Difference between revisions of "Topological Methods in Data Analysis - Journal Club (Winter 2019/20)"
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| − | |Statistics of Persistence Diagrams | + | |Statistics of Persistence Diagrams |
| − | | | + | |E. Berry, Y.-C. Chen, J. Cisewski-Kehe, B. T. Fasy (2018): ''Functional Summaries of Persistence Diagrams'' [https://arxiv.org/abs/1804.01618 arXiv] <ref>Berry, Eric, Yen-Chi Chen, Jessi Cisewski-Kehe, and Brittany Terese Fasy. ‘Functional Summaries of Persistence Diagrams’. 4 April 2018. http://arxiv.org/abs/1804.01618 </ref> |
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Revision as of 14:34, 2 October 2019
Topological Data Analysis (TDA) is a recent developmentin mathematics that actually offers real world applications. The basic idea is using a homology theory - called persistent homology - to identify structures in data. However, interpreting these structures is by no means an easy task, and depends on the specific details of the underlying system.
In this journal club we will take a detailed look at foundational articles, specific applications and recent developments in the field.
Coordinates
Wednesday 9.15-11.45h
Mathematikon, Seminar Room 9
Schedule
| Date | Topic | Article | Speaker |
|---|---|---|---|
| 16.10. | Organizational Meeting | Michael Bleher Daniel Spitz | |
| 23.10. | An Application of the Mapper Algorithm | M. Nicolau, A. J. Levine, and G. Carlsson (2011): Topology Based Data Analysis Identifies a Subgroup of Breast Cancers with a Unique Mutational Profile and Excellent Survival doi [1] | NA |
| 30.10. | Stability Theorems | D. Cohen-Steiner, H. Edelsbrunner, and J. Harer (2007): Stability of Persistence Diagrams doi [2]
D. Cohen-Steiner, H. Edelsbrunner, J. Harer (2010): Lipschitz Functions Have L^p -Stable Persistence doi [3] |
NA |
| 6.11. | Stability Theorems II | U. Bauer, M. Lesnick (2016): Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem arXiv [4] | NA |
| 13.11. | Statistics of Persistence Diagrams | E. Berry, Y.-C. Chen, J. Cisewski-Kehe, B. T. Fasy (2018): Functional Summaries of Persistence Diagrams arXiv [5] | |
| 20.11. | |||
| 27.11. |
Future Directions:
Further examples and applications, multi-persistence, machine learning & TDA, discrete Morse theory & persistent homology ...
Articles
- ↑ Nicolau, Monica, Arnold J. Levine, and Gunnar Carlsson. ‘Topology Based Data Analysis Identifies a Subgroup of Breast Cancers with a Unique Mutational Profile and Excellent Survival’. Proceedings of the National Academy of Sciences of the United States of America 108, no. 17 (26 April 2011): 7265–70. https://doi.org/10.1073/pnas.1102826108
- ↑ Cohen-Steiner, David, Herbert Edelsbrunner, and John Harer. ‘Stability of Persistence Diagrams’. Discrete & Computational Geometry 37, no. 1 (1 January 2007): 103–20. https://doi.org/10.1007/s00454-006-1276-5.
- ↑ Cohen-Steiner, David, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko. ‘Lipschitz Functions Have L p -Stable Persistence’. Foundations of Computational Mathematics 10, no. 2 (April 2010): 127–39. https://doi.org/10.1007/s10208-010-9060-6.
- ↑ Bauer, Ulrich, and Michael Lesnick. ‘Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem’, 31 October 2016. https://arxiv.org/abs/1610.10085v2.
- ↑ Berry, Eric, Yen-Chi Chen, Jessi Cisewski-Kehe, and Brittany Terese Fasy. ‘Functional Summaries of Persistence Diagrams’. 4 April 2018. http://arxiv.org/abs/1804.01618