Andrew Jones

[CANCELLED] Visualizing dynamic networks through unfolded adjacency spectral embedding

Given communication data for users in a network, a typical approach to visualizing patterns in behaviour is to assign to each user a point in some low-dimensional vector space and consider the geometry of the resulting point cloud. One well-studied technique is adjacency spectral embedding (ASE) in which, considering the network as a graph – with edges indicating communication between users – we scale and combine several eigenvectors of the resulting adjacency matrix to obtain a list of low-dimensional representations for these users. The behaviour of this embedding is well-understood, with known asymptotic distributional results for several common classes of randomly-generated networks.

Of course, networks are generally dynamic rather than static, with users’ communication preferences changing over time, and so single-graph techniques become unsuitable, prompting us to develop new approaches. In this talk, I will give a whistle-stop tour of spectral embedding and random graph models before introducing recent work by myself, Patrick Rubin-Delanchy and Ian Gallagher concerning unfolded adjacency spectral embedding – a multi-graph analogue of ASE – and hopefully convincing you (through both solid theoretical results and pretty pictures) that this is the ideal technique for dynamic network analysis.