Koopman Spectral Kernels for Comparing Complex Dynamics: Application to Multiagent Sport Plays

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10536)


Understanding the complex dynamics in the real-world such as in multi-agent behaviors is a challenge in numerous engineering and scientific fields. Spectral analysis using Koopman operators has been attracting attention as a way of obtaining a global modal description of a nonlinear dynamical system, without requiring explicit prior knowledge. However, when applying this to the comparison or classification of complex dynamics, it is necessary to incorporate the Koopman spectra of the dynamics into an appropriate metric. One way of implementing this is to design a kernel that reflects the dynamics via the spectra. In this paper, we introduced Koopman spectral kernels to compare the complex dynamics by generalizing the Binet-Cauchy kernel to nonlinear dynamical systems without specifying an underlying model. We applied this to strategic multiagent sport plays wherein the dynamics can be classified, e.g., by the success or failure of the shot. We mapped the latent dynamic characteristics of multiple attacker-defender distances to the feature space using our kernels and then evaluated the scorability of the play by using the features in different classification models.



We would like to thank Charlie Rohlf and the STATS team for their help and support for this work. This work was supported by JSPS KAKENHI Grant Numbers 16H01548.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Center for Advanced Intelligence Project, RIKENOsakaJapan
  2. 2.Japanese Institute of Sports SciencesTokyoJapan
  3. 3.The Institute of Scientific and Industrial Research, Osaka UniversityOsakaJapan

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