Learning manifolds with k-means and k-flats
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Poggio_learning manifolds.pdf
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675.32 KB
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Author(s)
Canas, Guillermo D.
Poggio, Tomaso A.
Rosasco, Lorenzo Andrea
Date Issued
February 2013
Journal
Advances in Neural Information Processing Systems (NIPS)
Publisher
Neural Information Processing Systems Foundation
Citation
Canas, Guillermo D., Tomaso Poggio, and Lorenzo A. Rosasco. "Learning manifolds with k-means and k-flats." Advances in Neural Information Processing Systems 25 (NIPS 2012).
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Center for Biological & Computational Learning
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
McGovern Institute for Brain Research at MIT
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