The key with Ayasdi's work is that they manage to layer the TDA with different ML filters, which does stunningly well for the datasets they like talking about.

The key with Ayasdi's work is that they manage to layer the TDA with different ML filters, which does stunningly well for the datasets they like talking about. I also second the notion to read papers from the Carlsson lab, particularly one of the more application-oriented papers such as this one: http://www.nature.com/srep/2013/130207/srep01236/pdf/srep01236.pdf http://www.nature.com/srep/2013/130207/srep01236/pdf/srep012...