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
@article{arxiv.1209.1121,
title = {Learning Manifolds with K-Means and K-Flats},
author = {Guillermo D. Canas and Tomaso Poggio and Lorenzo Rosasco},
journal= {arXiv preprint arXiv:1209.1121},
year = {2015}
}
Comments
19 pages, 2 figures; Advances in Neural Information Processing Systems, NIPS 2012