Selection of entropy-measure parameters for knowledge discovery in heart rate variability data

Abstract

BackgroundHeart rate variability is the variation of the time interval between consecutive heartbeats. Entropy is a commonly used tool to describe the regularity of data sets. Entropy functions are defined using multiple parameters, the selection of which is controversial and depends on the intended purpose. This study describes the results of tests conducted to support parameter selection, towards the goal of enabling further biomarker discovery.MethodsThis study deals with approximate, sample, fuzzy, and fuzzy measure entropies. All data were obtained from PhysioNet, a free-access, on-line archive of physiological signals, and represent various medical conditions. Five tests were defined and conducted to examine the influence of: varying the threshold value r (as multiples of the sample standard deviation σ, or the entropy-maximizing rChon), the data length N, the weighting factors n for fuzzy and fuzzy measure entropies, and the thresholds rF and rL for fuzzy measure entropy. The results were tested for normality using Lilliefors' composite goodness-of-fit test. Consequently, the p-value was calculated with either a two sample t-test or a Wilcoxon rank sum test.ResultsThe first test shows a cross-over of entropy values with regard to a change of r. Thus, a clear statement that a higher entropy corresponds to a high irregularity is not possible, but is rather an indicator of differences in regularity. N should be at least 200 data points for r = 0.2 σ and should even exceed a length of 1000 for r = rChon. The results for the weighting parameters n for the fuzzy membership function show different behavior when coupled with different r values, therefore the weighting parameters have been chosen independently for the different threshold values. The tests concerning rF and rL showed that there is no optimal choice, but r = rF = rL is reasonable with r = rChon or r = 0.2σ.ConclusionsSome of the tests showed a dependency of the test significance on the data at hand. Nevertheless, as the medical conditions are unknown beforehand, compromises had to be made. Optimal parameter combinations are suggested for the methods considered. Yet, due to the high number of potential parameter combinations, further investigations of entropy for heart rate variability data will be necessary.

Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

“…It could be suggested that the selection of m between 1 and 2 and r between 0.10 and 0.25 in FuzzyMEn would probably yield fine classification results between NSR and CHF groups. This result supports our hypothesis that FuzzyMEn would demonstrate better relative consistency as compared to SampEn and agrees the previous conclusion that the selection of r for SampEn appears to be more difficult than the selection of m [10,11,18].Typically it is suggested that for clinical data, m is to be set at 2 for SampEn [2,12]. Besides, an m of 3 has been found to be acceptable for SampEn in [8].…”

“…This is especially true for studies with pathological populations that are limited in their clinical measurement. However, caution has been advised when using time series of less than 200 points for either ApEn or SampEn [10,11].…”

“…A greater SD will increase the r value for consideration of a vector matching and vice versa with a smaller SD. To avoid a significant noise contribution on SampEn computation, one must choose r larger than most of the noise [11,14]. So the original suggestion between 0.1 and 0.25 times the SD of the time series for r does not always demonstrate the best results for all data sets and therefore, elaborate methods to choose r have been developed.…”

A Comparison of Nonlinear Measures for the Detection of Cardiac Autonomic Neuropathy from Heart Rate Variability

“…This can take multiple values and so provides multiple measures. Previous work has compared several entropy measures in terms of their efficacy in distinguishing congestive heart failure and arrhythmia from normal sinus rhythm [13]. However in this work we aim to compare two commonly applied multiscale entropy measures and MFDFA, and focus on a single morbidity, CAN, in its early and later stages in asymptomatic individuals with no cardiovascular disease or diabetes.…”

Voice Activity Detection Using Fuzzy Entropy and Support Vector Machine

“…Based on fuzzy set theory, to measure the complexity of the time series data, fuzzy entropy (FuzzyEn) [22] was introduced. FuzzyEn is a modified algorithm of sample entropy (SampEn) [23][24][25][26][27]. Since then, FuzzyEn has been successful in feature extraction.…”