Spatiotemporal Feature Extraction with Data-Driven Koopman Operators

Dimitrios Giannakis, Joanna Slawinska, Zhizhen Zhao

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

Abstract

We present a framework for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. Unlike feature extraction techniques based on kernel operators, our approach is to construct feature maps using eigenfunctions of the Koopman group of unitary operators governing the dynamical evolution of observables and probability measures. We compute the eigenvalues and eigenfunctions of the Koopman group through a Galerkin scheme applied to time-ordered data without requiring a priori knowledge of the dynamical evolution equations. This scheme employs a data-driven set of basis functions on the state space manifold, computed through the diffusion maps algorithm and a variable-bandwidth kernel designed to enforce orthogonality with respect to the invariant measure of the dynamics. The features extracted via this approach have strong timescale separation, favorable predictability properties, and high smoothness on the state space manifold. The extracted features are also invariant under weakly restrictive changes of observation modality. We apply this scheme to a synthetic dataset featuring superimposed traveling waves in a one-dimensional periodic domain and satellite observations of organized convection in the tropical atmosphere.
Original languageEnglish (US)
Title of host publicationProceedings of the 1st International Workshop on Feature Extraction: Modern Questions and Challenges at NIPS 2015
EditorsDmitry Storcheus, Afshin Rostamizadeh, Sanjiv Kumar
Place of PublicationMontreal
PublisherPMLR
Pages103-115
Number of pages13
Volume44
StatePublished - Nov 1 2015
Externally publishedYes

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR

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  • Cite this

    Giannakis, D., Slawinska, J., & Zhao, Z. (2015). Spatiotemporal Feature Extraction with Data-Driven Koopman Operators. In D. Storcheus, A. Rostamizadeh, & S. Kumar (Eds.), Proceedings of the 1st International Workshop on Feature Extraction: Modern Questions and Challenges at NIPS 2015 (Vol. 44, pp. 103-115). (Proceedings of Machine Learning Research). PMLR. http://proceedings.mlr.press/v44/giannakis15.html