3 years ago

# Ricci Curvature and the Manifold Learning Problem.

Antonio G. Ache, Micah W. Warren

Consider a sample of $n$ points taken i.i.d from a submanifold $\Sigma$ of Euclidean space. We show that there is a way to estimate the Ricci curvature of $\Sigma$ with respect to the induced metric from the sample. Our method is grounded in the notions of \emph{Carr\'{e} du Champ} for diffusion semi-groups, the theory of Empirical processes and local Principal Component Analysis.

Publisher URL: http://arxiv.org/abs/1410.3351

DOI: arXiv:1410.3351v3

You might also like
Never Miss Important Research

Researcher is an app designed by academics, for academics. Create a personalised feed in two minutes.
Choose from over 15,000 academics journals covering ten research areas then let Researcher deliver you papers tailored to your interests each day.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.