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

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-EAFE-C Version Permalink: https://hdl.handle.net/21.11116/0000-0002-8E6E-4

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Schölkopf, B^{1, 2}, Author
Smola, AJ, Author
Müller, K-R, Author

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1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497797
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794

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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 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.

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Dates: Published in Print: 1996-12

Publication Status: Published in print

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Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics

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Identifiers: Report Nr.: 44
BibTex Citekey: 1509

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Title: Technical Report of the Max Planck Institute for Biological Cybernetics

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Pages: - Volume / Issue: 44 Sequence Number: - Start / End Page: - Identifier: -