If you want to read up on ayasdi go straight to the Source: http://www.ayasdi.com/resources/ http://www.ayasdi.com/resources/ (click on publications) There are

If you want to read up on ayasdi go straight to the Source: http://www.ayasdi.com/resources/ http://www.ayasdi.com/resources/ (click on publications) There are probably some talks by Gunnar Carlsson around on the web too. There is also a great overview from Larry Wassermann on his outstanding blog: http://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/ http://normaldeviate.wordpress.com/2012/07/01/topological-da... Other examples of manifold inspired math in data analysis that I find more useful as they describe ways to solve complex problems with simple systems: http://web.stanford.edu/~yyye/hodgeRank2011.pdf http://web.stanford.edu/~yyye/hodgeRank2011.pdf http://www.cs.jhu.edu/~misha/Fall09/Hirani03.pdf http://www.cs.jhu.edu/~misha/Fall09/Hirani03.pdf A really interesting method for learning manifolds from heterogeneous data (decision trees can be extended for categorical data, text data, almost anything) that doesn't boil down to just choosing a metric: http://research.microsoft.com/apps/pubs/default.aspx?id=155552 http://research.microsoft.com/apps/pubs/default.aspx?id=1555... Edit: Also they do have a really slick UI and I like the math involved. I wanted to like their product however I worry that the math just serves to lend legitimacy when the results aren't as exciting/promising as advances being made in other areas of data analysis on similar datasets. Also them keeping it proprietary makes it hard for people to do legitimate comparisons. We implemented some of our own versions of their stuff to tory on other cancer datasets but it just didn't work very well because of numerous issues with lack normalization, batch effect, bias and noise.