Determining the number of independent sources of the EEG: a simulation study on information criteria

The separation of signal and noise is an important problem in the analysis of EEG and MEG data. Furthermore, many source localisation strategies need the number of independent signal components as input parameter (e.g., dipole fit, multiple signal classification). Information criteria offer a relatively objective way to separate the space spanned by the principal components of the data covariance matrix into a signal and a noise part. Eighteen such criteria were extensively tested by simulations. They differ with respect to the statistical model of the data, the assumptions on the noise, and the correction term. In the simulations, different dipole sources were used to generate EEG, which was then distorted by Gaussian correlated or uncorrelated noise. The noise level, the accuracy of the noise covariance matrix used by the criteria, the numbers of channels and time samples, and the stochastic or deterministic nature of the source waveforms were varied. The performance of the criteria was very variable. For each criterion, limits for the noise level and the relative inaccuracy of the noise covariance matrix could be established. Taking more channels or time steps did increase the criteria's ability to tolerate noise, but at the same time, made them more vulnerable to inaccuracies in the (estimated) noise covariance matrices. Out of the eighteen criteria investigated, we recommend two criteria that are best suited for the cases of (1) high noise and accurate covariances and (2) low noise and less accurate covariances.