On the Dimensionality of Sleep-EEG Data

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Abstract
Sleep-EEG data of 16 healthy subjects, classified according to the Rechtschaffen and Kales criteria, were taken to determine the correlation exponent (CE) or dimensionality (D2) of the data using the Corex program. We tested the applicability of this program to the analysis of sleep-EEG data changing systematically the embedding dimension (ED), the time lag (τ), the number of involved pairs of vectors and the EEG segment by split half. We could confirm the results of other authors according to which the complexity of the EEG signal decreases from stage ‘awake, eyes closed’ to sleep stages 1, 2, 3 and 4. The differences between the various sleep stages were significant. Stage REM could be differentiated from every stage but stage 1. The most important finding of our study was that the absolute value of the dimensionality depends on almost all the parameters tested: with increasing τ up to τ = 200 the CE increases, which means a 1.56-second shift. A higher number of pairs is needed when the signal is more complex. The ED is selected well between 6 and 11, that means reasonably higher or close to the dimensionalities for that purpose as presented in the literature. Different segments of one sleep stage in 1 subject led to different CE values, thus demonstrating that the EEG signal is not stationary over a segment of 2 min time. Although using chaos mathematics seems to be a useful tool in analyzing EEG data to explore their complexity, we could demonstrate the urgent need of calibrations and conventions to be able to interpret the absolute values.

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