Learning Manifolds with K-Means and K-Flats
Abstract
We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for k-means in two separate directions. First, we provide new results for k-means reconstruction on manifolds and, secondly, we prove reconstruction bounds for higher-order approximation (k-flats), for which no known results were previously available. While the results for k-means are novel, some of the technical tools are well-established in the literature. In the case of k-flats, both the results and the mathematical tools are new.
Cite
Text
Canas et al. "Learning Manifolds with K-Means and K-Flats." Neural Information Processing Systems, 2012.Markdown
[Canas et al. "Learning Manifolds with K-Means and K-Flats." Neural Information Processing Systems, 2012.](https://mlanthology.org/neurips/2012/canas2012neurips-learning/)BibTeX
@inproceedings{canas2012neurips-learning,
title = {{Learning Manifolds with K-Means and K-Flats}},
author = {Canas, Guillermo and Poggio, Tomaso and Rosasco, Lorenzo},
booktitle = {Neural Information Processing Systems},
year = {2012},
pages = {2465-2473},
url = {https://mlanthology.org/neurips/2012/canas2012neurips-learning/}
}