Researchers in the School of Mathematics at the University of Bristol have been working with collaborators in the Societal Resilience team at Microsoft Research on advanced graph analysis techniques to help reveal the hidden structure of corruption.
The University of Bristol team, led by Dr. Patrick Rubin-Delanchy and Prof. Nick Whiteley, has developed statistical techniques to help analyse complex patterns of behaviour and relatedness in procurement ecosystems.
The underlying method, called Unfolded Spectral Embedding (USE), offers a principled statistical foundation for comparing behaviour at different points in time, with provable stability guarantees that constant node behaviour at any time results in a constant node position. The same method also allows for combining behavioural signals from all time periods into a single vector representation for each node, enabling state-of-the-art statistical inference. These are precisely the qualities we need to establish a principled measure of relatedness, informed by manifold geometry in the embedded space, that accounts for all the different kinds of relationship that can be observed in real-world data.
The work was based on two papers published at NeurIPS 2021:
Matrix factorisation and the interpretation of geodesic distance, Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy (link)
Spectral embedding for dynamic networks with stability guarantees, Ian Gallagher, Andrew Jones, Patrick Rubin-Delanchy (link) arXiv:2202.03945
And the following paper:
The Multilayer Random Dot Product Graph, Andrew Jones, Patrick Rubin-Delanchy (link to PDF).