Semantic geodesic maps: a unifying geometrical approach for studying the structure and dynamics of single trial...

A general framework for identifying and describing structure in a given sample of evoked response single-trial signals (STs) is introduced. The approach is based on conceptually simple geometrical ideas and enables the convergence of pattern analysis and non-linear time series analysis.

Classical steps for analyzing the STs by waveform are first employed and the ST-analysis is transferred to a multidimensional space, the feature space, the geometry of which is systematically studied via multidimensional scaling (MDS) techniques giving rise to semantic maps. The structure in the feature space characterizes the trial-to-trial variability and this is utilized to probe functional connectivity between two brain areas. The underlying dynamic process responsible for the emerged structure can be described by a multidimensional trajectory in the feature space. This in turn enables the detection of dynamical interareal coupling as similarity between the corresponding trajectories.

The utility of semantic maps was demonstrated using magnetoencephalographic data from a simple auditory paradigm. The coupling of ongoing activity and evoked response is vividly demonstrated and contrasted with the apparent deflection from zero baseline that survives averaging. Prototypes are easily identified as the end points of distinct paths in the semantic map representation, and their neighborhood is populated by STs with distinct properties not only in the latencies where the evoked response is expected to be strong, but also and very significantly in the prestimulus period. Finally our results provide evidence for interhemispheric binding in the (4-8 Hz) range and dynamical coupling at faster time scales.