Multiscale Tsallis permutation entropy analysis for complex physiological time series

Abstract

Discussing the complexity of time series has been a long-standing problem, including the use of information entropy to determine the complexity of the sequence. Permutation entropy (PE) has been regarded as a learning process to investigate the complexity of time series, such as financial time series and physiological time series. The permutation entropy, which is based on the Shannon entropy (SE), has undeniable shortcomings in dealing with some specific problems. Hence in this paper, we propose the multiscale Tsallis permutation entropy (MTPE) as an improved measuring tool for assessing the hidden temporal correlations in time series. The modified method not only presents a different way showing clear characteristics but also provides more significant results compared with the SE. Robustness of the hypothesis is proved by the correlation between Tsallis permutation entropy (TPE) and HURST exponent obtained from the sequences which are generated from fractional brownian motion stochastic model. Experimental results of autoregressive sequences (AR) and electroencephalograph time series (EEG) make the advantages of Tsallis permutation entropy more obvious, which also well validate the efficiency and integrity of principle of maximum entropy (PME). Multiscale analysis provides us with another perspective to analyze permutation entropy, which also allows us to better analyze the complexity of the sequence.