Kernels, pre-images and optimization

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

Research output: Chapter in Book/Report/Conference proceedingChapter

8 Citations (Scopus)


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
Number of pages15
ISBN (Electronic)9783642411366
ISBN (Print)9783642411359
Publication statusPublished - 2013 Jan 1

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013.

ASJC Scopus subject areas

  • Computer Science(all)


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