TY - GEN
T1 - Koopman Spectral Kernels for Comparing Complex Dynamics
T2 - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2017
AU - Fujii, Keisuke
AU - Inaba, Yuki
AU - Kawahara, Yoshinobu
N1 - Funding Information:
Acknowledgements. 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.
Publisher Copyright:
© 2017, Springer International Publishing AG.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-319-71273-4_11
DO - 10.1007/978-3-319-71273-4_11
M3 - Conference contribution
AN - SCOPUS:85040258077
SN - 9783319712727
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 127
EP - 139
BT - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2017, Proceedings
A2 - Ceci, Michelangelo
A2 - Dzeroski, Saso
A2 - Malerba, Donato
A2 - Altun, Yasemin
A2 - Das, Kamalika
A2 - Read, Jesse
A2 - Zitnik, Marinka
A2 - Stefanowski, Jerzy
A2 - Mielikäinen, Taneli
PB - Springer Verlag
Y2 - 18 September 2017 through 22 September 2017
ER -