Editing Holonomy (section)

====Machine Learning====
Computing the holonomy of Riemannian manifolds has been suggested as a way to learn the structure of data manifolds in [[machine learning]], in particular in the context of [[manifold learning]]. As the holonomy group contains information about the global structure of the data manifold, it can be used to identify how the data manifold might decompose into a product of submanifolds. The holonomy cannot be computed exactly due to finite sampling effects, but it is possible to construct a numerical approximation using ideas from [[spectral graph theory]] similar to Vector Diffusion Maps. The resulting algorithm, the Geometric Manifold Component Estimator ({{Smallcaps|GeoManCEr}}) gives a numerical approximation to the de Rham decomposition that can be applied to real-world data.<ref>{{citation |last1=Pfau |first1=David |last2=Higgins |first2=Irina |last3=Botev |first3=Aleksandar |last4=Racanière |first4=Sébastien |title=Disentangling by Subspace Diffusion |journal=Advances in Neural Information Processing Systems |date=2020 |arxiv=2006.12982}}</ref>