Nonlinear Component Analysis as a Kernel Eigenvalue Problem
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.
Cite
Text
Schölkopf et al. "Nonlinear Component Analysis as a Kernel Eigenvalue Problem." Neural Computation, 1998. doi:10.1162/089976698300017467Markdown
[Schölkopf et al. "Nonlinear Component Analysis as a Kernel Eigenvalue Problem." Neural Computation, 1998.](https://mlanthology.org/neco/1998/scholkopf1998neco-nonlinear/) doi:10.1162/089976698300017467BibTeX
@article{scholkopf1998neco-nonlinear,
title = {{Nonlinear Component Analysis as a Kernel Eigenvalue Problem}},
author = {Schölkopf, Bernhard and Smola, Alexander J. and Müller, Klaus-Robert},
journal = {Neural Computation},
year = {1998},
pages = {1299-1319},
doi = {10.1162/089976698300017467},
volume = {10},
url = {https://mlanthology.org/neco/1998/scholkopf1998neco-nonlinear/}
}