Graph embedding: time and space

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Advances in the analysis of large networks have benefitted very many fields, from cyber-security in the identification of intruders by modelling when two IP addresses should normally communicate, to neuroscience in which differences in brain connectivity could be an indication of schizophrenia. Analyses like these often involve a first step where the network data is represented as a lower-dimensional vector space known as an embedding, in which nodes that behave similarly are ""close"".This project will focus on producing embeddings that correctly represent large dynamic networks. This involves taking ""snapshots"" of the dynamic network over time and then calculating an embedding representation of each snapshot such that communities of nodes are positioned correctly over time.A simple method of modelling a network with community structure is the stochastic block model. This is an example of a latent position model which generates random networks where nodes of the same community will behave similarly and share latent positions. From this, we can consider a dynamic stochastic block model where communities and latent positions will move (or stay static) over time. The goal of this project is then to discover a method that can perfectly recover the community membership of each node in a dynamic stochastic block model as the network becomes asymptotically large. If achieved, this will be an incredibly important result with simple implications for the correct analysis to perform across many application domains.