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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: http://hdl.handle.net/11858/00-001M-0000-0013-D05B-D Version Permalink: http://hdl.handle.net/21.11116/0000-0004-9AAA-F
Genre: Conference Paper

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 Creators:
Hein, M1, 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: 2006-09
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1007/11776420_7
BibTex Citekey: 3893
 Degree: -

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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:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 50 - 64 Identifier: ISBN: 978-3-540-35294-5