Equivalence of modified k-means and tensor decomposition in EEG microstates: Implications for analysis and interpretation

In the resting state, the human brain quickly transitions among a limited set of quasi-stable states known as EEG microstates, which characterize brain spatio-temporal activity with high temporal resolution. EEG microstates are typically identified using a clustering algorithm that analyzes peaks in the EEG global field power. In this study, we focus on the modified k-means algorithm (modKM), one of the most commonly employed methods for detecting EEG microstates. We demonstrate, both theoretically and through simulation and real EEG data, its equivalence with a different method known as the Implicit Slice Canonical Decomposition (IMSCAND), which is a special kind of tensor decomposition for symmetric higher order arrays. This relationship opens new avenues for EEG microstate detection, interpretation, and analysis by utilizing tensor decomposition methods and related techniques.