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Reverse Weighted-Permutation Entropy: A Novel Complexity Metric Incorporating Distance and Amplitude Information

School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, China
Presented at the 5th International Electronic Conference on Entropy and Its Applications, 18–30 November 2019; Available online: https://ecea-5.sciforum.net/.
Proceedings 2020, 46(1), 1; https://doi.org/10.3390/ecea-5-06688
Published: 17 November 2019
Permutation entropy (PE), as one of the effective complexity metrics to represent the complexity of time series, has the merits of simple calculation and high calculation efficiency. In view of the limitations of PE, weighted-permutation entropy (WPE) and reverse permutation entropy (RPE) were proposed to improve the performance of PE. WPE introduces amplitude information to weigh each arrangement pattern, it can not only better reveal the complexity of time series with a sudden change of amplitude, but it also has better robustness to noise; by introducing distance information, RPE is defined as the distance to white noise, it has the reverse trend to traditional PE and has better stability for time series of different lengths. In this paper, we propose a novel complexity metric incorporating distance and amplitude information, and name it reverse weighted-permutation entropy (RWPE), which incorporates the advantages of both WPE and RPE. Three simulation experiments were conducted, including mutation signal detection testing, robustness testing to noise based on complexity, and complexity testing of time series with various lengths. The simulation results show that RWPE can be used as a complexity metric, which has the ability to accurately detect the abrupt amplitudes of time series and has better robustness to noise. Moreover, it also shows greater stability than the other three kinds of PE for time series with various lengths.
Keywords: permutation entropy (PE); weighted-permutation entropy (WPE); reverse permutation entropy (RPE); reverse weighted-permutation entropy (RWPE); time series; complexity permutation entropy (PE); weighted-permutation entropy (WPE); reverse permutation entropy (RPE); reverse weighted-permutation entropy (RWPE); time series; complexity
MDPI and ACS Style

Li, Y. Reverse Weighted-Permutation Entropy: A Novel Complexity Metric Incorporating Distance and Amplitude Information. Proceedings 2020, 46, 1.

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