Greater robustness of second order statistics than higher order statistics algorithms to distortions of the mixing matrix in blind source separation of human EEG: Implications for single-subject and group analyses

A mandatory assumption in blind source separation (BSS) of the human electroencephalogram (EEG) is that the mixing matrix remains invariant, i.e., that the sources, electrodes and geometry of the head do not change during the experiment. Actually, this is not often the case. For instance, it is common that some electrodes slightly move during EEG recording. This issue is even more critical for group independent component analysis (gICA), a method of growing interest, in which only one mixing matrix is estimated for several subjects. Indeed, because of interindividual anatomo-functional variability, this method violates the mandatory principle of invariance. Here, using simulated (experiments 1 and 2) and real (experiment 3) EEG data, we test how eleven current BSS algorithms undergo distortions of the mixing matrix. We show that this usual kind of perturbation creates non-Gaussian features that are virtually added to all sources, impairing the estimation of real higher order statistics (HOS) features of the actual sources by HOS algorithms (e.g., Ext-INFOMAX, FASTICA). HOS-based methods are likely to identify more components (with similar properties) than actual neurological sources, a problem frequently encountered by BSS users. In practice, the quality of the recovered signal and the efficiency of subsequent source localization are substantially impaired. Performing dimensionality reduction before applying HOS-based BSS does not seem to be a safe strategy to circumvent the problem. Second order statistics (SOS)-based BSS methods belonging to the less popular SOBI family class are much less sensitive to this bias.