Uncovering relationships in multi-channel EEG data using principal Hessian directions and Ricci flow

Objective.The high-dimensional nature of multi-channel EEG data poses major challenges for downstream classification. Uncovering connectivity relationships and network structure between EEG channels can improve high-dimensional EEG signal recovery by identifying redundant inputs and guiding more targeted feature selection. In this study, we aim to demonstrate a systematic framework for extracting useful interchannel structure in EEG data.Approach.We present two complementary methods for inferring network structure and connectivity in EEG data: (1) a new supervised algorithm for inferring classification-relevant community structure based on principal Hessian directions (pHds), and (2) a discrete Ricci flow-based unsupervised community detection algorithm. We demonstrate these systematic methods on high-dimensional real-world EEG datasets involving classifying imagined digits versus non-digits and detecting emotional valence.Main results.We show that our pHd and Ricci flow methods-when combined-can detect interchannel relationships that meaningfully hold on unseen test classification data. Moreover, we demonstrate that this interchannel structure extracted via pHd and Ricci flow can enable subsequent improvements in downstream EEG signal classification.Significance.Our combined pHd-Ricci flow method expands the existing EEG preprocessing toolkit by offering a systematic framework for extracting meaningful network structure from high-dimensional EEG data. By facilitating more targeted and effective feature selection, our method has the potential to improve EEG signal recovery in real-world applications.