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