Singular value decomposition of operators on reproducing kernel Hilbert spaces

Mattes Mollenhauer, Ingmar Schuster, Stefan Klus*, Christof Schütte

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron–Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples.

Original languageEnglish
Title of host publicationAdvances in Dynamics, Optimization and Computation. SON 2020
PublisherSpringer
Pages109-131
Number of pages23
ISBN (Electronic)9783030512644
ISBN (Print)9783030512637
DOIs
Publication statusPublished - 2020

Publication series

NameStudies in Systems, Decision and Control
Volume304
ISSN (Print)2198-4182
ISSN (Electronic)2198-4190

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Control and Systems Engineering
  • Automotive Engineering
  • Social Sciences (miscellaneous)
  • Economics, Econometrics and Finance (miscellaneous)
  • Control and Optimization
  • Decision Sciences (miscellaneous)

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