Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Schölkopf, B; Smola, AJ; Müller, K-R

doi:10.1162/089976698300017467

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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

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Schölkopf, B
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://www.mitpressjournals.org/doi/10.1162/089976698300017467
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Schölkopf, B., Smola, A., & Müller, K.-R. (1998). Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural computation, 10(5), 1299-1319. doi:10.1162/089976698300017467.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E845-9

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.