Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf; Alexander Smola; Klaus Robert Müller

doi:10.1162/089976698300017467

Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf, Alexander Smola, Klaus Robert Müller

Research output: Contribution to journal › Article › peer-review

6278 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 language	English
Pages (from-to)	1299-1319
Number of pages	21
Journal	Neural Computation
Volume	10
Issue number	5
DOIs	https://doi.org/10.1162/089976698300017467
Publication status	Published - 1998 Jul 1

ASJC Scopus subject areas

Arts and Humanities (miscellaneous)
Cognitive Neuroscience

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10.1162/089976698300017467

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AB - 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.

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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Abstract

ASJC Scopus subject areas

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