Kernel methods for detecting coherent structures in dynamical data

Stefan Klus, Brooke E. Husic, Mattes Mollenhauer, Frank Noé

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely, the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition called coherent mode decomposition. Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods.

Original languageEnglish
Article number123112
JournalChaos
Volume29
Issue number12
DOIs
Publication statusPublished - Dec 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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