Does anyone know what would be a good source of bibliography for this talk? I'm more interested in the math aspects of what he is doing, for instance, where the topology comes to the play.
Oh that's great! (You then may know more math than I do, haha). You might want to start with this introductory/programmatic paper by Carlsson himself: "Topology and Data" www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf If you're unsure about some construction or concept you may consult the references therein :) Hope that helps
Actually here he describes Mapper tool and there is no topology at all. But if you are interested in topological methods, there is another tool, widely promoted by Gunnar Carlsson called Persistent Homology geometry.stanford.edu/papers/zc-cph-05/zc-cph-05.pdf
That was absolutely bizarre at the end. Anyway, does anyone know if we can use any of these methods to preprocess data and pass it, to say, a neural network?