Kernel principal component analysis

Bernhard Schölkopf, Alexander Smola, Klaus Muller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

702 Citations (Scopus)

Abstract

A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one 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 d-pixel products in images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages583-588
Number of pages6
Volume1327
ISBN (Print)3540636315, 9783540636311
Publication statusPublished - 1997
Externally publishedYes
Event7th International Conference on Artificial Neural Networks, ICANN 1997 - Lausanne, Switzerland
Duration: 1997 Oct 81997 Oct 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1327
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Conference on Artificial Neural Networks, ICANN 1997
CountrySwitzerland
CityLausanne
Period97/10/897/10/10

Fingerprint

Kernel Principal Component Analysis
Principal component analysis
Pattern recognition
Mathematical operators
Feature extraction
Pixels
Polynomials
Nonlinear Map
Principal Components
Kernel Function
Feature Space
Integral Operator
Principal Component Analysis
Feature Extraction
Pattern Recognition
High-dimensional
Pixel
Polynomial
Experimental Results
Form

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Schölkopf, B., Smola, A., & Muller, K. (1997). Kernel principal component analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1327, pp. 583-588). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1327). Springer Verlag.

Kernel principal component analysis. / Schölkopf, Bernhard; Smola, Alexander; Muller, Klaus.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1327 Springer Verlag, 1997. p. 583-588 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1327).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Schölkopf, B, Smola, A & Muller, K 1997, Kernel principal component analysis. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1327, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1327, Springer Verlag, pp. 583-588, 7th International Conference on Artificial Neural Networks, ICANN 1997, Lausanne, Switzerland, 97/10/8.
Schölkopf B, Smola A, Muller K. Kernel principal component analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1327. Springer Verlag. 1997. p. 583-588. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Schölkopf, Bernhard ; Smola, Alexander ; Muller, Klaus. / Kernel principal component analysis. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1327 Springer Verlag, 1997. pp. 583-588 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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