Topological Methods in Data Analysis - Journal Club (Summer 2020)
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.
In case of questions, do not hesitate to contact us, the organizers of this Journal Club, via mail at structures-hiwi@mathi.uni-heidelberg.de.
Coordinates and Organization
Time: Tuesdays
even weeks: 16.15h to 17.45h
odd weeks: 17.00h to 18.00h(ish)
Location: Zoom meeting-ID: 830 4593 4507. Please get in touch with us to receive the password.
Organizers: Michael Bleher, Maximilian Schmahl, Daniel Spitz. Mail: structures-hiwi@mathi.uni-heidelberg.de.
Material and recordings are available on MaMpf, the mathematical media platform of Heidelberg university. Having registered from in- or outside Heidelberg university, you can find the Journal Club under the rubric interdisciplinary events.
Schedule
| Date | Topic | Info | Speaker | Slides |
|---|---|---|---|---|
| 21.04. | Test-run | This meeting will be dedicated to testing the technical setup with heiCONF and to discuss ideas for giving talks from home.
Feel free to join us - we would also be happy to use the opportunity and collect input from you! |
Daniel Spitz, Maximilian Schmahl & Michael Bleher | |
| 28.04. | Introduction and Organization | Maximilian Schmahl | Notes | |
| 05.05. 17h | Bauer: Ripser (Computing Barcodes for Persistent Homology Quickly) | https://arxiv.org/abs/1908.02518 | Maximilian Schmahl | Notes |
| 12.05. | Bardin, Spreemann, Hess: Topological exploration of artificial neuronal network dynamics | ArXiv: 1810.01747 | Aljosa | Slides |
| 19.05. 17h | Edelsbrunner, Wagner: Topological data analysis with Bregman divergences | ArXiv: 1607.06274 | Máté | |
| 26.05. | Chan, Carlsson & Rabadan: Topology of viral evolution | PNAS November 12, 2013 110 (46) 18566-18571 | Lukas | Slides |
| 02.06. 17h | Bauer & Edelsbrunner: The Morse theory of Čech and Delaunay complexes | Trans. Amer. Math. Soc. 369 (2017), 3741-3762 | Daniel Spitz | Slides |
| 09.06. | Zomorodian & Carlsson: Localized Homology | Computational Geometry 41, Nr. 3 (2008): 126–48 | Michael Bleher | Notes |
| 16.06.
17h |
--- | --- | --- | |
| 23.06. | --- | --- | --- | |
| 30.06.
17h |
Usher, Zhang: Persistent homology and Floer-Novikov theory | https://arxiv.org/abs/1502.07928 | Levin | Notes |
| 07.07. | A model category of tame parametrised chain complexes | Abstract: Persistent theory is a useful tool to extract information from real-world data sets, and profits of techniques from different mathematical disciplines, such as Morse theory and quiver representation. In this seminar, I am going to present a new approach for studying persistence theory using model categories. I will briefly introduce model categories and then describe how to define a model structure on the category of the tame parametrised chain complexes, which are chain complexes that evolve in time, describing why such an approach can be useful in topological data analysis. In particular, I will use the model category structure to retrieve two invariants that extract homotopical and homological information from any tame parametrised chain complex. | Barbara Giunti (University of Modena) | |
| 14.07.
17h |
Niyogi, Smale & Weinberger: Finding the Homology of Submanifolds with High Confidence from Random Samples | Discrete & Computational Geometry 39 (2008): 419–441 | Ruth | |
| 21.07. |
Further reading
For somewhat more details and introductory material on topological data analysis we refer to the literature section of this Wiki, which can be found here.