Chaos Analysis of Transcranial Doppler Signals for Feature Extraction

Abstract

In this study, chaos theory tools were used for feature extraction from Transcranial Doppler (TCD) signals. The surrogates data sets of the TCD signals which were used for the nonlinearity analysis were extracted as the first feature set. The nonlinear cross prediction errors which were used for the stationary analysis were also extracted for the TCD signals as another feature set. The chaotic invariant features like correlation dimension, maximum Lyapunov exponent, recurrence quantification measures etc. give quantitative values of complexity of the TCD signals. The correlation dimension and maximum Lyapunov exponent were already used as features for classification of TCD signals in the literature. As another chaotic feature set, the statistical quantitative values were extracted from the recurrence plots. The correct calculation of the time delay and the minimum embedding dimension is crucial to correctly estimate all of the chaotic features. These two data were calculated via mutual information and false nearest neighbours approaches, respectively. The space-time separation plots were used in order to find the ideal dimension of Theiler window w which is another important value for the correct estimate of chaotic measures. The reconstructed chaotic attractors with 3-D embedding and 1-step time delay represent the visual phase space portrait of the TCD signals. The attractors were also suggested as another candidate feature set.