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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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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: http://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.