Club Exco: clustering brain extreme communities from multi-channel EEG data

Current methods for clustering nodes over time in a brain network are determined by cross-dependence measures, which are computed from the entire range of values of the electroencephalogram (EEG) signals, from low to high amplitudes. We here developed the Club Exco method for clustering brain communities that exhibit synchronized extreme behaviors. To cluster multi-channel EEG data, Club-Exco uses a spherical $k$-means procedure applied to the ``pseudo-angles,'' derived from extreme absolute amplitudes of EEG signals. With this approach, a cluster center is considered an ``extremal prototype,'' revealing a community of EEG nodes sharing the same extreme behavior, a feature that traditional methods fail to identify. Hence, Club Exco serves as an exploratory tool to classify EEG channels into mutually asymptotically dependent or asymptotically independent groups. It provides insights into how the brain network organizes itself during an extreme event (e.g., an epileptic seizure) in contrast to a baseline state. We apply the Club Exco method to investigate temporal differences in EEG brain connectivity networks of a patient diagnosed with epilepsy, a chronic neurological disorder affecting more than 50 million people globally. Our extreme-value method reveals substantial differences in alpha (8--12 Hertz) oscillations across the brain network compared to coherence-based methods.