An index of signal mode complexity based on orthogonal transformation
Dr. Joydeep Bhattacharya
Commission for Scientific Visualization, Austrian Academy of
Last modified: April 25, 2006
Nature is abound with dynamical systems producing irregular and complex signals with examples ranging from pulsating stars, spatiotemporal spreading of virus, to beating heart and brain rhythms. The aim of the present paper is to devise an index to quantify the degree of complexity of such signal based on the distribution of the strengths of its orthogonal oscillatory modes which were estimated by the application of an orthogonal transformation technique, singular value decomposition (SVD). The index was first successfully applied to simulated chaotic and/or stochastic maps and flows; analysis based on surrogate data was also presented to detect the underlying nonlinearity. Then we applied the index to evaluate the tonic-clonic seizure electroencephalogram (EEG) signals, and found a conspicuous change in the complexity values of delta band (1-3.5 Hz) oscillations at the onset of seizure. Finally, the index was 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 large changes in the complexity values, consistent over various scalp regions, during listening to music from resting condition, whereas such changes were minimal for non-musicians. We conclude that this measure may be useful for the quantification of the observed signal characteristics.