Spatial Neighboring Scattering Transform: A Cross-Channel Amplitude Coupling Measure for EEG Connectivity

Md. Taksimul Ahsan Tawhid, Nasif Ahmed Rafe, Alif Tahmid Priyom, K. M. Mustafizur Rahman

The functional organization of the brain relies on coordinated activity across spatially distributed regions, making the analysis of inter-regional dependencies fundamental. Existing connectivity measures address this predominantly through phase synchronization, which is vulnerable to volume conduction artifacts and discards amplitude-domain coupling. This study introduces the Spatial Neighboring Scattering Transform, which extends the wavelet scattering transform to the multichannel setting, yielding two descriptors that jointly capture amplitude-envelope coupling between channels and its modulation across frequency scales. SNST was evaluated on the BCI Competition IV-2a motor imagery dataset using a bias-corrected, false-discovery-rate-controlled statistical pipeline, with the validation criterion defined as spatial consistency of significant coupling across subjects. The first-order descriptor identified statistically significant amplitude coupling within a central-parietal electrode neighborhood, reproduced consistently across all subjects and both imagery conditions. The second-order descriptor revealed that this coupling is periodically gated by slow rhythms, indicating a cross-frequency amplitude-modulation structure absent from single-frequency connectivity measures. Phase lag index and weighted phase lag index, computed under an identical correction procedure and verified robust to volume conduction, identified negligible significant coupling with zero overlap with SNST findings, demonstrating that amplitude envelope coupling constitutes a largely distinct connectivity signal. These results establish SNST as a cross-channel scattering-based connectivity descriptor that recovers amplitude-envelope and cross-frequency coupling structure systematically, applicable to any multichannel EEG analysis where amplitude-domain inter-regional dependence is of interest.