EEG Multi-Mode Oscillatory Brain State Allocation Using Switching Spectral Gaussian Processes

We propose a new model for the non-stationary brain state allocation problem from electroencephalography (EEG) data, based on spectral features and their interaction. Spontaneous EEG data are modeled as continuous Gaussian Processes (GPs) emissions governed by discrete states, represented by a hidden semi-Markov model, that switch in time (HsMM-SGP). The GPs are defined by multivariate spectral kernels, covariance functions parameterized in the frequency domain. The multivariate spectral kernels describe oscillatory modes at specific frequencies and their interactions across channels, encapsulating periodicity, amplitude, and spread. Multivariate spectral kernels enable the GPs to represent temporal patterns with fine-grained frequency-specific structures and interactions, a unique spectral “fingerprint” per state, making it particularly suited for capturing non-stationary oscillatory behaviour in the neural time series. The model parameters were estimated using the Expectation-Maximization approach. The inference scheme was validated on data generated from the HsMM-SGP generative model to evaluate the accuracy in recovering the ground truth parameters. Next, we generated time-series from a metastable connectome-connected whole brain network to demonstrate the HsMM-SGP’s capability to infer meaningful oscillatory modes that reflect the changes in the underlying dynamics due to varying structural connectivity parameters. Finally, a practical application of the HsMM-SGP is illustrated using EEG data from a healthy control and an AD patient. We show that the inferred brain states exhibit distinct spectral properties across both conditions, with the AD states marked slower frequencies. We conclude that the proposed HsMM-SGP offers a method for estimating physiologically meaningful dynamical brain states.