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Semi-Supervised Learning$
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Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien

Print publication date: 2006

Print ISBN-13: 9780262033589

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262033589.001.0001

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PRINTED FROM MIT PRESS SCHOLARSHIP ONLINE (www.mitpress.universitypressscholarship.com). (c) Copyright The MIT Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use.date: 16 September 2021

Discrete Regularization

Discrete Regularization

Chapter:
(p.236) (p.237) 13 Discrete Regularization
Source:
Semi-Supervised Learning
Author(s):

Zhou Dengyong

Schülkopf Bernhard

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262033589.003.0013

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.

Keywords:   systemic framework, differential operators, graph Laplacian-based approaches, learning from finite sets, pairwise relationships, graph theory

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