Fusion entropy and its spatial post-multiscale version: Methodology and application

Dispersion entropy (DE) and its improved versions have become effective methods for analyzing signals complexity, which characterizes signals amplitude differences more accurately than permutation entropy (PE) and sample entropy (SE). However, they only consider the time-domain information of the signals and are influenced by parameter selection of embedding dimensions and class number. To address these limitations, fusion entropy (FE) is proposed as a comprehensive measure to characterize the complexity of signals by fusing time-frequency information, which also effectively addresses the issue of parameter selection encountered in DE by employing the gray scale matrix instead of the phase space reconstruction matrix. Moreover, spatial post-multiscale fusion entropy (SPMFE) is proposed as an improved multiscale version of FE, which use spatial post-multiscale technology to effectively avoid the problem of information loss before time-frequency transformation caused by traditional multiscale technologies. Three sets of simulation experiments indicate that SPMFE has superior stability, computational efficiency, and distinguish capability. In addition, two sets of realistic experiments demonstrate that SMFE has significant advantages in signals feature extraction compared to five types of entropy.