Nonlinear Component Analysis as a Kernel Eigenvalue Problem


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.

DOI: 10.1162/089976698300017467

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@article{Schlkopf1998NonlinearCA, title={Nonlinear Component Analysis as a Kernel Eigenvalue Problem}, author={Bernhard Sch{\"{o}lkopf and Alexander J. Smola and Klaus-Robert M{\"{u}ller}, journal={Neural Computation}, year={1998}, volume={10}, pages={1299-1319} }