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Introduction to Persistent Homology
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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.
Citations and links to papers referenced in this video:
Robert Ghrist, "Barcodes: The Persistent Topology of Data"
Herbert Edelsbrunner and John Harer, "Persistent Homology -- A Survey", in Twenty Years After, AMS (2007).
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer, "Stability of Persistence Diagrams", in Discrete and Computational Geometry, vol. 37 (2007), p. 103-120.
Afra Zomorodian and Gunnar Carlsson, "Computing Persistent Homology", in Discrete and Computational Geometry, vol. 33 (2005), p. 249-274.
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.
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.
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.
Citations and links to papers referenced in this video:
Robert Ghrist, "Barcodes: The Persistent Topology of Data"
Herbert Edelsbrunner and John Harer, "Persistent Homology -- A Survey", in Twenty Years After, AMS (2007).
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer, "Stability of Persistence Diagrams", in Discrete and Computational Geometry, vol. 37 (2007), p. 103-120.
Afra Zomorodian and Gunnar Carlsson, "Computing Persistent Homology", in Discrete and Computational Geometry, vol. 33 (2005), p. 249-274.
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.
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.
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.
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