Abstract
In this paper, the methods of principal component analysis (PCA) and dynamical component analysis (DyCA) are investigated in the application of sparse identification of nonlinear dynamics (SINDy) on high-dimensional simulated and real-world data. Since SINDy requires low-dimensional data, high-dimensional data has to be reduced in a preprocessing step. This can be done using dimension reduction methods such as PCA or DyCA. SINDy is applied to these low-dimensional signals and the performance is examined with respect to these methods. Investigated datasets consist of the Rössler attractor and measured EEG data of epileptic seizures. The results demonstrate the advantage of DyCA as a preprocessing step to eliminate component noise in data governed by a certain type of differential equations.
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Acknowledgments
We thank the German Federal Ministry of Education and Research (BMBF, Funding number: 05M20WBA) for financial support and the Epilepsy Centre at the Department of Neurology, Universitätsklinikum Erlangen for providing the EEG data.
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Paglia, C., Stiehl, A., Uhl, C. (2022). Identification of Low-Dimensional Nonlinear Dynamics from High-Dimensional Simulated and Real-World Data. In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. https://doi.org/10.1007/978-3-031-10047-5_18
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