Kernels, pre-images and optimization

John C. Snyder, Sebastian Mika, Kieron Burke, Klaus Robert Müller

    Research output: Chapter in Book/Report/Conference proceedingChapter

    9 Citations (Scopus)

    Abstract

    In the last decade, kernel-based learning has become a state-of-the-art technology in Machine Learning. We briefly review kernel PCAKernel principal component analysis (kPCA) (kPCA) and the pre-image problem that occurs in kPCA. Subsequently, we discuss a novel direction where kernel-based models are used for property optimization. For this purpose, a stable estimation of the model’s gradient is essential and non-trivial to achieve. The appropriate use of pre-image projections is key to successful gradient-based optimization—as will be shown for toy and real-world problems from quantum chemistry and physics.

    Original languageEnglish
    Title of host publicationEmpirical Inference
    Subtitle of host publicationFestschrift in Honor of Vladimir N. Vapnik
    PublisherSpringer Berlin Heidelberg
    Pages245-259
    Number of pages15
    ISBN (Electronic)9783642411366
    ISBN (Print)9783642411359
    DOIs
    Publication statusPublished - 2013 Jan 1

    Bibliographical note

    Publisher Copyright:
    © Springer-Verlag Berlin Heidelberg 2013.

    ASJC Scopus subject areas

    • General Computer Science

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