Learning manifolds with k-means and k-flats

TitleLearning manifolds with k-means and k-flats
Publication TypeConference Paper
Year of Publication2012
AuthorsCanas, GD, Poggio, T, Rosasco, L
Conference NameAdvances in Neural Information Processing Systems 25 (NIPS 2012)
Date Published12/2012

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.


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