Indications of nonlinearity, intraindividual specificity and stability of human EEG: The unfolding dimension.

G.B. Schmid & R.M. Dünki, PHYSICA D 93:165 - 190 (1996)
Keywords:
Chaos, dynamical analysis, correlation dimension, unfolding dimension, Kolmogorov entropy,
f( )-spectra, EEG

With the help of a parameter which we call the "unfolding dimension", we provide a bivariate representation of dynamical EEG analysis. Applied to human EEG, our approach successfully discriminates surrogate data from raw EEG, and similarly, shows human EEG to be both, intraindividually specific and stable over time. The heart of our approach is the Grassberger-Procaccia Algorithm (Grassberger und Procaccia 1983a) for the determination of the correlation dimension D within the context of the well-known "Method of Time Delays" (Takens 1981). To guarantee the reproducibility of results, this algorithm as well as an estimate for the K entropy (Kolmogorov 1959, Grassberger & Procaccia 1983b) and the determination of
f( )-spectra (Atmanspacher et al. 1989) have been integrated into a computer program which encompasses an operator/user-independent, automatic and reproducible specification of both an "optimal" time-delay for calculating the correlation integral as well as an "optimal" (scalar invariant) plateau region for the extraction of D and K . Our embedding protocall applied to mathematical systems is shown to be consistent with findings based on other algorithms, in particular, with false nearest neighbors considerations and Sauer' s minimal embedding criteria. Particular "intelligent" features of the automation and optimization logic plus the inclusion of estimates of the inherent systematic error make the proposed algorithm especially appropriate for applications to biological/psychological data.