An index of signal mode complexity based on orthogonal transformation

Irregular and complex signals are ubiquitous in nature. The principal aim of this paper is to develop an index, quantifying the complexity of such signals, which is based on the distribution of the strengths of its orthogonal oscillatory modes estimated by singular value decomposition. The index is first tested with simulated chaotic and/or stochastic maps and flows. Among neural data analysis, the index is first applied to a cognitive EEG data set recorded from two groups, musicians and non-musicians, during listening to music and resting state. In the gamma band (30–50 Hz), musicians showed robust changes in complexity, consistent over various scalp regions, during listening to music from resting condition, whereas such changes were minimal for non-musicians. Then the index is used to separate healthy participants from epileptic and manic patients based on spontaneous EEG analysis. Finally, it is used to track a tonic-clonic seizure EEG signal, and a conspicuous change was found in the complexity profiles of delta band (1–3.5 Hz) oscillations at the onset of seizure. We conclude that this index would be useful for quantification of a wide range of time series including neural oscillations.