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ISSN 1812-7231 Klin.inform.telemed. Volume 10, Issue 11, 2014, Pages 10–20


O. Yu. Mayorov1, 2, 3, V. N. Fenchenko1, 2, 4


1Institute for Medical Informatics and Telemedicine LTD, Kharkiv, Ukraine 2Kharkiv Medical Academy of Postgraduate Education, Ministry of Healthcare of Ukraine 3Institute of Children and Adolescents Health protection NAMS of Ukraine, Kharkiv 4B. Verkin Physical-technical Institute of Low Temperature NAS of Ukraine, Kharkiv

Article title

Calculation of the correlation dimension and entropy of EEG signals in cluster computing systems

Abstract (resume)

Introduction. During the study of the multifractals of bioelectrical brain (EEG, ERP) and heart (ECG, Heart Rate Variability) signals, the correct calculation of correlation dimensions D2 is essential.

Formulation of the problem. Methodology. In order to avoid system errors, the segment of the EEG signal should be stationary and extensive. According to the Tsonis criteria (A. Tsonis), the duration of EEG series with D2=4±8 is equal to (1±2)105 counts. It is a time consuming process which requires powerful computing systems. However, unified criteria which are necessary for the selection of the following parameters: 1) offset amount (delay) d for the attractor reconstruction, 2) estimation of the required dimensionality of the reconstruction area m, 3) selection of the minimal size of cells ε, 4) number of points K for the calculation of the D2 value limits, are missing. Subjective selection of the parameters excludes the opportunity of cluster systems application, makes difficult the comparison of results obtained by different researches.

The object of the study is to design methods of computerization of correlation dimensions D2 and correlation entropy H2, for using cluster computing systems without operator's participation for subjective selection of computation parameters.

Study results. The attractor reconstruction based on cluster systems with different d values for choosing of the optimal offset amount (delay) d has been proposed. The modification of the Theiler computational procedure (Theiler J.) which helps to avoid errors caused by the insufficient length of the biological signals has been developed. In this case, too closely located points are not taken into account for the summation, and Gauss nucleus (J. C. Gauss) is used instead of Heaviside function (O. Heaviside). The algorithm of automatic search of correlation dimension values D2(m) and correlation entropy H2 on the Rapp (P. Rapp) plot's plateau have been proposed.

Conclusion. Automatic computation of the correlation dimension D2(m) and correlation entropy H2 of biological signals allows to use the cluster system, reduces labor intensiveness, removes subjective factor in selecting of attractor reconstruction parameters, and allows to obtain comparable results in different laboratories.


EEG, Bioelectrical activity, Deterministic chaos, Reconstruction, Entropy, Dimension, Cluster computing systems


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