Hermite Interpolation Multiscale Adaptive Dispersion Entropy and Its Application in Feature Extraction

Dispersion entropy (DE) and its multiscale version multiscale DE (MDE) are effective measures of time series complexity. DE, however, ignores skewness information, which can lead to inaccurate entropy estimates, and is sensitive to the choice of category number, whereas MDE suffers from loss of information as the scale factor increases. In order to address the problems in DE, adaptive DE (ADE) is proposed, which selects the appropriate mapping method according to the skewness of the signal and solves the parameter selection problem by evaluating the complexity and data fitting goodness through the Akaike information criterion (AIC). In addition, Hermite interpolation multiscale ADE (HIMADE) is proposed by introducing the Hermite interpolation technique to approximately reconstruct the coarse-grained series to the original series, which solves the issue of information loss in MDE. Five sets of simulation signal analysis verify that the ADE is more sensitive to dynamic changes and has greater consistency, and HIMADE has greater stability, differentiation ability, and noise immunity. Three sets of real-world signal cases from different datasets show that HIMADE has the highest accuracy in feature extraction compared with existing entropy metrics.