Fitting a Putative Manifold to Noisy Data

Charles Fefferman, Sergei Ivanov, Yaroslav Kurylev, Matti Lassas, Hariharan Narayanan
Proceedings of the 31st Conference On Learning Theory, PMLR 75:688-720, 2018.

Abstract

In the present work, 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 manifold $M$, and corrupted by a small amount of gaussian noise. How can we produce a manifold $M’$ whose Hausdorff distance to $M$ is small and whose reach is not much smaller than the reach of $M$?

Cite this Paper

BibTeX
@InProceedings{pmlr-v75-fefferman18a, title = {Fitting a Putative Manifold to Noisy Data}, author = {Fefferman, Charles and Ivanov, Sergei and Kurylev, Yaroslav and Lassas, Matti and Narayanan, Hariharan}, booktitle = {Proceedings of the 31st Conference On Learning Theory}, pages = {688--720}, year = {2018}, editor = {Bubeck, Sébastien and Perchet, Vianney and Rigollet, Philippe}, volume = {75}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v75/fefferman18a/fefferman18a.pdf}, url = {https://proceedings.mlr.press/v75/fefferman18a.html}, abstract = {In the present work, 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 manifold $M$, and corrupted by a small amount of gaussian noise. How can we produce a manifold $M’$ whose Hausdorff distance to $M$ is small and whose reach is not much smaller than the reach of $M$?} }
Endnote
%0 Conference Paper %T Fitting a Putative Manifold to Noisy Data %A Charles Fefferman %A Sergei Ivanov %A Yaroslav Kurylev %A Matti Lassas %A Hariharan Narayanan %B Proceedings of the 31st Conference On Learning Theory %C Proceedings of Machine Learning Research %D 2018 %E Sébastien Bubeck %E Vianney Perchet %E Philippe Rigollet %F pmlr-v75-fefferman18a %I PMLR %P 688--720 %U https://proceedings.mlr.press/v75/fefferman18a.html %V 75 %X In the present work, 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 manifold $M$, and corrupted by a small amount of gaussian noise. How can we produce a manifold $M’$ whose Hausdorff distance to $M$ is small and whose reach is not much smaller than the reach of $M$?
APA
Fefferman, C., Ivanov, S., Kurylev, Y., Lassas, M. & Narayanan, H.. (2018). Fitting a Putative Manifold to Noisy Data. Proceedings of the 31st Conference On Learning Theory, in Proceedings of Machine Learning Research 75:688-720 Available from https://proceedings.mlr.press/v75/fefferman18a.html.

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