embedding is comparatively in its infancy. In this paper, we propose that we can take a wide class of established single-graph embedding methods and use them to produce interpretable and powerful dynamic graph embeddings by simply applying them to the dilated unfolded matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings over time and space, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space.

Figure: A one-dimensional URLSE displaying the average temporal structure of airports in Italy, the UK and across Europe. The embedding encodes the two main European waves of COVID-19 as well as an annual periodic structure before and after the pandemic. We also see that the pandemic hit Italy slightly before the UK and the rest of Europe.

Preprint link

Accomplishments

Award-Winning Data Visualisation

Runner-up in the Jean Golding Institute's Beauty of Data competition. This visualisation was presented at the Bristol Data and AI Showcase 2022. This visualisation displays an embedding of a friendship network between countries on the world stage based on their alliances.

(Click image for full-size)