Invitation to Topological Data Analysis
Summer Term 2022Modern topology has found its way through computations into applications. In this lecture we will discuss basic tools of topological data analysis: homology and persistent homology theory, discrete Morse theory, Reeb graphs and mapper algorithms and more. In particular, a number of applications of those techniques will be highlighted. We will show how those methods can be integrated with statistics and machine learning. By doing so will lay down solid theoretical foundations and learn to use the techniques in practice.
Prior knowledge of algebraic topology is desired. Ability to program in Python or R is required.
LectureFridays 12:00 - 13:30
MIMUW, room 5840
LabsFridays 14:00 - 15:30
Davide Gurnari, Niklas Hellmer
MIMUW, room 3045
- Herbert Edelsbrunner and John Harer, Computational Topology, an introduction, AMS 2011.
- Paweł Dłotko, Applied and computational topology Tutorial, arXiv
- Mischaikow, Kaczynski, Mrozek, Computational Topology, Springer 2004.
- Gudhi library: gudhi.inria.fr