Hierarchical Clustering for Complex Systems
R.S.MacKay@warwick.ac.uk, Mathematics

Examine hierarchical clustering methods and come up with a general synthesis.

There are various schemes for hierarchical clustering of graphs, e.g. Newman MEJ, Networks, Sec 11.11.2 (probably you can find more easy to obtain reviews by googling).  A question is to decide what constitutes a sensible motion of similarity in various contexts, e.g. oscillator networks, large Markov chains, road networks.  For some background, read relevant parts of our HACS bid to the EC (I've attached it near the bottom of http://www2.warwick.ac.uk/fac/sci/maths/people/staff/robert_mackay/aggregation).

Can you find a general useful way to cluster a complex system?  Start with some specific classes of system and work out from there.

This has potential connections to many end-users, as spelt out in the HACS bid.

It has potential to lead to a PhD project on any of the themes of the HACS bid. Potential co-supervision with Artur Czumaj (Comp Sci) or Tom Nichols (Stats) or someone from one of the other nodes (especially if HACS is funded).