Higher-Order Interaction Analysis via Hypergraph Models for Studying Multidimensional Neuroscience Data.

Higher-Order Interaction (HOI) theory offers a powerful framework for capturing complex, non-linear relationships within multidimensional systems, moving beyond traditional pairwise graph methods to encompass multi-way interactions. This study applies HOI analysis, specifically using hypergraph theory, to explore intricate connectivity patterns in electrophysiological signals from neuroscience. Hypergraphs were constructed from connectivity data across various frequency bands, characterized through metrics such as spectral entropy, hyperedge centrality, and vertex centrality, and compared using spectral and centrality distance measures. Three distinct neurophysiological datasets were analyzed: intracranial EEG signals from rats during different sleep stages, scalp EEG data to distinguish between epilepsy types, and MEG recordings of seizure dynamics. The findings highlight the effectiveness of hypergraph-based HOI analysis in mapping neural dynamics across normal and pathological brain states. In sleep studies, it reveals distinct connectivity patterns between REM and NREM stages, while in epilepsy, it differentiates seizure types and stages, identifying spectral entropy as a potential marker for seizure onset. Notably, HOI analysis captures differences between primary and secondary generalized epilepsy, suggesting enhanced diagnostic accuracy. This approach provides a powerful tool for understanding complex neural interactions in high-dimensional data.