Can anyone say if they have used ideas of computational topology as a means of predictive analytics in quantitative finance? It seems that may be an under-represented technology area.

I follow a couple of (general) machine learning blogs, and haven't seen anyone discuss applications. Any tips?

Sounds like a solution that is looking for problems. Homotopy theory has applications (nonlinear solvers) but in general?

There seems to be more developing interest, for example topological data analysis topology of financial modeling and algebraic geometry and topology mention this kind of thing.I'm more familiar with applications in other areas (for example, gene expression data analysis), but would like to know how people are applying this to quantitative finance.Christopher

Christopher,Do you have any articles on CT 'for idiots'?

By definition, a set S has a topology if for every point p in S and every subset X of S, the question "is p a limit point of X?" can answered.An example is the metric topology in nd space, which makes things concrete.Is this true in the current case? So I suppose "ranking" induces some metric? QuoteYou can predictively rank a set of bonds on expected performance etc.In the sense of distance of a bond from some baseline object or from another bond?

As far as a beginners introduction, I have been using 'Computational Topology' by Edelsbrunner and Harer at Duke. We have spoken with John Harer about the application of persistent homology type things for other (non finance) problem sets. I think there is the possibility to, just as you say, use this to reduce model risk, with some caveats. For their time series processing, they do assume some complex cyclical behavior that can be estimated using a statistical view of persistent homology, and have applied it to biological systems. That would be better than a Markov process for finding and utilizing 'patterns', if they exist.