Reduced-observable dynamic mode decomposition for identifying theta and beta activity in working-memory EEG
The analysis of transient oscillatory activity in neural recordings remains challenging for linear methods, particularly when signals are nonlinear, noisy, and distributed across multiple channels. This paper introduces a Reduced-Observable Extended Dynamic Mode Decomposition (RO-eDMD) algorithm using a Random Fourier Features dictionary to characterize high-dimensional data in electroencephalography (EEG) recordings. The method extends the Koopman operator framework by incorporating rank reduction directly in the observable space and employing a randomized feature map that approximates the Gaussian kernel, enabling the capture of transient components without explicit dictionary optimization. To assess the method and demonstrate applicability, a logistic regression model is trained using a working memory paradigm as a test case, using dominant power values extracted via RO-eDMD in the theta band as a predictor and the type of event (encoding vs.\ fixation) as the dependent variable. We find correlations between oscillatory power and memory encoding events in the analyzed bands. Additionally, we find an increase in correlation associated with theta power and memory load, replicating similar results in the literature. The presented algorithm offers a computationally efficient, interpretable framework applied to a working memory paradigm dataset, but is relevant to the analysis of neural time series from diverse experimental contexts.