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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf, Alexander Johannes Smola, Klaus‐Robert Müller

Neural Computation · 1998 · 8,176 citations

doi.org/10.1162/089976698300017467

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.

Cite this paper

Schölkopf, B., Smola, A. J., & Müller, K. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319. https://doi.org/10.1162/089976698300017467

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