263-4510-00L Introduction to Topological Data Analysis
| Semester | Spring Semester 2023 |
| Lecturers | P. Schnider |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| Abstract | Topological Data Analysis (TDA) is a relatively new subfield of computer sciences, which uses techniques from algebraic topology and computational geometry and topology to analyze and quantify the shape of data. This course will introduce the theoretical foundations of TDA. | |||||||||||||||||||||||||||
| Learning objective | The goal is to make students familiar with the fundamental concepts, techniques and results in TDA. At the end of the course, students should be able to read and understand current research papers and have the necessary background knowledge to apply methods from TDA to other projects. | |||||||||||||||||||||||||||
| Content | Mathematical background (Topology, Simplicial complexes, Homology), Persistent Homology, Complexes on point clouds (Čech complexes, Vietoris-Rips complexes, Delaunay complexes, Witness complexes), the TDA pipeline, Reeb Graphs, Mapper | |||||||||||||||||||||||||||
| Literature | Main reference: Tamal K. Dey, Yusu Wang: Computational Topology for Data Analysis, 2021 https://www.cs.purdue.edu/homes/tamaldey/book/CTDAbook/CTDAbook.html Other references: Herbert Edelsbrunner, John Harer: Computational Topology: An Introduction, American Mathematical Society, 2010 https://bookstore.ams.org/mbk-69 Gunnar Carlsson, Mikael Vejdemo-Johansson: Topological Data Analysis with Applications, Cambridge University Press, 2021 Link Robert Ghrist: Elementary Applied Topology, 2014 https://www2.math.upenn.edu/~ghrist/notes.html Allen Hatcher: Algebraic Topology, Cambridge University Press, 2002 https://pi.math.cornell.edu/~hatcher/AT/ATpage.html | |||||||||||||||||||||||||||
| Prerequisites / Notice | The course assumes knowledge of discrete mathematics, algorithms and data structures and linear algebra, as supplied in the first semesters of Bachelor Studies at ETH. | |||||||||||||||||||||||||||
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