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Stochastics and Statistics Seminar

# Fitting a putative manifold to noisy data

## May 25, 2018 @ 11:00 am - 12:00 pm

Hariharan Narayanan (Tata Institute of Fundamental Research, Mumbai)

E18-304

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** Abstract: **We give a solution to the following question from manifold learning.

Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded compact manifold *M*, and is corrupted by a small amount of i.i.d gaussian noise. How can we produce a manifold *M* whose Hausdorff distance to *M* is small and whose reach (normal injectivity radius) is not much smaller than the reach of *M*?

This is joint work with Charles Fefferman, Sergei Ivanov, Yaroslav Kurylev, and Matti Lassas.

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