Test for low-dimensional determinism in electroencephalograms
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We tested low-dimensional determinism in an electroencephalogram ͑EEG͒, based on the fact that smoothness ͑continuity͒ 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 ͑1994͔͒ was used. In our method, we chose a box randomly and then estimated the mean directional element in the box containing the dϩ1 data points, where d is the embedding dimension. The global average for the
... bal 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 ͑1992͔͒ 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.