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A diffusion-map-based algorithm for gradient computation on manifolds and applications. (arXiv:2108.06988v3 [cs.LG] UPDATED)
cs.LG updates on arXiv.org arxiv.org
We recover the Riemannian gradient of a given function defined on interior
points of a Riemannian submanifold in the Euclidean space based on a sample of
function evaluations at points in the submanifold. This approach is based on
the estimates of the Laplace-Beltrami operator proposed in the diffusion-maps
theory. The Riemannian gradient estimates do not involve differential terms.
Analytical convergence results of the Riemannian gradient expansion are proved.
We apply the Riemannian gradient estimate in a gradient-based algorithm
providing a …