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  Learning with Transformation Invariant Kernels

Walder, C., & Chapelle, O.(2007). Learning with Transformation Invariant Kernels (165). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-CC0D-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-1DCE-6
Genre: Report

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MPIK-TR-165.pdf (Publisher version), 362KB
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 Creators:
Walder, C1, 2, Author              
Chapelle, O, Author              
Affiliations:
1Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
2Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497795              

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 Abstract: 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 thin-plate 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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 Dates: 2007-09
 Publication Status: Published in print
 Pages: 12
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Identifiers: Report Nr.: 165
BibTex Citekey: 4737
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
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Pages: - Volume / Issue: 165 Sequence Number: - Start / End Page: - Identifier: -