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The Kernel Trick for Distances

2001

Conference Paper

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A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as norm-based distances in Hilbert spaces. It turns out that the common kernel algorithms, such as SVMs and kernel PCA, are actually really distance based algorithms and can be run with that class of kernels, too. As well as providing a useful new insight into how these algorithms work, the present work can form the basis for conceiving new algorithms.

Author(s): Schölkopf, B.
Book Title: Advances in Neural Information Processing Systems 13
Journal: Advances in Neural Information Processing Systems 13
Pages: 301-307
Year: 2001
Month: April
Day: 0
Editors: TK Leen and TG Dietterich and V Tresp
Publisher: MIT Press

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

Event Name: 14th Annual Neural Information Processing Systems Conference (NIPS 2000)
Event Place: Denver, CO, USA

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-12241-3
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{3781,
  title = {The Kernel Trick for Distances},
  author = {Sch{\"o}lkopf, B.},
  journal = {Advances in Neural Information Processing Systems 13},
  booktitle = {Advances in Neural Information Processing Systems 13},
  pages = {301-307},
  editors = {TK Leen and TG Dietterich and V Tresp},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = apr,
  year = {2001},
  month_numeric = {4}
}