2024/2025
Research Seminar "Topological Data Analysis"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Instructors:
Vasily Gorbounov
Language:
English
ECTS credits:
6
Course Syllabus
Abstract
Topological Data Analysis (TDA) is a field that lies at the intersection of data analysis, algebraictopology, computational geometry, computer science, statistics, and other related areas. The main goal of TDAis to use ideas and results from geometry and topology to develop tools for studying qualitative features ofdata. To achieve this goal, one needs precise definitions of qualitative features, tools to compute them inpractice, and some guaranteeabout the robustness of those features. One way to address all three points is amethod in TDA called persistent homology (PH). This method is appealing for applications because it is basedon algebraic topology, which gives a well-understood theoretical framework to study qualitative features ofdata with complex structure, is computable via linear algebra, and is robust with respect to small perturbationsin input data
Course Contents
- Simplicial complexes.
- Homologies of simplicial complexes.
- Theory of persistent modules.
- Persistent homologies of a filtered simplicial complex.
- Persistent Laplacian.
- Stability of persistent homology and persistent Laplacian.
Interim Assessment
- 2024/2025 4th moduleThe mark will be calculated based on the exam and a talk given in the course or a project with the software for calculation of persistent homology
