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Learning with Transformation Invariant Kernels

2008

Conference Paper

ei


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).

Author(s): Walder, C. and Chapelle, O.
Book Title: Advances in neural information processing systems 20
Journal: Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007
Pages: 1561-1568
Year: 2008
Month: September
Day: 0
Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis
Publisher: Curran

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007)
Event Place: Vancouver, BC, Canada

Address: Red Hook, NY, USA
Digital: 0
ISBN: 978-1-605-60352-0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{4736,
  title = {Learning with Transformation Invariant Kernels},
  author = {Walder, C. and Chapelle, O.},
  journal = {Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007},
  booktitle = {Advances in neural information processing systems 20},
  pages = {1561-1568},
  editors = {Platt, J. C., D. Koller, Y. Singer, S. Roweis},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  month = sep,
  year = {2008},
  month_numeric = {9}
}