Grouped Successive Multivariate Variational Mode Decomposition with Application to EEG Signal Processing and Connectivity Analysis

The traditional multivariate signal decomposition algorithm presumes that the multi-channel signal has co-frequency components. However, in real signals, the frequencies of these components are not precisely aligned and exhibit some differences. This paper introduces a novel multi-channel signal processing algorithm, termed Grouped Successive Multivariate Variational Mode Decomposition (GSMVMD). GSMVMD adopts a unique grouped expansion strategy to produce more effective co-frequencies, while we have also improved the algorithm frame-work by combining successive extraction strategy. GSMVMD first uses channel-by-channel Variational Mode Decomposition (VMD) to determine the center frequency of each channel, and then performs frequency-grouped normalization. Subsequently, a variational optimization model is established based on the grouped results, and the optimal solution for GSMVMD model is obtained using the Alternate Direction Method of Multipliers (ADMM). Finally, we conduct experiments using multi-channel electroencephalogram (EEG) signals as an example to verify the superiority of the GSMVMD algorithm, and design a Grouped Standard Deviation of degree (GSD) parameters to measure the connectivity between EEG channels, providing a new analytical perspective.