Jump to ContentJump to Main Navigation
Semi-Supervised Learning$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

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: 23 September 2021

Discrete Regularization

Discrete Regularization

(p.236) (p.237) 13 Discrete Regularization
Semi-Supervised Learning

Zhou Dengyong

Schülkopf Bernhard

The MIT Press

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

MIT Press Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs, and if you can't find the answer there, please contact us.