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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

1996

Technical Report

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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5-pixel products in 16 x 16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.

Author(s): Schölkopf, B. and Smola, AJ. and Müller, K-R.
Number (issue): 44
Year: 1996
Month: December
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: Max Planck Institute for Biological Cybernetics Tübingen

Digital: 0
Note: This technical report has also been <a href="/main/publication.php?machwas=view_e&edit_lfnr=730">published elsewhere</a>
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

BibTex

@techreport{1509,
  title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem},
  author = {Sch{\"o}lkopf, B. and Smola, AJ. and M{\"u}ller, K-R.},
  number = {44},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max Planck Institute for Biological Cybernetics Tübingen},
  school = {Biologische Kybernetik},
  month = dec,
  year = {1996},
  note = {This technical report has also been <a href="/main/publication.php?machwas=view_e&edit_lfnr=730">published elsewhere</a>},
  month_numeric = {12}
}