16th November 2023: Alexander Modell (Imperial College London)

Title: "Spectral approaches to representation learning for network data"
Abstract: Analysis of network data, describing relationships, interactions and dependencies between entities, often begins with representation learning: the process of mapping these entities into a vector space in a way which preserves salient information in the data. Exploratory analysis of these representations can reveal patterns and latent structures, such as communities, and they may serve as inputs to learning algorithms such as clustering, regression, classification and neighbour recommendation. Spectral embedding, in which representations are constructed from the eigenvectors of a specially designed matrix, has emerged as a simple yet effective approach which is both highly scalable and interpretable. In the first part of this talk, I will provide a statistical lens into spectral embedding, elucidating how the eigenvectors of different matrices extract different information from the network and exploring model-based explanations the geometric patterns it produces. In particular, I will focus on spectral embedding with the random walk Laplacian matrix, and show how unlike other popular matrix constructions, it produces representations which are agnostic to node degrees. In the second part of this talk, I will present a framework for representation learning for dynamic network data describing instantaneous interactions between entities which occur in continuous time. The framework produces continuously evolving vectors trajectories which reflect the continuously evolving structural roles of the nodes in the network and allows nodes to be meaningfully compared at different points in time.
This talk is based on joint works with Patrick Rubin-Delanchy, Nick Whiteley, Ian Gallagher and Emma Ceccherini.