Fuzzy permutation entropy derived from a novel distance between segments of time series

Abstract

As effective tools for time series analyzing, a variety of information entropies have been widely applied in engineering, economic, biomedicine and other fields. In this paper, we define a new distance between finite sequence based on inversion and derive a new entropy, Fuzzy Permutation Entropy(FPE). A comparison of recognition performance for WGN, 1/f noise, periodical, or chaotic sequence and sine waves shows that FPE is valid on distinguishing deterministic signals from stochastic signals. Further contrast studying versus FE and PE shows that FPE is more sensitive to the alteration of the complexity of time series and more effective on separating different signals. Moreover, FPE is used to explore the distinction of the complexity of various traffic flows via the time headways which is simulated from the improved brake light rule model. We hope it is conducive to design Intelligent Transportation Management System.