Kernel PCA and De-Noising in Feature Spaces
Abstract
Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be con(cid:173) sidered as a natural generalization of linear principal component anal(cid:173) ysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by ker(cid:173) nel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approxi(cid:173) mate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.
Cite
Text
Mika et al. "Kernel PCA and De-Noising in Feature Spaces." Neural Information Processing Systems, 1998.Markdown
[Mika et al. "Kernel PCA and De-Noising in Feature Spaces." Neural Information Processing Systems, 1998.](https://mlanthology.org/neurips/1998/mika1998neurips-kernel/)BibTeX
@inproceedings{mika1998neurips-kernel,
title = {{Kernel PCA and De-Noising in Feature Spaces}},
author = {Mika, Sebastian and Schölkopf, Bernhard and Smola, Alex J. and Müller, Klaus-Robert and Scholz, Matthias and Rätsch, Gunnar},
booktitle = {Neural Information Processing Systems},
year = {1998},
pages = {536-542},
url = {https://mlanthology.org/neurips/1998/mika1998neurips-kernel/}
}