Search results for "high dimensional approximation"

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Approximation of functions over manifolds : A Moving Least-Squares approach

2021

We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. We use the Manifold Moving Least-Squares approach of (Sober and Levin 2016) to reconstruct the atlas of charts and the approximation is built on-top of those charts. The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold. In other words, given a new point, located near the manifold, the approximation can be evaluated…

Computational Geometry (cs.CG)FOS: Computer and information sciencesComputer Science - Machine LearningClosed manifolddimension reductionMachine Learning (stat.ML)010103 numerical & computational mathematicsComplex dimensionTopology01 natural sciencesMachine Learning (cs.LG)Volume formComputer Science - GraphicsStatistics - Machine Learningmanifold learningApplied mathematics0101 mathematicsfunktiotMathematicsManifold alignmentAtlas (topology)Applied Mathematicshigh dimensional approximationManifoldGraphics (cs.GR)Statistical manifold010101 applied mathematicsregression over manifoldsComputational Mathematicsout-of-sample extensionComputer Science - Computational Geometrynumeerinen analyysimonistotapproksimointimoving least-squaresCenter manifold
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