Uniform Convergence of Adaptive Graph-Based Regularization

Hein, M

doi:10.1007/11776420_7

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Uniform Convergence of Adaptive Graph-Based Regularization

Hein, M. (2006). Uniform Convergence of Adaptive Graph-Based Regularization. In G. Lugosi, & H. Simon (Eds.), Learning Theory: 19th Annual Conference on Learning Theory, COLT 2006, Pittsburgh, PA, USA, June 22-25, 2006 (pp. 50-64). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-D05B-D Version Permalink: https://hdl.handle.net/21.11116/0000-0004-9AAA-F

Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F11776420_7.pdf (Publisher version) Open Access status unknown

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Creators:
Hein, M^{1, 2}, Author

Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794

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Abstract: The regularization functional induced by the graph Laplacian of a random
neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying
manifold structure and second to the density of the data-generating probability measure.
We identify in this paper the limit of the regularizer and show
uniform convergence over the space of Hoelder functions. As an intermediate
step we derive upper bounds on the covering numbers of Hoelder functions on
compact Riemannian manifolds, which are of independent interest
for the theoretical analysis of manifold-based learning methods.

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Dates: Date issued: 2006-09

Publication Status: Issued

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Identifiers: DOI: 10.1007/11776420_7
BibTex Citekey: 3893

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Title: 19th Annual Conference on Learning Theory (COLT 2006)

Place of Event: Pittsburgh, PA, USA

Start-/End Date: 2006-06-22 - 2006-06-25

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Title: Learning Theory: 19th Annual Conference on Learning Theory, COLT 2006, Pittsburgh, PA, USA, June 22-25, 2006

Source Genre: Proceedings

Creator(s):
Lugosi, G, Editor
Simon, HU, Editor

Affiliations:
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Publ. Info: Berlin, Germany : Springer

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 50 - 64 Identifier: ISBN: 978-3-540-35294-5