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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… Click to show full abstract
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 Carre du Champ for diffusion semi-groups, the theory of Empirical processes and local Principal Component Analysis.
Keywords:
ricci curvature;
learning problem;
curvature manifold;
manifold learning;
curvature
Journal Title: Advances in Mathematics
Year Published: 2019
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Journal Title: Advances in Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!