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

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 rmax (ApEn(m,rmax,N)=ApEnmax) can also be used as a feature to discern between dynamics. Moreover, the combined use of ApEnmax and rmax 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 ApEnmax is incapable of discerning between different dynamics because of the noise presence, our results suggest that rmax 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 ApEnmax and rmax can significantly decrease the misclassification rate of a linear classifier in comparison with their isolated use.