Carl sent me a YouTube video by Dr Gunnar Carlsson on the application of Topology to Data Mining (Topological Data Analysis).
Dr. Carlsson created a short 5 minute introduction, and a longer video of one of his lectures.
For more information, check out “Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and
excellent survival” by Nicolaua, Levineb, and Carlsson.
Also, Bansal and Choudhary put together a nice set of slides on the subject with applications to clustering and visualization.