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NECO
1998

Nonlinear Component Analysis as a Kernel Eigenvalue Problem

13 years 3 months ago
Nonlinear Component Analysis as a Kernel Eigenvalue Problem
We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can e ciently 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 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 rst experimental results on nonlinear feature extraction for pattern recognition. AS and KRM are with GMDFirst (Forschungszentrum Informationstechnik), Rudower Chaussee 5, 12489 Berlin. AS and BS were supported by grants from the Studienstiftung des deutschen Volkes. BS thanks the GMD First for hospitality during two visits. AS and BS thank V. Vapnik for introducing them to kernel representations of dot products during joint work on Support Vector machines. This work pro ted from discussions with V. Blanz, ...
Bernhard Schölkopf, Alex J. Smola, Klaus-Robe
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where NECO
Authors Bernhard Schölkopf, Alex J. Smola, Klaus-Robert Müller
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