A new entropy based summary function for topological data analysis

Abstract

Topological data analysis (TDA) aims to obtain useful information from data sets using topological concepts. In particular, it may help to infer from nite sample when a con guration space is a manifold. So far, there is no automatic process to decide the main topological features of a given sampled manifold. In this article, we present an entropy-based summary function which may help to decide the most relevant Betti numbers from nite samples of a given manifold.