Assessing multi-layered nonlinear characteristics of ECG/EEG signal via adaptive kernel density estimation-based hierarchical entropies

Coarse-grained analysis-based entropies are capable of quantifying the nonlinear characteristic of signals in different scales but they ignore the high-frequency information. We here proposed hierarchical entropies via which the low- and high-frequency information of a signal can be both revealed so that better understanding of signal’s dynamic characteristics can be reached. In this paper, adaptive kernel density estimation was used to estimate probability densities for distribution entropy (DistEn), fuzzy DistEn (FDistEn), complex-valued DistEn (CVFDistEn) and complex-valued FDistEn (CVFDistEn). Totally six hierarchical entropies were then raised, to overcome the defects of traditional coarse-grained operation and to assess the complexity of the full-band components of a signal. Fusion methods of distribution entropy-derived hierarchical entropies and probabilistic neural network (PNN) were finally put forward to identify normal and congestive heart failure (CHF) electrocardiogram (ECG) as well as normal, interictal and ictal electroencephalography (EEG) signals. Experimental results indicate the proposed hierarchical entropies can characterize the complexity of ECG and EEG signals in different scales. Moreover, fusion methodology of hierarchical FDistEn and PNN achieved the highest mean Matthews correlation coefficient of 100 % in distinguishing normal and CHF ECG signals, while combination of hierarchical CVFDistEn and PNN reported the best mean accuracy of 99.23 ± 0.23 % for identification of normal, interictal and ictal EEG signals. Our proposed adaptive kernel density estimation-based hierarchical entropies can characterize ECG and EEG signals effectively. The fusion methods of hierarchical entropies and PNN bring a new tool for identification of different types of ECG and EEG signals.