A Physiologically Guided, Model-Based Framework for Multichannel EEG
EEG signals are multichannel recordings of underlying neural activity observed at the scalp. Since channels reflect spatial projections of common latent sources, they should not be treated as independent time series. This makes EEG a natural setting for multichannel models combining temporal flexibility and physiologically meaningful spatial structure. We study structural restrictions for the multichannel Frequency-Modulated Möbius (FMM) model from its 3D interpretation, where each component is viewed as an oscillatory trajectory observed across channels. In EEG, short time windows are often dominated by sources with approximately fixed orientation. Motivated by this, we propose a reduced-rank formulation in which the block of channel-specific linear coefficients of each component has rank one. The resulting model is more parsimonious, preserves interpretability, and provides a source-oriented framework for EEG decomposition and feature extraction.
Keywords: Multichannel EEG reduced-rank models interpretable signal decomposition Frequency-Modulated Möbius