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Diffusion Curvature for Estimating Local Curvature in High Dimensional Data
[article]
2022
arXiv
pre-print
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic
arXiv:2206.03977v1
fatcat:ulva4dtedffnpn6vqccll33b5u