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  From Graphs to Manifolds: Weak and Strong Pointwise Consistency of Graph Laplacians

Hein, M., Audibert, J., & von Luxburg, U. (2005). From Graphs to Manifolds: Weak and Strong Pointwise Consistency of Graph Laplacians. In P. Auer, & R. Meir (Eds.), Learning Theory: 18th Annual Conference on Learning Theory, COLT 2005, Bertinoro, Italy, June 27-30, 2005 (pp. 470-485). Berlin, Germany: Springer.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D6D7-0 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-38C8-B
Genre: Conference Paper

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 Creators:
Hein, M1, 2, Author              
Audibert, J, Author
von Luxburg, U, 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: In the machine learning community it is generally believed that graph Laplacians corresponding to a finite sample of data points converge to a continuous Laplace operator if the sample size increases. Even though this assertion serves as a justification for many Laplacian-based algorithms, so far only some aspects of this claim have been rigorously proved. In this paper we close this gap by establishing the strong pointwise consistency of a family of graph Laplacians with data-dependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of R^d.

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 Dates: 2005-06
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 3213
 Degree: -

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Title: 18th Annual Conference on Learning Theory (COLT 2005)
Place of Event: Bertinoro, Italy
Start-/End Date: 2005-06-27 - 2005-06-30

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Source 1

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Title: Learning Theory: 18th Annual Conference on Learning Theory, COLT 2005, Bertinoro, Italy, June 27-30, 2005
Source Genre: Proceedings
 Creator(s):
Auer, P, Editor
Meir, R, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 470 - 485 Identifier: ISBN: 978-3-540-26556-6

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Title: Lecture Notes in Computer Scienc
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 3559 Sequence Number: - Start / End Page: - Identifier: -