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?

score 4 · Answer 1 · edited Apr 20 '20 at 20:16

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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.

edited Apr 20 '20 at 20:16

Mike Pierce

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answered Sep 18 '16 at 23:47

Jacob Bond

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The basketball link is broken. – 0x90 May 06 '20 at 05:57
Mapper doesn't use persistent homology, does it? Or in the clustering phase of the algorithm with something like ToMATo? – user388557 Jan 11 '21 at 17:16

score 1 · Answer 2 · edited Apr 20 '20 at 20:18

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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

edited Apr 20 '20 at 20:18

Mike Pierce

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answered Sep 19 '16 at 00:33

cocoahomology

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First link is dead – Mike Pierce Apr 20 '20 at 19:02

score 1 · Answer 3 · answered May 08 '24 at 08:14

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Have a look at this curated and quite extensive list of articles and studies that use Persistent Homology:

https://donut.topology.rocks/?q=tag%3A%22Persistent+homology%22

answered May 08 '24 at 08:14

Jjm

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Applications of Persistent Homology

3 Answers3