Empirische Inferenz Technical Report 2000

The Kernel Trick for Distances

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 normbased distances in Hilbert spaces. It turns out that 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.
Number (issue): MSR-TR-2000-51
Year: 2000
Day: 0
Bibtex Type: Technical Report (techreport)
Digital: 0
Electronic Archiving: grant_archive
Institution: Microsoft Research, Redmond, WA, USA
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@techreport{1839,
  title = {The Kernel Trick for Distances},
  abstract = {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 normbased distances in Hilbert spaces. It turns out that 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.},
  number = {MSR-TR-2000-51},
  organization = {Max-Planck-Gesellschaft},
  institution = {Microsoft Research, Redmond, WA, USA},
  school = {Biologische Kybernetik},
  year = {2000},
  slug = {1839},
  author = {Sch{\"o}lkopf, B.}
}