Fitting a Putative Manifold to Noisy Data
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
Text
Fefferman et al. "Fitting a Putative Manifold to Noisy Data." Annual Conference on Computational Learning Theory, 2018.Markdown
[Fefferman et al. "Fitting a Putative Manifold to Noisy Data." Annual Conference on Computational Learning Theory, 2018.](https://mlanthology.org/colt/2018/fefferman2018colt-fitting/)BibTeX
@inproceedings{fefferman2018colt-fitting,
title = {{Fitting a Putative Manifold to Noisy Data}},
author = {Fefferman, Charles and Ivanov, Sergei and Kurylev, Yaroslav and Lassas, Matti and Narayanan, Hariharan},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2018},
pages = {688-720},
url = {https://mlanthology.org/colt/2018/fefferman2018colt-fitting/}
}