Séminaire Stéphanois de Mathématiques Accessibles

How topology can be used to quantify the intrinsic geometry of data

by Christian Lehn (TU Chemnitz, GER)

Salle C 112 (UJM Campus Métare)

Salle C 112

UJM Campus Métare

Faculté des Sciences et Techniques 23 rue du Docteur Paul Michelon 42000 SAINT-ETIENNE

Abstract: Topological data analysis is a relatively new field whose goal is to extract information from data by topological methods. The basic philosophy is that data has an inherent geometry, it has "shape", and this shape carries information that we would like to quantify. The goal is to make this hidden information visible using algebraic topology. In a joint work with S. Kalisnik and V. Limic we put forward some aspects of the probabilistic foundations of the theory in order to make it more useful for statistical applications.



basic topology: topological space, metric space, knowledge of homology is a psychological advantage, but not necessary to be able to follow. (I will briefly explain what I need)

basic algebra: field, group, vector spaces

basic probability theory and analysis: measure, random variable, Banach space, completion