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Comparison of Mode Selection and Reconstructions Obtained by DyCA and DMD with Respect to Noise Robustness and Sampling

Stiehl, Annika; Weeger, Nicolas; Uhl, Christian (2025)

In: Aguiar, A.P., Rocha Malonek, P., Pinto, V.H., Fontes, F.A.C.C., Chertovskih, R. (eds) CONTROLO 2024. CONTROLO 2024. Lecture Notes in Electrical Engineering, vol 1325. Springer 2025.
DOI: 10.1007/978-3-031-81724-3_23


Peer Reviewed
 

Dynamical Component Analysis (DyCA) and Dynamic Mode Decomposition (DMD), both data-driven dimension reduction methods, are introduced. After application to multivariate simulated signals the techniques of mode selection and the resulting amplitudes are compared with respect to noise robustness and sampling periods. The results indicate that DyCA is a useful alternative to DMD and outperforms DMD under certain conditions. These conditions are based on the underlying dynamics in the terms of differential equations and on the noise ratios of the signals.

mehr

Comparison of Classical EEG Source Analysis with Deep Learning

Winkler, Jakob; Uhl, Christian; Geißelsöder, Stefan; Erdbrügger, Tim...

In: Aguiar, A.P., Rocha Malonek, P., Pinto, V.H., Fontes, F.A.C.C., Chertovskih, R. (eds) CONTROLO 2024. CONTROLO 2024. Lecture Notes in Electrical Engineering, vol 1325. Springer 2025.
DOI: 10.1007/978-3-031-81724-3_24


Peer Reviewed
 

This paper discusses the challenges and methods for source reconstruction of evoked potentials using deep learning in the context of electroencephalography (EEG). We propose the use of deep learning to address known challenges and improve traditional approaches. We explain the creation of a suitable dataset for solving the inverse problem, including the simulation of neural activity and the use of lead field matrices for the forward solution. Furthermore, we undertake a comparative analysis of some initial deep learning models with similar classical methods.

mehr

Dynamical Component Analysis (DyCA) Python Code

Stiehl, Annika; Uhl, Christian (2024)


Open Access
mehr

DyCA and DMD: Differences and Similarities in Theory and Application

Uhl, Christian; Stiehl, Annika; Weeger, Nicolas (2024)

SIAM Conference on Mathematics of Data Science (MDS24) 2024.


Peer Reviewed

Disentangling dynamic and stochastic modes in multivariate time series

Uhl, Christian; Stiehl, Annika; Weeger, Nicolas; Schlarb, Markus; Hüper, Knut (2024)

Frontiers in Applied Mathematics and Statistics 10-2024.
DOI: 10.3389/fams.2024.1456635


Open Access Peer Reviewed
mehr

DyCA - Dynamical Component Analysis: Theory and Applications

Uhl, Christian (2024)

Physics Colloquium, Department of Pysics in partnership with Center of Complex Systems, Florida Atlantic University, Boca Raton, Florida, USA.



Cost Function Approach for Dynamical Component Analysis: Full Recovery of Mixing and State Matrix

Hüper, Knut; Schlarb, Markus; Uhl, Christian (2024)

Automation 2024, 5(3) | 360-372.
DOI: 10.3390/automation5030022


Open Access Peer Reviewed
 

A reformulation of the dynamical component analysis (DyCA) via an optimization-free approach is presented. The original cost function approach is converted into a numerical linear algebra problem, i.e., the computation of coupled singular-value decompositions. A simple algorithm is presented together with numerical experiments to document the feasability of the approach. This methodology is able to recover the mixing and state matrices of multivariate signals from high-dimensional measured data fully.

mehr

Signal analysis and classification of interictal epileptiform discharges from EEG with machine learning

Stiehl, Annika; Geißelsöder, Stefan; Anselstetter, Fabienne; Bornfleth, Harald...

BMT 2023, Abstracts of the 57th Annual Meeting of the German Society of Biomedical Engineering 26 – 28 September 2023, Duisburg 2023.
DOI: 10.1515/bmte-2023-2001


Open Access Peer Reviewed
mehr

Topological Analysis of Low Dimensional Phase Space Trajectories of High Dimensional EEG Signals For Classification of Interictal Epileptiform Discharges

Stiehl, Annika; Flammer, M; Anselstetter, Fabienne; Ille, Nicole; Bornfleth, Harald...

2023 IEEE International Conference on Acoustics, Speech, and Signal Processing Workshops (ICASSPW), Rhodes Island, Greece, 1-5.
DOI: 10.1109/ICASSPW59220.2023.10193167


Peer Reviewed
mehr

Robust Dynamical Component Analysis and its Application on Epileptic EEG and Motion Sense Data

Warmuth, Monika; Romberger, Philipp; Uhl, Christian; Hüper, Knut (2022)

Proceedings of the Workshop Biosignal 2022, August 24th - 26th, Dresden.



A Matrix Formulation of Dynamical Component Analysis (DyCA)

Romberger, Philipp; Warmuth, Monika; Uhl, Christian; Hüper, Knut (2022)

Proceedings of the Workshop Biosignal 2022, August 24th - 26th, Dresden .



Different montages and dimension reduction methods for EEG signal analysis of Interictal Epileptic Discharges

Stiehl, Annika; Anselstetter, Fabienne; Ille, Nicole; Bornfleth, Harald...

BMT 2022, Abstracts of the 2022 Joint Annual Conference of the Austrian (ÖGBMT), German (VDE DGBMT) and Swiss (SSBE)Societies for Biomedical Engineering 67 (S1), 88.
DOI: 10.1515/bmt-2022-2001


Open Access Peer Reviewed
mehr

Dimension reduction methods, persistent homology ans machine learning for EEG signal analysis of Interictal Epileptic Discharges

Stiehl, Annika; Geißelsöder, Stefan; Ille, Nicole; Anselstetter, Fabienne...

Proceedings of the Workshop Biosignale 2022 (24. - 26.08.2022).
DOI: 10.48550/arXiv.2502.12814


Peer Reviewed
mehr

Identification of Low-Dimensional Nonlinear Dynamics from High-Dimensional Simulated and Real-World Data

Paglia, Chiara; Stiehl, Annika; Uhl, Christian (2022)

CONTROLO 2022. Lecture Notes in Electrical Engineering 930, 205-213.
DOI: 10.1007/978-3-031-10047-5_18


Peer Reviewed
mehr

Dynamical Component Analysis: Matrix Case and Differential Geometric Point of View

Romberger, Philipp; Warmuth, Monika; Uhl, Christian; Hüper, Knut (2022)

CONTROLO 2022. Lecture Notes in Electrical Engineering 930, 385-394.
DOI: 10.1007/978-3-031-10047-5_34


Peer Reviewed
mehr

Dynamical Component Analysis: Updated and improved algorithm, applications, and limitations

Warmuth, Monika; Romberger, Philipp; Hüper, Knut; Uhl, Christian (2022)

Vortrag auf der International Conference on Time Series and Forecasting (ITISE) 2022, Gran Canaria, Spanien 2022.


Peer Reviewed

A Comparative Study of Dynamic Mode Decomposition (DMD) and Dynamical Component Analysis (DyCA)

Kern, Moritz; Uhl, Christian; Warmuth, Monika (2021)

CONTROLO 2020. Lecture Notes in Electrical Engineering 695, 93-103.
DOI: 10.1007/978-3-030-58653-9_9


Peer Reviewed
mehr

Dimension Reduction: from Principle Component Analysis (PCA) to Dynamical Component Analysis (DyCA)

Frühauf, Christine; Kern, Moritz; Korn, Katharina; Uhl, Christian (2020)

Ute Ambrosius und Patrick Gröner (Hg.): Ansbacher Kaleidoskop 2020. Düren: Shaker Verlag (campus_edition Hochschule Ansbach), 192-209.



Determinismus-Test von niedrigdimensionalen Signalen eingebettet in hochdimensionalen multivariaten Zeitreihen: Anwendung auf EEG-Daten

Frühauf, Christine; Hartmann, Steffen; Seifert, Bastian; Uhl, Christian (2020)

Workshop Biosignale 2020, Kiel, 11.03.2020.



Dimensionsreduktion von EEG-Daten mit Dynamical Component Analysis (DyCA)

Kern, Moritz; Korn, Katharina; Uhl, Christian (2020)

Workshop Biosignale 2020. Kiel, 11.03.2020.



Prof. Dr. Christian Uhl


Hochschule Ansbach

Hochschule Ansbach - Fakultät Technik
Residenzstr. 8
91522 Ansbach

T 0981 4877-251
christian.uhl[at]hs-ansbach.de