Learning manifolds with k-means and k-flats
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 resu...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Neural Information Processing Systems Foundation
2014
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| Online Access: | http://hdl.handle.net/1721.1/92317 https://orcid.org/0000-0002-3944-0455 https://orcid.org/0000-0001-6376-4786 |
| Summary: | 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. |
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