Difference between revisions of "Topological Methods in Data Analysis - Journal Club (Winter 2019/20)"
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|23.10. | |23.10. | ||
|An Application of the Mapper Algorithm | |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'' [https://doi.org/10.1073/pnas.1102826108 doi] <ref> 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 </ref> | + | |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'' [https://doi.org/10.1073/pnas.1102826108 doi] <ref>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 </ref> |
|NA | |NA | ||
|- | |- | ||
|30.10. | |30.10. | ||
|Stability Theorems | |Stability Theorems | ||
| − | |D. Cohen-Steiner, H. Edelsbrunner, and J. Harer (2007): ''Stability of Persistence Diagrams'' [https://doi.org/10.1007/s00454-006-1276-5 doi] <ref> 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.</ref> | + | |D. Cohen-Steiner, H. Edelsbrunner, and J. Harer (2007): ''Stability of Persistence Diagrams'' [https://doi.org/10.1007/s00454-006-1276-5 doi] <ref>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.</ref> |
D. Cohen-Steiner, H. Edelsbrunner, J. Harer (2010): ''Lipschitz Functions Have L^p -Stable Persistence'' [https://doi.org/10.1007/s10208-010-9060-6 doi] <ref>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.</ref> | D. Cohen-Steiner, H. Edelsbrunner, J. Harer (2010): ''Lipschitz Functions Have L^p -Stable Persistence'' [https://doi.org/10.1007/s10208-010-9060-6 doi] <ref>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.</ref> | ||
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|6.11. | |6.11. | ||
|Stability Theorems II | |Stability Theorems II | ||
| − | |U. Bauer, M. Lesnick (2016): ''Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem'' [https://arxiv.org/abs/1610.10085v2 arXiv] <ref> Bauer, Ulrich, and Michael Lesnick. ‘Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem’, 31 October 2016. https://arxiv.org/abs/1610.10085v2. | + | |U. Bauer, M. Lesnick (2016): ''Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem'' [https://arxiv.org/abs/1610.10085v2 arXiv] <ref>Bauer, Ulrich, and Michael Lesnick. ‘Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem’, 31 October 2016. https://arxiv.org/abs/1610.10085v2. |
</ref> | </ref> | ||
|NA | |NA | ||
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|13.11. | |13.11. | ||
|Statistics of Persistence Diagrams | |Statistics of Persistence Diagrams | ||
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|20.11. | |20.11. | ||
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|27.11. | |27.11. | ||
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| + | ==== Future Directions: ==== | ||
| + | Further examples and applications, multi-persistence, machine learning & TDA, discrete Morse theory & persistent homology ... | ||
| + | |||
| + | === Articles === | ||
| + | <references /> | ||
Revision as of 14:31, 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 | ||
| 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.