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

• Published in: Physica. D Vol. 203; no. 3; pp. 198 - 208
• Main Authors: van den Broek, Philip L.C., van Egmond, Jan, van Rijn, Clementina M., Takens, Floris, Coenen, Anton M.L., Booij, Leo H.D.J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.04.2005; Elsevier
• Subjects: Anesthetic-depth; Chaos; EEG; Exact sciences and technology; Monitoring; Nonlinear; Physics; Time-series analysis; Chaos; Nonlinear; EEG; 05.45; 87.90; Time-series analysis; Monitoring; Anesthetic-depth; Exclusions; Correlation dimension; Variability; 87.90 Nonlinear; Feasibility studies; Time series; Time correlation; Non linear phenomenon; Correlation time
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2005.03.012

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. 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. 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. 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.