Ricci Curvature and the Manifold Learning Problem

2014/10/13 by Ache, Antonio G., Warren, Micah W. · 1 citation
#58J35 #68T05 #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1410.3351

Abstract

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

Cited by

• Curvature of high-dimensional data

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