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          Institute: MPI für biologische Kybernetik     Collection: Biologische Kybernetik     Display Documents



ID: 420064.0, MPI für biologische Kybernetik / Biologische Kybernetik
Learning with Transformation Invariant Kernels
Authors:Walder, C.; Chapelle, O.
Editors:Platt, J. C.; Koller, D.; Singer, Y.; Roweis, S.
Date of Publication (YYYY-MM-DD):2008-09
Title of Proceedings:Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference
Start Page:1561
End Page:1568
Physical Description:8
Audience:Not Specified
Intended Educational Use:No
Abstract / Description: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).
External Publication Status:published
Document Type:Conference-Paper
Communicated by:Holger Fischer
Affiliations:MPI f�r biologische Kybernetik/Empirical Inference (Dept. Sch�lkopf)
Identifiers:LOCALID:4736
URL:http://books.nips.cc/papers/files/nips20/NIPS2007_...
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