A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds
نویسندگان
چکیده
منابع مشابه
A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds
Given data points p0, . . . , pN on a closed submanifold M of R n and time instants 0 = t0 < t1 < . . . < tN = 1, we consider the problem of finding a curve γ on M that best approximates the data points at the given instants while being as “regular” as possible. Specifically, γ is expressed as the curve that minimizes the weighted sum of a sum-of-squares term penalizing the lack of fitting to t...
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We consider the minimization of a function defined on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradient descent (SGD) on M to an averaged iterate sequence with a robust and fast O(1/n) convergence rate. We then present an application of our...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2011
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-011-9091-7