Temporal correlations versus noise in the correlation matrix formalism: an example of the brain auditory response

Abstract

We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from human auditory cortex in epoch mode during delivery of sound stimuli to the left or right ear. We look into statistical properties and the eigenvalue spectrum of the correlation matrix C calculated for signals corresponding to different trials and originating from the same or opposite hemispheres. The spectrum of C largely agrees with the universal properties of the Gaussian orthogonal ensemble of random matrices, with deviations characterised by eigenvectors with high eigenvalues. The properties of these eigenvectors and eigenvalues provide an elegant and powerful way of quantifying the degree of the underlying collectivity during well defined latency intervals with respect to stimulus onset. We also extend this analysis to study the time-lagged interhemispheric correlations, as a computationally less demanding alternative to other methods such as mutual information.