Difference between revisions of "Topological Methods in Data Analysis - Journal Club (Winter 2021/22)"
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− | In recent years there has been a somewhat surprising flow of ideas from the mathematical branch of topology towards applications in the natural sciences. The tale of Topological Data Analysis (TDA) has it, that these methods provide a highly flexible, nonparametric approach to data analysis. Indeed, there are by now several well-known mathematical results that make statements of this kind rigorous. However, successful examples of TDA often build on a deep intuition about the system in question and many aspects of topological methods in data analysis remain a field of active research | + | In recent years there has been a somewhat surprising flow of ideas from the mathematical branch of topology towards applications in the natural sciences. The tale of Topological Data Analysis (TDA) has it, that these methods provide a highly flexible, nonparametric approach to data analysis. Indeed, there are by now several well-known mathematical results that make statements of this kind rigorous. However, successful examples of TDA often build on a deep intuition about the system in question and many aspects of topological methods in data analysis remain a field of active research. |
− | + | The goal of this seminar is to offer a platform where we can learn about the TDA toolkit, discuss articles and new developments, and exchange ideas for the analysis of concrete datasets. | |
==Coordinates and Organization == | ==Coordinates and Organization == | ||
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!Slides | !Slides | ||
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− | | | + | |25.10. |
|Introduction and Organization | |Introduction and Organization | ||
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|Michael Bleher, Maximilian Schmahl, Daniel Spitz | |Michael Bleher, Maximilian Schmahl, Daniel Spitz | ||
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|01.11. | |01.11. | ||
− | | | + | |<i> Allerheiligen, holiday </i> |
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|08.11. | |08.11. | ||
− | | | + | |Embedding of persistence diagrams |
− | | | + | |Mitra A. <b>Proc. Amer. Math. Soc. 149 (2021)</b>, 2693-2703 <br> https://arxiv.org/abs/1905.09337 |
− | | | + | |Atish Mitra |
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|15.11. | |15.11. | ||
− | | | + | |Applications of topological data analysis on DNA data |
− | | | + | |Hahn H, Neitzel C, Kopečná O, Heermann DW, Falk M, Hausmann M. <b>Cancers. 2021; 13(21)</b>:5561.<br> https://doi.org/10.3390/cancers13215561 |
− | | | + | |Jonas Weidner |
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|22.11. | |22.11. | ||
− | | | + | |Compact representations of simplicial complexes and classification algorithms |
− | | | + | |Rolando Kindelan Nuñez (2021) <br> https://arxiv.org/abs/2102.03709 |
− | | | + | |Rolando Kindelan |
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|29.11. | |29.11. | ||
− | | | + | |UMap and manifold learning |
− | | | + | |McInnes et al. <b> Journal of Open Source Software, 3(29), 861 (2018) </b><br> https://arxiv.org/abs/1802.03426 |
− | | | + | |Paul Snopov |
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|06.12. | |06.12. | ||
+ | |Optimal embedding of manifolds into Euclidean spaces | ||
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− | | | + | |Ilja Sirajlovic |
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|10.01. | |10.01. | ||
+ | |On UMAP's True Loss Function | ||
+ | |Damrich S, Hamprecht FA. <b>NeurIPS 2021 (pre-proceedings)</b> <br> https://papers.nips.cc/paper/2021/hash/2de5d16682c3c35007e4e92982f1a2ba-Abstract.html | ||
+ | |Sebastian Damrich | ||
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− | | | + | |17.01. |
+ | |Circle Valued Persistence | ||
+ | |Burghelea, D., Dey, T.K. Topological Persistence for Circle-Valued Maps. <i>Discrete Comput Geom</i> <b>50</b>, 69–98 (2013).<br>https://doi.org/10.1007/s00454-013-9497-x | ||
+ | |Clemens Bannwart | ||
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− | | | + | |24.01. |
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Latest revision as of 10:42, 3 January 2022
In recent years there has been a somewhat surprising flow of ideas from the mathematical branch of topology towards applications in the natural sciences. The tale of Topological Data Analysis (TDA) has it, that these methods provide a highly flexible, nonparametric approach to data analysis. Indeed, there are by now several well-known mathematical results that make statements of this kind rigorous. However, successful examples of TDA often build on a deep intuition about the system in question and many aspects of topological methods in data analysis remain a field of active research.
The goal of this seminar is to offer a platform where we can learn about the TDA toolkit, discuss articles and new developments, and exchange ideas for the analysis of concrete datasets.
Coordinates and Organization
Time: Mondays 11h15 - 12h45
Zoom 830 4593 4507
Please get in touch with us to receive the password.
Organizers: Michael Bleher, Maximilian Schmahl, Daniel Spitz.
structures-hiwi@mathi.uni-heidelberg.de
Schedule
Date | Topic | Info | Speaker | Slides |
---|---|---|---|---|
25.10. | Introduction and Organization | Michael Bleher, Maximilian Schmahl, Daniel Spitz | ||
01.11. | Allerheiligen, holiday | |||
08.11. | Embedding of persistence diagrams | Mitra A. Proc. Amer. Math. Soc. 149 (2021), 2693-2703 https://arxiv.org/abs/1905.09337 |
Atish Mitra | |
15.11. | Applications of topological data analysis on DNA data | Hahn H, Neitzel C, Kopečná O, Heermann DW, Falk M, Hausmann M. Cancers. 2021; 13(21):5561. https://doi.org/10.3390/cancers13215561 |
Jonas Weidner | |
22.11. | Compact representations of simplicial complexes and classification algorithms | Rolando Kindelan Nuñez (2021) https://arxiv.org/abs/2102.03709 |
Rolando Kindelan | |
29.11. | UMap and manifold learning | McInnes et al. Journal of Open Source Software, 3(29), 861 (2018) https://arxiv.org/abs/1802.03426 |
Paul Snopov | |
06.12. | Optimal embedding of manifolds into Euclidean spaces | Ilja Sirajlovic | ||
13.12. | ||||
20.12. | ||||
--- Christmas Break --- | ||||
10.01. | On UMAP's True Loss Function | Damrich S, Hamprecht FA. NeurIPS 2021 (pre-proceedings) https://papers.nips.cc/paper/2021/hash/2de5d16682c3c35007e4e92982f1a2ba-Abstract.html |
Sebastian Damrich | |
17.01. | Circle Valued Persistence | Burghelea, D., Dey, T.K. Topological Persistence for Circle-Valued Maps. Discrete Comput Geom 50, 69–98 (2013). https://doi.org/10.1007/s00454-013-9497-x |
Clemens Bannwart | |
24.01. | ||||
31.01. | ||||
07.02. |