  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.
