Effect of data length and bin numbers on distribution entropy (DistEn) measurement in analyzing healthy aging

Complexity analysis of a given time series is executed using various measures of irregularity, the most commonly used being Approximate entropy (ApEn), Sample entropy (SampEn) and Fuzzy entropy (FuzzyEn). However, the dependence of these measures on the critical parameter of tolerance `r' leads to precarious results, owing to random selections of r. Attempts to eliminate the use of r in entropy calculations introduced a new measure of entropy namely distribution entropy (DistEn) based on the empirical probability distribution function (ePDF). DistEn completely avoids the use of a variance dependent parameter like r and replaces it by a parameter M, which corresponds to the number of bins used in the histogram to calculate it. When tested for synthetic data, M has been observed to produce a minimal effect on DistEn as compared to the effect of r on other entropy measures. Also, DistEn is said to be relatively stable with data length (N) variations, as far as synthetic data is concerned. However, these claims have not been analyzed for physiological data. Our study evaluates the effect of data length N and bin number M on the performance of DistEn using both synthetic and physiologic time series data. Synthetic logistic data of `Periodic' and `Chaotic' levels of complexity and 40 RR interval time series belonging to two groups of healthy aging population (young and elderly) have been used for the analysis. The stability and consistency of DistEn as a complexity measure as well as a classifier have been studied. Experiments prove that the parameters N and M are more influential in deciding the efficacy of DistEn performance in the case of physiologic data than synthetic data. Therefore, a generalized random selection of M for a given data length N may not always be an appropriate combination to yield good performance of DistEn for physiologic data.