Repository: Freie Universität Berlin, Math Department

Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces

Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Schütte, Christof (2020) Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces. Advances in Dynamics, Optimization and Computation . pp. 109-131.

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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.

Item Type:Article
Additional Information:Erschienen in: Advances in Dynamics, Optimization and Computation
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2742
Deposited By: Monika Drueck
Deposited On:15 Feb 2022 18:17
Last Modified:15 Feb 2022 18:17

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