A local tangent space based approach for single-trial representation of event-related potentials

The common approach in research on event-related potentials (ERPs) is to assume that the stimulus-related potentials can be extracted from ongoing EEG by simple averaging. There is great interest in processing ERPs in single-trial level to get more exact information. In this work, a single-trial ERPs representation scheme based on local tangent space analysis is proposed. By analyzing a number of time-lagged versions of single-trial ERPs data points sampled with noise (i.e., stochastic ongoing EEG) from the embedded one-dimensional manifold, the local tangent space based data-driven approach performs a local geometrical approximation for waveforms, which fits ERPs structure very well and is persistent in all trials. The variation of the ERPs component can also be reflected in one-dimensional representation, which explicitly illustrates the distortion of the simple averaging technique for late ERPs component.