Topological data analysis

Topological Data Analysis (TDA) is a recent field that has enjoyed growing success in recent years. It aims to understand, analyze and exploit the topological and geometric structure of data, often represented by point clouds in Euclidean spaces or more general metric spaces. With the emergence of topological persistence theory, geometry and algorithmic topology have provided new and effective mathematical and algorithmic tools to tackle this subject. Combined with statistical methods, these tools have recently given rise to original applications and results in data analysis and statistical learning.