Applications of Persistent Homology

Question

Can anyone describe to me in Layman's terms what kind of use topology has through applying techniques of persistent homology in data analysis? Can you give me some real life examples in which which this has been used with success?

Answer 1

Identifying a subgroup of breast cancer is the most significant one that I know of.

• Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival

But it has also been used to classify players in basketball, finding that there are thirteen types of players rather than the usual five positions they are grouped into, and to study swarming behavior in insects. I'm sure it has found countless other applications as well. Check out Ayasdi.

Answer 2

To add to the list, it was used to study images and to help develop new compression algorithms:

• http://redwood.berkeley.edu/vs265/carlsson-ijcv08.pdf

This is a nice survey I found.

• Three Examples of Applied & Computational Homology