Nonlinear component analysis as a kernel eigenvalue problem

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Nonlinear component analysis as a kernel eigenvalue problem (1996)

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by Bernhard Schölkopf , Alexander Smola , Klaus-Robert Müller

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Citations:	1572 - 83 self

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@MISC{Schölkopf96nonlinearcomponent,
    author = {Bernhard Schölkopf and Alexander Smola and Klaus-Robert Müller},
    title = {Nonlinear component analysis as a kernel eigenvalue problem},
    year = {1996}
}

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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 16x16 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.

Keyphrases

kernel eigenvalue problem nonlinear component analysis possible 5-pixel product pattern recognition new method nonlinear form high-dimensional feature space integral operator kernel function nonlinear map first experimental result principal component principal component analysis kernel approach nonlinear feature extraction

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