Recurrence-based estimation of time-distortion functions for ERP waveform reconstruction.

We introduce an approach to compensate for temporal distortions of repeated measurements in event-related potential research. The algorithm uses a combination of methods from nonlinear time-series analysis and is based on the construction of pairwise registration functions from cross-recurrence plots of the phase-space representations of ERP signals. The globally optimal multiple-alignment path is approximated by hierarchical cluster analysis, i.e. by iteratively combining pairs of trials according to similarity. By the inclusion of context information in form of externally acquired time markers (e.g. reaction time) into a regularization scheme, the extracted warping functions can be guided near paths that are implied by the experimental procedure. All parameters occurring in the algorithm can be optimized based on the properties of the data and there is a broad regime of parameter configurations where the algorithm produces good results. Simulations on artificial data and the analysis of ERPs from a psychophysical study demonstrate the robustness and applicability of the algorithm.