Blind separation and localization of correlated P300 subcomponents from single trial recordings using extended PARAFAC2 tensor model

A novel mathematical model based on multi-way data construction and analysis with the goal of simultaneously separating and localizing the brain sources specially the subcomponents of event related potentials (ERPs) is introduced. We represent multi-channel EEG data using a third-order tensor with modes: space (channels), time samples, and number of segments. Then, a multi-way technique, in particular, generalized version of PARAFAC2 method, is developed to blindly separate and localize mutually/temporally correlated P3a and P3b sources as subcomponents of P300 signal. In this paper the non-orthogonality of the ERP subcomponents is defined within the tensor model. In order to obtain essentially unique estimation of the signal components one parametric and one structural constraint are defined and imposed. The method is applied to both simulated and real data and has been shown to perform very well even in low signal to noise ratio situations. In addition, the method is compared with spatial principal component analysis (sPCA) and its superiority is demonstrated by using simulated signals.