ISSN: 1223-1533

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Authors: Tamara Ceranic, Branislav Milovanovic, Nina Japundzic-Zigon, Tatjana Loncar-Turukalo, Dragana Bajic


Background/aims: Approximate Entropy (ApEn) is a common method for quantifying the signal complexity. For unbiased estimation, parameters (pattern length, normalized threshold and time delay) should be chosen carefully. The most critical parameter and the major cause of instability in entropy estimation is the threshold r. In order to avoid the safest, but time consuming, estimations over wide range of values r, a formula for automatic selection of threshold value r that ensures the maximal ApEn value was derived.

Cross-entropy (CrossEn) is a measure of dissimilarity of two parallel time series. In spite of being important for understanding the signals relationship, it is a subject of a very few studies. The aim of this paper is to derive a formula for the threshold value r that ensures the maximal value for CrossEn thus avoiding time consuming estimations, and to explore formula accuracy using real recorded pulse interval and systolic blood pressure signals.



Methods: Experimental data consisted of pulse interval (PI) and systolic blood pressure (SBP) parallel series. In order to verify the formula, short series (recorded from 42 healthy human subjects) and long data series (recorded from laboratory animals, 6 Wistar and 6 BHR rats, exposed to two types of stress) were observed. Only at least wide sense stationary signals were observed. Method for automatic threshold estimation r for maximum CrossEn is developed. In order to verify its accuracy, the complete CrossEn profile was calculated and compared to the automatically derived value. CrossEn is an asymmetric measure, so both PI vs. SBP and SBP vs. PI entropies were observed.


Results and conclusion: Results showed high precision in assessing maximum value CrossEn(SBP,PI) as well as CrossEn(PI,SBP) for all experimental data, the same or better than in. Since the undesired flip-flop effect was noticed in parallel time series as well, the necessity of such an evaluation is confirmed.