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

TL;DR

This paper introduces a novel approach combining maximum approximate entropy and r threshold to improve the detection of regularity changes in noisy short-length signals, enhancing classification accuracy.

Contribution

It proposes using r_max alongside ApEn_max as features for better discrimination of dynamics in noisy data, which is a new methodology.

Findings

Combined use of ApEn_max and r_max reduces misclassification rates.

r_max provides additional information when ApEn_max fails due to noise.

Method effective on physiological and simulated signals.

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.