Abstract
High-dimensional multivariate time series often consist of a low-dimensional deterministic part. To extract this contribution it is crucial to reduce the dimension of the signal using a dimensionality reduction method. There are three possible approaches, which are compared in this paper: Takens’ delay embedding theorem, a combinatorial approach and projection approaches. After dimensionality reduction of the time-series, the Kaplan-Glass determinism test is applied to compare the obtained signals with respect to deterministic behavior. All introduced methods are applied to simulated noisy data and to EEG data during and out of epileptic seizures.
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References
D.T. Kaplan, L. Glass, Direct test for determinism in a time series. Phys. Rev. Lett. 68(4), 427–430 (1992)
F. Takens, in Dynamical Systems and Turbulence, Warwick, 1980, ed. by D.A. Rand, L.S. Young (Springer, 1981), p. 366
K. Pearson, On lines and planes of closest fit to a system of points in space. The London, Edinburgh, and Dublin Philos. Mag. J. Sci. 6(2), 559–572 (1901)
A. Hyvärinen, E. Oja, Independent component analysis: algorithms and applications. Neural Netw. 13(4–5), 411–430 (2000)
B. Seifert, K. Korn, S. Hartmann, C. Uhl, Dynamical component analysis (DyCA): dimensionality reduction for high-dimensional deterministic time-series, in Proceedings of the IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP 2018)
A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33(2), 1134–1140 (1986)
E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)
O.E. Rössler, An equation for continuous chaos. Phys. Lett. 57A(5), 397–398 (1976)
L. van Veen, D.T.J. Liley, Chaos via Shilnikov’s saddle-node bifurcation in a theory of the electroencephalogram. Phys. Rev. Lett. 97, 208101 (2006)
K. Korn, B. Seifert, C. Uhl, Dynamical component analysis (DYCA) and its application on epileptic EEG, ICASSP 2019, in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, United Kingdom (2019)
Acknowledgements
We thank the Epilepsy Centre at the Department of Neurology, Universitätsklinikum Erlangen for provided data and for fruitful ideas and discussions.
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Frühauf, C., Hartmann, S., Seifert, B., Uhl, C. (2020). Determinism Testing of Low-Dimensional Signals Embedded in High-Dimensional Multivariate Time Series. In: Stavrinides, S., Ozer, M. (eds) Chaos and Complex Systems. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-35441-1_1
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DOI: https://doi.org/10.1007/978-3-030-35441-1_1
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