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  Discrete Regularization

Zhou, D., & Schölkopf, B. (2006). Discrete Regularization. In O. Chapelle, B. Schölkopf, & A. Zien (Eds.), Semi-Supervised Learning (pp. 237-250). Cambridge, MA, USA: MIT Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-CF91-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-9CED-2
Genre: Book Chapter

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 Creators:
Zhou, D1, 2, Author              
Schölkopf, B1, 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: This chapter presents a systemic framework for learning from a finite set represented as a graph. Discrete analogues are developed here of a number of differential operators, and then a discrete analogue of classical regularization theory is constructed based on those discrete differential operators. The graph Laplacian-based approaches are special cases of this general discrete regularization framework. More importantly, new approaches based on other different differential operators are derived as well. A variety of approaches for learning from finite sets has been proposed from different motivations and for different problems. In most of those approaches, a finite set is modeled as a graph, in which the edges encode pairwise relationships among the objects in the set. Consequently many concepts and methods from graph theory are applied, in particular, graph Laplacians.

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 Dates: 2006
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 3789
DOI: 10.7551/mitpress/9780262033589.003.0013
 Degree: -

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Title: Semi-Supervised Learning
Source Genre: Book
 Creator(s):
Chapelle, O1, Editor            
Schölkopf, B1, Editor            
Zien, A1, Editor            
Affiliations:
1 Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794            
Publ. Info: Cambridge, MA, USA : MIT Press
Pages: 508 Volume / Issue: - Sequence Number: 13 Start / End Page: 237 - 250 Identifier: ISBN: 0-262-03358-5