Considering the sensitivity of amplitude information Faldalllah et al developed Weighted-Permutation Entropy WPE by the variance of neighboring elements in the calculation of PE Subsequently Azami et

with high accuracy.

In addition to the traditional PE-based algorithms, several modified versions have also been proposed to address specific issues in different applications. For example, Bandt and Pompe introduced the concept of permutation patterns to PE, which led to the development of Symbolic Dynamic Analysis (SDA) for the analysis of nonlinear dynamical systems. Li et al. proposed Multi-Scale Permutation Entropy (MSPE), which can extract multi-scale features from complex time series. Jiang et al. presented a time-frequency analysis based PE algorithm for the detection of epileptic seizures.

Overall, permutation entropy and its variants have been widely used in various fields, such as neuroscience, engineering, finance, and biology. These algorithms provide a powerful tool for the analysis and classification of complex time series, and have shown promising results in many real-world applications.