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  Learning with Transformation Invariant Kernels

Walder, C., & Chapelle, O. (2008). Learning with Transformation Invariant Kernels. In C. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007 (pp. 1561-1568). Red Hook, NY, USA: Curran.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C749-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-389F-C
Genre: Conference Paper

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 Creators:
Walder, C1, 2, 3, Author              
Chapelle, O, Author              
Affiliations:
1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
3Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_2528702              

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 Abstract: This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d. case and provide some novel analysis, including an elementary derivation of a c.p.d. representer theorem. On the practical side, we give a support vector machine (s.v.m.) algorithm for arbitrary c.p.d. kernels. For the thinplate kernel this leads to a classifier with only one parameter (the amount of regularisation), which we demonstrate to be as effective as an s.v.m. with the Gaussian kernel, even though the Gaussian involves a second parameter (the length scale).

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Language(s):
 Dates: 2008-09
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 4736
 Degree: -

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Title: Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2007-12-03 - 2007-12-06

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Title: Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007
Source Genre: Proceedings
 Creator(s):
Platt, C, Editor
Koller, D, Editor
Singer, Y, Editor
Roweis, ST, Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1561 - 1568 Identifier: ISBN: 978-1-605-60352-0