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Asymptotically Optimal Method for Manifold Estimation Problem

P. 325-325.
Bernstein A., Kuleshov A. P., Yanovich Y.

Let X be an unknown nonlinear smooth q-dimensional Data manifold (D-manifold) embedded in a p-dimensional space (p> q) covered by a single coordinate chart. It is assumed that the manifold's condition number is positive so X has no self-intersections. Let Xn={X1, X2,..., Xn}⊂ X⊂ Rp be a sample randomly selected from the D-manifold Xindependently of each other according to an unknown probability measure on X with strictly positive density.

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Budapest: Bernoulli Society, 2013.