A novel method based on machine learning is developed to estimate event-related potentials from single trial electroencephalography. This paper builds a basic framework using classification and an optimization model based on this framework for estimating event-related potentials. Then the SingleTrialEM algorithm is derived by introducing a logistic regression model, which could be obtained by training before SingleTrialEM is used, to instantiate the optimization model. The simulation tests demonstrate that the proposed method is correct and solid. The advantage of this method is verified by the comparison between this method and the Woody filter in simulation tests. Also, the cognitive test results are consistent with the conclusions of cognitive science.
Cognitive functions are often studied using eventrelated potentials（ERPs）that are usually estimated by an averaging algorithm.Clearly,estimation of single-trial ERPs can provide researchers with many more details of cognitive activity than the averaging algorithm.A novel method to estimate single-trial ERPs is proposed in this paper.This method includes two key ideas.First,singular value decomposition was used to construct a matrix,which mapped singletrial electroencephalographic recordings（EEG）into a low-dimensional vector that contained little information from the spontaneous EEG.Second,we used the theory of compressed sensing to build a procedure to restore single-trial ERPs from this low-dimensional vector.ERPs are sparse or approximately sparse in the frequency domain.This fact allowed us to use the theory of compressed sensing.We verified this method in simulated and real data.Our method and dVCA（differentially variable component analysis）,another method of single-trial ERPs estimation,were both used to estimate single-trial ERPs from the same simulated data.Results demonstrated that our method significantly outperforms dVCA under various conditions of signal-to-noise ratio.Moreover,the single-trial ERPs estimated from the real data by our method are statistically consistent with the theories of cognitive science.
