Skip to main content

Algorithmic Foundations of Geometry Understanding in Higher Dimensions

Final Report Summary - GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions)

The central goal of the project has been to settle the algorithmic foundations of Topological Data Analysis (TDA).

The need to understand geometric structures is ubiquitous in science and has become an essential part of scientific computing and data analysis. Many applications in physics, biology, and engineering involve a variety of higher dimensional spaces such as phase space in particle physics, invariant manifolds in dynamical systems, configuration spaces of mechanical systems, energy landscapes of molecules.

Understanding the geometry of such spaces faces many challenges addressed in the GUDHI project : choosing appropriate representations of highly non-linear shapes, bypassing the curse of dimensionality, inferring stable properties from data, and providing software that scale with real applications. We developed in particular data structures and algorithms for simplicial complexes, non-linear manifold learning, persistent homology, geometric and topological inference, and produced a state-of-the-art open source software library named GUDHI.