Kernel PCA and De-noising in feature spaces

Mika, S; Schölkopf, B; Smola, AJ; Müller, KR; Scholz, M; Rätsch, G

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Kernel PCA and De-noising in feature spaces

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https://papers.nips.cc/paper/1491-kernel-pca-and-de-noising-in-feature-spaces.pdf
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Mika, S., Schölkopf, B., Smola, A., Müller, K., Scholz, M., & Rätsch, G. (1999). Kernel PCA and De-noising in feature spaces. Advances in Neural Information Processing Systems 11, 536-542.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E699-C

Abstract

Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis.
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 kernel PCA live in some high dimensional feature space and need not have
pre-images in input space. This work presents ideas for finding approximate 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.