@conference {4886,
	title = {Learning manifolds with k-means and k-flats},
	booktitle = {Advances in Neural Information Processing Systems 25 (NIPS 2012)},
	year = {2012},
	month = {12/2012},
	abstract = {<p>We study the problem of estimating a manifold from random samples. In partic- ular, 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.</p>
},
	url = {https://papers.nips.cc/paper/2012/hash/b20bb95ab626d93fd976af958fbc61ba-Abstract.html},
	author = {Guillermo D. Canas and Tomaso Poggio and Lorenzo Rosasco}
}
