2023/2024

Research Seminar "Topological Data Analysis. Persistent Homology"

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Vasily Gorbounov

Language: English

ECTS credits: 6

Contact hours: 60

Course Syllabus

Abstract

"Topological Data Analysis (TDS) is a field that lies at the intersection of data analysis, algebraic topology, computational geometry, computer science, statistics, and other related areas. The main goal of TDA is to use ideas and results from geometry and topology to develop tools for studying qualitative features of data. To achieve this goal, one needs precise definitions of qualitative features, tools to compute them in practice, and some guaranteeabout the robustness of those features. One way to address all three points is a method in TDA called persistent homology (PH). This method is appealing for applications because it is based on algebraic topology, which gives a well-understood theoretical framework to study qualitative features of data with complex structure, is computable via linear algebra, and is robust with respect to small perturbations in input data. In the course, we will discuss the connections of PH to other new interesting areas, namely the path homology and random graphs."