A short introduction to persistent homology for data analysis

Topological Data Analysis (TDA) is a relatively recent field whose goal is to explore and leverage the structure of complex data. With the emergence of persistent homology theory, geometry and topology have provided new mathematical and statistical tools that are both powerful and efficient for addressing these challenges. In this talk, we will present the main questions that arise when trying to understand the global topological structure of data and we will introduce persistent homology, a mathematical tools that make it possible to construct robust descriptors of data topology and to study their properties. If time permits, we will discuss and illustrate through a few concrete examples the relevance of topological approaches for data analysis and machine learning.