Topological Data Analysis

Instructor: Vincent Divol

PariSantéCampus, January-March

Topological data analysis (TDA) consists in a set of methods used to extract meaningful topological and geometric features from complex datasets. The purpose of this course is to review the main concepts and methods used in TDA. We will first focus on shape reconstruction methods in low-dimensional settings (3D) by exhibiting practical algorithms with theoretical guarantees. We will then introduce persistent homology, a powerful tool that captures in a quantative way the topology of a given dataset. We will see on several examples how incorporating topological methods in a machine learning pipeline can be used to improve its efficiency (e.g. in computational biology or for graph classification).

Content: dimensionality reduction, reconstruction of sets with positive reach, simplicial complexes (Delaunay, Rips, Cech), homology, persistent homology, statistics and machine learning with persistence diagrams