Maximum approximate entropy and 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 r m a x ( A p E n ( m , r m a x , N ) = A p E n m a x ) can also be used as a feature to discern between dynamics. Moreover, the combined use of A p E n m a x and r m a x 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 A p E n m a x is incapable of discerning between different dynamics because of the noise presence, our results suggest that r m a x 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 A p E n m a x and r m a x can significantly decrease the misclassification rate of a linear classifier in comparison with their isolated use.