Topological Methods in Data Analysis - Journal Club (Winter 2021/22)

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.