Data Dialogue Seminar
Thursday, November 3, 2016, 11:45am, Gross 330
David Levin (Tel Aviv University)
Approximating manifolds in high dimensions

Abstract:

We propose a method for approximating a d-dimensional smooth submanifold M residing in R^n (d << n) based upon noisy scattered measurements (i.e., a data cloud). It is assumed that the data points are located near M, and we present a non-linear moving least-squares projection procedure constructing the approximating d-dimensional manifold. Under some mild assumptions, the resulting approximation is shown to be infinitely smooth and of high approximation order, i.e., O(h^{m+1}), where h is the fill distance and m is the degree of a local polynomial approximation

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