Amplitude-Aware Permutation Entropy: A Comprehensive Review and Applications

Considering the sensitivity of amplitude information, Faldalllah et al. [14] developed Weighted-Permutation Entropy (WPE) by incorporating the variance of neighboring elements in the calculation of PE. Subsequently, Azami et al. [15] proposed Amplitude-Aware Permutation Entropy (AAPE) based on PE, which has been successfully applied to the feature extraction of complex time series. Gong et al. demonstrated that the AAPE algorithm can be applied to detect various working conditions of the rolling bearings [16]. In addition, Azami and Escudero [17] proposed a new version of PE, called Permutation Entropy with Quantization (PEQ), which incorporates quantization into the PE calculation to enhance the robustness of the method against amplitude variations. This method has been applied to analyze electroencephalogram (EEG) signals and has shown good performance in distinguishing different brain states [18]. Overall, these amplitude-aware permutation entropy methods have shown promise in analyzing complex time series data with varying amplitude levels.