Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf, Alexander Smola, Klaus Muller

Research output: Contribution to journalArticle

5197 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 five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.

Original languageEnglish
Pages (from-to)1299-1319
Number of pages21
JournalNeural Computation
Volume10
Issue number5
Publication statusPublished - 1998 Jul 1
Externally publishedYes

Fingerprint

Principal component analysis
Pattern recognition
Mathematical operators
Feature extraction
Pixels
Polynomials
Principal Component Analysis
Kernel
Operator
Pattern Recognition
Principal Components
Feature Extraction

ASJC Scopus subject areas

  • Artificial Intelligence
  • Control and Systems Engineering
  • Neuroscience(all)

Cite this

Schölkopf, B., Smola, A., & Muller, K. (1998). Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation, 10(5), 1299-1319.

Nonlinear Component Analysis as a Kernel Eigenvalue Problem. / Schölkopf, Bernhard; Smola, Alexander; Muller, Klaus.

In: Neural Computation, Vol. 10, No. 5, 01.07.1998, p. 1299-1319.

Research output: Contribution to journalArticle

Schölkopf, B, Smola, A & Muller, K 1998, 'Nonlinear Component Analysis as a Kernel Eigenvalue Problem', Neural Computation, vol. 10, no. 5, pp. 1299-1319.
Schölkopf B, Smola A, Muller K. Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation. 1998 Jul 1;10(5):1299-1319.
Schölkopf, Bernhard ; Smola, Alexander ; Muller, Klaus. / Nonlinear Component Analysis as a Kernel Eigenvalue Problem. In: Neural Computation. 1998 ; Vol. 10, No. 5. pp. 1299-1319.
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