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.
| Author(s): | Schölkopf, B. and Smola, AJ. and Müller, K-R. |
| Links: | |
| Journal: | Neural Computation |
| Volume: | 10 |
| Number (issue): | 5 |
| Pages: | 1299-1319 |
| Year: | 1998 |
| Month: | July |
| Day: | 0 |
| BibTeX Type: | Article (article) |
| DOI: | 10.1162/089976698300017467 |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@article{730,
title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem},
journal = {Neural Computation},
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.},
volume = {10},
number = {5},
pages = {1299-1319},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
month = jul,
year = {1998},
author = {Sch{\"o}lkopf, B. and Smola, AJ. and M{\"u}ller, K-R.},
doi = {10.1162/089976698300017467},
month_numeric = {7}
}