Input Space Regularization Stabilizes Pre-images for Kernel PCA De-noising

Trine Julie Abrahamsen, Lars Kai Hansen

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    Abstract

    Solution of the pre-image problem is key to efficient nonlinear de-noising using kernel Principal Component Analysis. Pre-image estimation is inherently ill-posed for typical kernels used in applications and consequently the most widely used estimation schemes lack stability. For de-noising applications we propose input space distance regularization as a stabilizer for pre-image estimation. We perform extensive experiments on the USPS digit modeling problem to evaluate the stability of three widely used pre-image estimators. We show that the previous methods lack stability when the feature mapping is non-linear, however, by applying a simple input space distance regularizer we can reduce variability with very limited sacrifice in terms of de-noising efficiency.
    Original languageEnglish
    Title of host publicationIEEE International Workshop on Machine Learning for Signal Processing, 2009. MLSP 2009.
    PublisherIEEE
    Publication date2009
    Pages1-6
    ISBN (Print)978-1-4244-4947-7
    DOIs
    Publication statusPublished - 2009
    Event2009 IEEE International Workshop on Machine Learning for Signal Processing - Grenoble, France
    Duration: 2 Sep 20094 Sep 2009
    http://mlsp2009.conwiz.dk/

    Workshop

    Workshop2009 IEEE International Workshop on Machine Learning for Signal Processing
    CountryFrance
    CityGrenoble
    Period02/09/200904/09/2009
    Internet address

    Bibliographical note

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    Keywords

    • De-noising
    • Kernel PCA
    • Pre-image

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