Carlsson has developed methods from applied topology to do clustering work. Robert Ghrist called a talk about this "Clusterfunctor" since it involves a functor from metric spaces to "persistent sets". It's talked about in [Topology and Data][1], a survey article about using topology to do data analysis.




  [1]: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf