Topological Data Analysis 2018
Every Monday (13:30–14:50) in room 379 at the Faculty of Mechanics and Mathematics.
Every Monday (15:05–16:25) in room 113/379 at the Faculty of Mechanics and Mathematics.
Monday, 28 May 2018 at 13:30 in lecture room 379 at the Faculty of Mechanics and Mathematics.
In the Lecture Course we shall cover the following topics:
1. Data representation.
2. Metrics, Hausdorff distance.
3. Simplices, complexes.
4. Building simplicial complexes from data. Clustering.
5. Cech complex and Vietoris-Rips complex.
6. Nerve of a cover.
7. The Mapper algorithm.
8. Reeb graph.
9. Simplicial homology groups, Betti numbers.
11. Persistent homology.
12. Persistent modules and persistence diagrams.
13. Metrics on the space of persistence diagrams.
14. Persistent homology and machine learning.
Textbooks and Other Materials
The course will be based on the following textbooks:
1. H. Edelsbrunner, J. Harer. Computational Topology: An Introduction. AMS Press, 2009.
2. Jean-Daniel Boissonnat Fr´ed´eric Chazal Mariette Yvinec, Geometric and Topological Inference, August 17, 2017