Inter-channel Covariance Matrices Based Analyses of EEG Baselines

Electroencephalographic (EEG) signals are used to assess neurological disorders as well as different states of the brain. The choice of EEG baseline in any analysis is crucial as the two EEG baselines (Eyes Open and Eyes Closed) have differences in connectivity and power levels. The work proposes the use of inter-channel covariance matrices of multi-channel EEG to differentiate the two baselines. Two avenues of approach are explored using: (1) Tangent Vectors of Riemannian Manifold and (2) Covariance matrix properties such as Eigen Values, Eigen Vectors, Spectral Radius and the coefficients of Characteristic Polynomial. K-nearest neighbors, Ensemble of Decision Tree classifier with Bagging and Support Vector Machines are used in both scenarios with 10-fold cross-validation repeated 10 times. Tangent Vectors, Eigen Values, Spectral Radius, coefficients of Characteristic Polynomial and Eigen Vectors result in a mean performance of 80.78%, 95.56%,95.05%, 95.15% and 94.5% respectively. Changes in the inter-dependencies of the considered brain regions are captured more effectively by the covariance matrix properties than by the direct use of covariance matrices. These analyses clearly show that the two baselines have different inter-dependencies of the considered brain regions. The properties of covariance matrices prove to be effective in exploiting these differences to distinguish the baselines.