Introduction to Persistent Homology

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by Super User, 4 weeks ago.
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This video gives an accessible introduction to persistent homology, which is a popular tool in topological data analysis and also a subject of my research.

This is a revised version of the video that first appeared at https://youtu.be/h0bnG1Wavag .

Citations and links to papers referenced in this video:

Robert Ghrist, "Barcodes: The Persistent Topology of Data"
http://www.ams.org/journals/bull/2008-45-01/S0273-0979-07-01191-3/

Herbert Edelsbrunner and John Harer, "Persistent Homology -- A Survey", in Twenty Years After, AMS (2007).
http://cygnus-x1.cs.duke.edu/~edels/Papers/2008-B-02-PersistentHomology.pdf

David Cohen-Steiner, Herbert Edelsbrunner, and John Harer, "Stability of Persistence Diagrams", in Discrete and Computational Geometry, vol. 37 (2007), p. 103-120.
ftp://ftp-sop.inria.fr/prisme/dcohen/Papers/Stability.pdf

Afra Zomorodian and Gunnar Carlsson, "Computing Persistent Homology", in Discrete and Computational Geometry, vol. 33 (2005), p. 249-274.
http://www.cs.dartmouth.edu/~afra/papers/socg04/persistence.pdf

Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, and Afra Zomorodian, "On the Local Behavior of Spaces of Natural Images", in International Journal of Computer Vision, vol. 76 (2008), p. 1-12.
http://pages.pomona.edu/~vds04747/public/papers/CIdSZ_natural.pdf

Jose Perea and Gunnar Carlsson, "A Klein-Bottle-Based Dictionary for Texture Representation", in International Journal of Computer Vision, vol. 107 (2014), p. 75-97.
https://fds.duke.edu/db/attachment/2638

Jose Perea and John Harer, "Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis", in Foundations of Computational Mathematics, vol. 15 (2015), p. 799-838.
http://arxiv.org/abs/1307.6188