Automatic Determination of Cross-Approximate Entropy Parameters for Cardiovascular Time Series

摘要

Cross-approximate entropy (XApEn) is a measurement of the mutual orderliness of two time series. The term “approximate” indicates the inability to calculate the exact entropy value, due to the limited time series length. The estimation of XApEn depends on the presumed values of three parameters: the threshold r, the length of the time series N, and the size of the segment m. An inadequate choice of parameters can lead to an unreliable estimate. In this study, we propose two methods that can attenuate the inconsistencies of XApEn estimation. A simple equation correction reduces the unreliability, but not completely. An alternative method proposes a set of formulae for automatic threshold r evaluation. This threshold provides a reliable estimation of XApEn. The proposed improvements are verified using the cardiovascular time series (humans and laboratory animals), as well as using artificial data.