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, 247–257.
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.
Comparison of Classical EEG Source Analysis with Deep Learning
Winkler, Jakob; Uhl, Christian; Geißelsöder, Stefan; Erdbrügger, Tim; Wolters, Carsten (2025)
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, 258–267.
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.
Dynamical Component Analysis (DyCA) Python Code
Stiehl, Annika; Uhl, Christian (2024)
Open Access
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
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.
Comparison of Classical EEG Source Analysis with Deep Learning
Winkler, Jakob; Uhl, Christian; Geißelsöder, Stefan; Erdbrügger, Tim; Wolters, Carsten (2024)
Winkler, Jakob; Uhl, Christian; Geißelsöder, Stefan; Erdbrügger, Tim...
Vortrag auf APCA International Conference on Automatic Control and Soft Computing (CONTROLO 2024) 2024.
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.
Comparison of Mode Selection and Reconstructions Obtained by DyCA and DMD with Respect to Noise Robustness and Sampling
Stiehl, Annika; Weeger, Nicolas; Uhl, Christian (2024)
Vortrag auf APCA International Conference on Automatic Control and Soft Computing (CONTROLO 2024) 2024.
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.
Signal analysis and classification of interictal epileptiform discharges from EEG with machine learning
Stiehl, Annika; Geißelsöder, Stefan; Anselstetter, Fabienne; Bornfleth, Harald; Ille, Nicole; Uhl, Christian (2023)
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
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; Geißelsöder, Stefan; Uhl, Christian (2023)
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
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; Geißelsöder, Stefan; Uhl, Christian (2022)
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
Dimension reduction methods, persistent homology ans machine learning for EEG signal analysis of Interictal Epileptic Discharges
Stiehl, Annika; Geißelsöder, Stefan; Ille, Nicole; Anselstetter, Fabienne; Bornfleth, Harald; Uhl, Christian (2022)
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
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
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
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
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.
Prof. Dr. Christian Uhl
Hochschule Ansbach
Hochschule Ansbach - Fakultät Technik
Residenzstr. 8
91522 Ansbach
T 0981 4877-251 christian.uhl[at]hs-ansbach.de