Test for low-dimensional determinism in electroencephalograms.
We tested low-dimensional determinism in an electroencephalogram (EEG), based on the fact that smoothness (continuity) on an embedded phase space is enough to imply determinism within time series. A modified version of the method developed by Salvino and Cawley [Phys. Rev. Lett. 73, 1091 (1994)] was used. In our method, we chose a box randomly and then estimated the mean directional element in the box containing the d+1 data points, where d is the embedding dimension. The global average for the mean local directional elements over the boxes, W, is a measure for smoothness. The nonlinear noise reduction method developed by Sauer [Physica D 58, 193 (1992)] is then applied to the EEG. We also compared the results for the EEG with those for its surrogate data. We found that the W values for the noise-reduced EEG had stable values around 0.35, which means that the EEG is not a low-dimensional deterministic signal. However, this method may not be applicable to the time series generated from high-dimensional deterministic systems. We cannot exclude the possibility that the determinism in the EEG may be too high-dimensional to be detected with current methods.
Jeong
J
J
Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea.
Kim
M S
MS
Kim
S Y
SY
D000465:Algorithms; D004569:Electroencephalography / Q000295:instrumentation* / Q000379:methods*; D006801:Humans; D015233:Models, Statistical; D015203:Reproducibility of Results; D013997:Time Factors