263-4510-00L  Introduction to Topological Data Analysis

Courses

Catalogue data

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.
Competencies	Subject-specific Competencies Concepts and Theories assessed Techniques and Technologies assessed Method-specific Competencies Analytical Competencies assessed Problem-solving assessed Project Management fostered Social Competencies Communication assessed Cooperation and Teamwork fostered Self-presentation and Social Influence fostered Personal Competencies Creative Thinking fostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits	8 credits
Examiners	P. Schnider
Type	session examination
Language of examination	English
Repetition	The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination	oral 30 minutes
Additional information on mode of examination	60% final oral exam: 30 minutes oral exam with 30 minutes preparation time (no material allowed) plus two graded homework (20% each). The two mandatory graded homework (compulsory continuous performance assessments) will be released throughout the semester, at specific dates that will be announced. Each graded homework will have a deadline two weeks after the release. The solutions must be typeset in LaTeX (or similar).
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Groups

Restrictions

Offered in

Programme	Section	Type
CAS in Computer Science	Focus Courses and Electives	W
Cyber Security Master	Elective Courses	W
Data Science Master	Subject-Specific Electives	W
Data Science Master	Core Electives	W
Computer Science Master	Elective Courses	W
Computer Science Master	Minor in Theoretical Computer Science	W
Mathematics Bachelor	Selection: Further Realms and Some UZH Courses	W
Mathematics Master	Recognised in the Spring Semester 2024 (!) for Mathematics Master	W