Kernels, pre-images and optimization

John C. Snyder, Sebastian Mika, Kieron Burke, Klaus Muller

Research output: Chapter in Book/Report/Conference proceedingChapter

6 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: Festschrift in Honor of Vladimir N. Vapnik
PublisherSpringer Berlin Heidelberg
Pages245-259
Number of pages15
ISBN (Print)9783642411366, 9783642411359
DOIs
Publication statusPublished - 2013 Jan 1

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Principal component analysis
Quantum chemistry
Learning systems
Physics

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Snyder, J. C., Mika, S., Burke, K., & Muller, K. (2013). Kernels, pre-images and optimization. In Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik (pp. 245-259). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-41136-6_21

Kernels, pre-images and optimization. / Snyder, John C.; Mika, Sebastian; Burke, Kieron; Muller, Klaus.

Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik. Springer Berlin Heidelberg, 2013. p. 245-259.

Research output: Chapter in Book/Report/Conference proceedingChapter

Snyder, JC, Mika, S, Burke, K & Muller, K 2013, Kernels, pre-images and optimization. in Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik. Springer Berlin Heidelberg, pp. 245-259. https://doi.org/10.1007/978-3-642-41136-6_21
Snyder JC, Mika S, Burke K, Muller K. Kernels, pre-images and optimization. In Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik. Springer Berlin Heidelberg. 2013. p. 245-259 https://doi.org/10.1007/978-3-642-41136-6_21
Snyder, John C. ; Mika, Sebastian ; Burke, Kieron ; Muller, Klaus. / Kernels, pre-images and optimization. Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik. Springer Berlin Heidelberg, 2013. pp. 245-259
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