https://doi.org/10.1140/epjs/s11734-025-01911-6
Regular Article
A continuous and robust version of dynamical component analysis
1
Center for Signal Analysis of Complex Systems, University of Applied Sciences Ansbach, Residenzstr. 8, 91522, Ansbach, Bavaria, Germany
2
Institute of Mathematics, Julius-Maximilians-Universität Würzburg, Emil-Fischer-Str. 30, 97074, Würzburg, Bavaria, Germany
a
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Received:
15
April
2025
Accepted:
1
September
2025
Published online:
12
September
2025
Abstract
Dynamical component analysis (DyCA) is a method for decomposing high-dimensional time-series data into meaningful spatial modes and time-dependent amplitudes governed by underlying dynamical equations. Its classical formulation works well in the presence of component noise, but lacks robustness in scenarios with additive noise or incomplete data sets. To address this, we introduce a continuous and robust variational approach to DyCA, embedding it within a unified variational denoising and reconstruction framework. Our approach couples DyCA’s least-squares minimization with 
-based regularization, enabling simultaneous data reconstruction and extraction of dynamical components. The mathematical foundations of our method are established by proving the existence of minimizers and ensuring well-posedness of the underlying operator equations. Numerical experiments on EEG recordings of absence epilepsy show that DyCA is a suitable tool for seizure detection and that robust DyCA effectively recovers the underlying dynamic structure from severely corrupted data sets.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
