persistent homology: the basics
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Persistent Homologythe basics
Image:Jean-Marie Hullot (CC BY 3.0)
kelly davis (founder forty.to)
http://bit.ly/13Vzp7Phttp://bit.ly/13Vzp7Phttp://bit.ly/13Vzp7Phttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://on.fb.me/12AmW9ahttp://on.fb.me/12AmW9ahttp://on.fb.me/12AmW9ahttp://www.forty.to/http://www.forty.to/http://www.fotopedia.com/users/jmhullothttp://www.fotopedia.com/users/jmhullot -
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problem:whats the topology of a point cloud?
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solution: persistent homology
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simplicial complex
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simplicial homology
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simplicial homology
i
K L
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simplicial filtrations
iK Ki
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birth, death, and taxes
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persistence
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so what!
H0
H1
H2
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calm before the algorithm
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the algorithm: betti numbers
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the algorithm: persistence
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implementations:
phat - c++ with c++ apidionysus - c++ with python api
plex - java with java api
I J M i H ll t (CC BY 3 0)
Persistent Homologythe basics
kelly davis (founder forty.to)
http://bit.ly/13Vzp7Phttp://bit.ly/13Vzp7Phttp://bit.ly/13Vzp7Phttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://linkd.in/10beY2Shttp://on.fb.me/12AmW9ahttp://on.fb.me/12AmW9ahttp://on.fb.me/12AmW9ahttp://www.forty.to/http://www.forty.to/http://www.fotopedia.com/users/jmhullothttp://comptop.stanford.edu/u/programs/jplex/http://comptop.stanford.edu/u/programs/jplex/http://www.mrzv.org/software/dionysushttp://www.mrzv.org/software/dionysushttps://code.google.com/p/phat/https://code.google.com/p/phat/