Maximum approximate entropy and threshold: A new approach for regularity changes detection

Abstract

Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system's dynamics when there is only available short-length noisy data. Incorrect parameter selection (embedding dimension m, threshold r and data length N) and the presence of noise in the signal can undermine the ApEn discrimination capacity. In this work we show that r max (ApEn(m, r max , N) = ApEn max ) can also be used as a feature to discern between dynamics. Moreover, the combined use of ApEn max and r max allows a better discrimination capacity to be accomplished, even in the presence of noise. We conducted our studies using real physiological time series and simulated signals corresponding to both low-and high-dimensional systems. When ApEn max is incapable of discerning between different dynamics because of the noise presence, our results suggest that r max provides additional information that can be useful for classification purposes. Based on cross-validation tests, we conclude that, for short length noisy signals, the joint use of ApEn max and r max can significantly decrease the misclassification rate of a linear classifier in comparison with their isolated use.

On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

“…The parameters necessary for XApEn estimation-time series length , threshold level , vector size , and time lag -create a huge working space, but with unstable regions. Recent ApEn contributions have reviewed this problem [4,19], earlier also noticed in [6,8,[15][16][17][18]20]. But parameter study for XApEn does not exist, except for a brief comment in [5] (to the best of the authors' knowledge).…”

“…The coefficients in (19) and (20) are obtained using the same data sets as for (17). In this case, the conditional probabilities were estimated, and the fitting was performed among the coefficients that yield less than 5% of unreliable probabilities, over all values of and over all data lengths: …”

“…(17)). (b) Threshold for which at least 95% of the probabilities satisfy weak criterion (see (19)). (c) Threshold for which at least 95% of the probabilities satisfy strong criterion (see (20)).…”

“…Research efforts are oriented towards modifications, including sample entropy (SampEn) [5], corrected conditional entropy (CApEn) [6], -nearest neighborhood entropy (KNNCE) [7], fuzzy entropy (FuzzyEn) [8], multiscale entropy (MultiScaleEn) [9], distance entropy (DistEn) [10], binarized entropy (BinEn) [11], ApEn based on wave mode [12], and speeding-up algorithms [13,14], and towards the consistency studies, including threshold selection [15][16][17][18][19][20], time lag [21], and consistency in general [4].…”

“…However, the reputation and deployment of its predecessor have never been reached. Except for a recent improvement [23], XApEn applications follow classical ApEn guidelines, although (a) the parameters should be adjusted even for ApEn (e.g., [4,[15][16][17][18][19][20]) and (b) properties of XApEn are different and straightforward ApEn guidelines might not be proper.…”