Feasibility of real-time calculation of correlation integral derived statistics applied to EEG time series

Abstract

This study assessed the feasibility of online calculation of the correlation integral (C(r)) aiming to apply C(r)-derived statistics. For real-time application it is important to reduce calculation time. It is shown how our method works for EEG time series. Methods: To achieve online calculation of C(r) a non-randomly subset of inter vector distances was chosen and computer code was optimized. The effect of distance exclusion was investigated for both non-randomly and randomly chosen subsets. A C(r)-derived statistic was computed: an effective correlation dimension (CD) following the Grassberger-Procaccia-Takens approach. Results: By taking a subset of the maximum possible number of distances, C(r)-computation time could be easily 100 times reduced with marginal changes and minor variability in the C(r)-derived statistic CD. Applied to the EEG CD gives a good indication of the depth of anesthesia. Conclusions: If applied to the EEG, apparently a large number of distances can be omitted in the calculation of C(r) with minimal consequences. This outcome confirms Hoeffding's theory of U-statistics and hence it is expected to occur generally, also for non-EEG time series.