Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf, Alexander Smola, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

6278 Citations (Scopus)


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
Issue number5
Publication statusPublished - 1998 Jul 1

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


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