Kernel principal component analysis

Bernhard Schölkopf; Alexander Smola; Klaus Robert Müller

doi:10.1007/bfb0020217

Kernel principal component analysis

Bernhard Schölkopf, Alexander Smola, Klaus Robert Müller

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1452 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 language	English
Title of host publication	Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings
Editors	Wulfram Gerstner, Alain Germond, Martin Hasler, Jean-Daniel Nicoud
Publisher	Springer Verlag
Pages	583-588
Number of pages	6
ISBN (Print)	3540636315, 9783540636311
DOIs	https://doi.org/10.1007/bfb0020217
Publication status	Published - 1997
Event	7th International Conference on Artificial Neural Networks, ICANN 1997 - Lausanne, Switzerland Duration: 1997 Oct 8 → 1997 Oct 10

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1327
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Conference on Artificial Neural Networks, ICANN 1997
Country/Territory	Switzerland
City	Lausanne
Period	97/10/8 → 97/10/10

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/bfb0020217

Cite this

Schölkopf, B., Smola, A., & Müller, K. R. (1997). Kernel principal component analysis. In W. Gerstner, A. Germond, M. Hasler, & J.-D. Nicoud (Eds.), Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings (pp. 583-588). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1327). Springer Verlag. https://doi.org/10.1007/bfb0020217

Kernel principal component analysis. / Schölkopf, Bernhard; Smola, Alexander; Müller, Klaus Robert.
Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings. ed. / Wulfram Gerstner; Alain Germond; Martin Hasler; Jean-Daniel Nicoud. 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 proceeding › Conference contribution

Schölkopf, B, Smola, A & Müller, KR 1997, Kernel principal component analysis. in W Gerstner, A Germond, M Hasler & J-D Nicoud (eds), Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings. 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. https://doi.org/10.1007/bfb0020217

Schölkopf B, Smola A, Müller KR. Kernel principal component analysis. In Gerstner W, Germond A, Hasler M, Nicoud JD, editors, Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings. Springer Verlag. 1997. p. 583-588. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/bfb0020217

Schölkopf, Bernhard ; Smola, Alexander ; Müller, Klaus Robert. / Kernel principal component analysis. Artificial Neural Networks - ICANN 1997 - 7th International Conference, Proceeedings. editor / Wulfram Gerstner ; Alain Germond ; Martin Hasler ; Jean-Daniel Nicoud. 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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Kernel principal component analysis

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