Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf; Alexander J. Smola; Klaus‐Robert Müller · Neural Computation · 1998

Resource page

Quick overview. Review the resource’s basic details, then access the content using the main button. This page shows only the information needed to identify, cite, and open the work.

Author / responsible party

Bernhard Schölkopf; Alexander J. Smola; Klaus‐Robert Müller

Publisher

Neural Computation

Year

1998

Language

English

Resource access

Open the content from the main option or choose another available source.

OpenAlex OpenAlex Works

Entrar por OpenAlex

Main access

Resource page

Resource reference page. Full text availability has not been automatically confirmed.

Open resource

Summary

Descripción general del contenido del recurso.

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.

How to cite

Elegí el formato que necesitás y copiá la referencia al portapapeles.

APA 7

Schölkopf, B, Smola, A. J, & Müller, K. (1998). Nonlinear Component Analysis as a Kernel Eigenvalue Problem. https://doi.org/10.1162/089976698300017467

MLA

Schölkopf, Bernhard, et al. "Nonlinear Component Analysis as a Kernel Eigenvalue Problem." 1998. https://doi.org/10.1162/089976698300017467.

Chicago

Schölkopf, Bernhard, Alexander J. Smola, and Klaus‐Robert Müller. 1998. "Nonlinear Component Analysis as a Kernel Eigenvalue Problem.". https://doi.org/10.1162/089976698300017467.

Harvard

Schölkopf, B, Smola, A. J. and Müller, K. 1998, Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, available at: https://doi.org/10.1162/089976698300017467 [Accessed 7 Aug. 2026].

Share and print

Save the record, copy its permanent link, or print it as a PDF.

Export reference

You can export the record in common formats for use in a reference manager.

RIS BibTeX

Resource details

Bibliographic information to help confirm that this is the correct material.

Title: Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Author / contributors: Bernhard Schölkopf; Alexander J. Smola; Klaus‐Robert Müller

Publisher: Neural Computation

Publication year: 1998

Language: English

Subjects

Explore related resources through these subjects.

Kernel principal component analysis; Principal component analysis; Eigenvalues and eigenvectors; Nonlinear system; Kernel (algebra); Mathematics; Pattern recognition (psychology); Pixel; Polynomial; Artificial intelligence; Kernel method; Polynomial kernel