Introduction to Persistent Homology
A revised version of this video is available at https://youtu.be/2PSqWBIrn90 .
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"
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
Видео Introduction to Persistent Homology канала Matthew Wright
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"
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
Видео Introduction to Persistent Homology канала Matthew Wright
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
![An introduction to persistent homology](https://i.ytimg.com/vi/UxEH7WySO60/default.jpg)
![Simplicial Complexes - Your Brain as Math Part 2 | Infinite Series](https://i.ytimg.com/vi/rlI1KOo1gp4/default.jpg)
![Scikit TDA: Topological Tools for the Python Ecosystem | SciPy 2019 | Nathaniel Saul](https://i.ytimg.com/vi/AWoeBzJd7uQ/default.jpg)
![Gunnar Carlsson: "Topological Modeling of Complex Data"](https://i.ytimg.com/vi/8nUBqawu41k/default.jpg)
![Gunnar Carlsson: The Shape of Data (DARPA "Wait, What?")](https://i.ytimg.com/vi/X9ktWgJ7ung/default.jpg)
![What is the difference between persistence barcodes and persistence diagrams? [Tutorial-a-thon]](https://i.ytimg.com/vi/py45mca57bQ/default.jpg)
![Henry Adams (6/2/20): From persistent homology to machine learning](https://i.ytimg.com/vi/C6xly6kNvO8/default.jpg)
![Merge trees and sublevelset persistent homology](https://i.ytimg.com/vi/l4vmErGufdY/default.jpg)
![Topology for Data Analysis](https://i.ytimg.com/vi/fUvl-B2lx5Q/default.jpg)
![What is the size of a function?](https://i.ytimg.com/vi/xrF5K9D9mMM/default.jpg)
![The things you'll find in higher dimensions](https://i.ytimg.com/vi/dr2sIoD7eeU/default.jpg)
![Prof. Gunnar Carlsson - Topological Data Analysis and Deep Learning](https://i.ytimg.com/vi/i-tpAxnrQ8s/default.jpg)
![What in the world is topological quantum matter? - Fan Zhang](https://i.ytimg.com/vi/GJHhnr9R_ZM/default.jpg)
![Applied topology 8: An introduction to persistent homology](https://i.ytimg.com/vi/OkDs9Wj5G1U/default.jpg)
![Introduction to Homological Algebra I: Motivation](https://i.ytimg.com/vi/9pPS7iJ4grM/default.jpg)
![Austin Lawson (7/15/20): A canonical framework for summarizing persistence diagrams](https://i.ytimg.com/vi/7Tp-mop1ox0/default.jpg)
![Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces](https://i.ytimg.com/vi/yuVqxCSsE7c/default.jpg)
![The derivative isn't what you think it is.](https://i.ytimg.com/vi/2ptFnIj71SM/default.jpg)
![Topological insulators: mind the gap! | Gene Mele | TEDxPenn](https://i.ytimg.com/vi/a9CeB3ahjtU/default.jpg)
![These changed how I think about higher dimensions](https://i.ytimg.com/vi/lmcT2mP2bfE/default.jpg)