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

    773 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
    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
    Country/TerritoryUnited States
    CityDenver, CO
    Period98/11/3098/12/5

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Information Systems
    • Signal Processing

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