Kernel PCA and de-noising in feature spaces

Sebastian Mika, Bernhard Schölkopf, Alex Smola, Klaus Robert Müller, Matthias Scholz, Gunnar Rätsch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

618 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 11 - Proceedings of the 1998 Conference, NIPS 1998
PublisherNeural information processing systems foundation
Pages536-542
Number of pages7
ISBN (Print)0262112450, 9780262112451
Publication statusPublished - 1999
Externally publishedYes
Event12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United States
Duration: 1998 Nov 301998 Dec 5

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Other

Other12th Annual Conference on Neural Information Processing Systems, NIPS 1998
CountryUnited States
CityDenver, CO
Period98/11/3098/12/5

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Mika, S., Schölkopf, B., Smola, A., Müller, K. R., Scholz, M., & Rätsch, G. (1999). Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems 11 - Proceedings of the 1998 Conference, NIPS 1998 (pp. 536-542). (Advances in Neural Information Processing Systems). Neural information processing systems foundation.