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  Regularization on Discrete Spaces

Zhou, D., & Schölkopf, B. (2005). Regularization on Discrete Spaces. In W. Kropatsch, R. Sablatnig, & A. Hanbury (Eds.), Pattern Recognition: 27th DAGM Symposium, Vienna, Austria, August 31 - September 2, 2005 (pp. 361-368). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-D4C7-A Version Permalink: https://hdl.handle.net/21.11116/0000-0005-213E-1
Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F11550518_45.pdf (Publisher version)
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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: We consider the classification problem on a finite set of objects.
Some of them are labeled, and the task is to predict the labels of
the remaining unlabeled ones. Such an estimation problem is
generally referred to as transductive inference. It is well-known
that many meaningful inductive or supervised methods can be
derived from a regularization framework, which minimizes a loss
function plus a regularization term. In the same spirit, we
propose a general discrete regularization framework defined on
finite object sets, which can be thought of as the discrete
analogue of classical regularization theory. A family of
transductive inference schemes is then systemically derived from
the framework, including our earlier algorithm for transductive
inference, with which we obtained encouraging results on many
practical classification problems. The discrete regularization
framework is built on the discrete analysis and geometry developed
by ourselves, in which a number of discrete differential operators
of various orders are constructed, which can be thought of as the
discrete analogue of their counterparts in the continuous case.

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 Dates: 2005-08
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 3209
DOI: 10.1007/11550518_45
 Degree: -

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Title: 27th Annual Symposium of the German Association for Pattern Recognition (DAGM 2005)
Place of Event: Wien, Austria
Start-/End Date: 2005-08-31 - 2005-09-02

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Source 1

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Title: Pattern Recognition: 27th DAGM Symposium, Vienna, Austria, August 31 - September 2, 2005
Source Genre: Proceedings
 Creator(s):
Kropatsch, WG, Editor
Sablatnig, R, Editor
Hanbury, A, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 361 - 368 Identifier: ISBN: 978-3-540-28703-2

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 3663 Sequence Number: - Start / End Page: - Identifier: -