Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Schölkopf, B; Smola, AJ; Müller, K-R

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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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Citation

Schölkopf, B., Smola, A., & Müller, K.-R.(1996). Nonlinear Component Analysis as a Kernel Eigenvalue Problem (44). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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

Abstract

We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we 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 5-pixel products in 16 x 16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.