Nonlinear Prediction of Chaotic Electrical Activity of the Brain

The random looking brain electrical activity patterns recorded as EEG is currently understood to be the outcome of a chaotic process. This study addresses the problem of nonlinear prediction of chaotic EEG data using a simplex method. A fixed length of EEG data is taken and a multidimensional attractor in phase-space is reconstructed from the time series. The first N points on the attractor serve as the base for making prediction for the next points. For a given point $x_i$ (i>N), the E+1 closest neighbors are determined. The predicted value is obtained by keeping track of where the neighbors moved, giving them an exponential weight depending upon the original distance. As the embedding dimension is increased, the predicted time series was a better correlation to the real signal until about twice the expected value of the correlation dimension D and then the correlation falls off. The results indicate that the EEG prediction falls off rapidly for longer prediction lengths, thus validating the chaotic nature of the EEG signal. Also, as the frequency of the signal increases, the prediction length decreases. The effect of the predictive parameters on different EEG activities is discussed