Phase Analysis of Event-Related Potentials Based on Dynamic Mode Decomposition

Real-time detection of event-related potentials (ERPs) and exploration of ERPs generation mechanisms are vital to practical application of brain–computer interfaces (BCI). Traditional methods for ERPs analysis often fall into time domain, time–frequency domain, or spatial domain. Methods which can reveal spatiotemporal interactions by simultaneously analyzing multi-channel EEG signals may provide new insights into ERP research and is highly desired. Additionally, although phase information has been investigated to describe the phase consistency of a certain frequency component across different ERP trials, it is of research significance to analyze the phase reorganization across different frequency components that constitute a single-trial ERP signal. To address these problems, dynamic mode decomposition (DMD) was applied to decompose multi-channel EEG into a series of spatial–temporal coherent DMD modes, and a new metric, called phase variance distribution (PVD) is proposed as an index of the phase reorganization of DMD modes during the ERP in a single trial. Based on the PVD, a new error-related potential (ErrP) detection method based on symmetric positive defined in Riemann manifold is proposed to demonstrate the significant PVD differences between correct and error trials. By including the phase reorganization index, the 10-fold cross-validation results of an ErrP detection task showed that the proposed method is 4.98%, 27.99% and 7.98% higher than the counterpart waveform-based ErrP detection method in the terms of weighted accuracy rate, precision and recall of the ErrP class, respectively. The resulting PVD curve shows that with the occurrence of ERP peaks, the phases of different frequency rhythms are getting to aligned and yields a significant smaller PVD. Since the DMD modes of different frequencies characterize spatiotemporal coherence of multi-channel EEG at different functional regions, the new phase reorganization index, PVD, may indicate the instantaneous phase alignment of different functional networks and sheds light on a new interpretation of ERP generation mechanism.