Abstract
Measuring the complexity of time series provides an important indicator for characteristic analysis of nonlinear systems. The permutation entropy (PE) is widely used, but it still needs to be modified. In this paper, the PE algorithm is improved by introducing the concept of the network, and the network PE (NPE) is proposed. The connections are established based on both the patterns and weights of the reconstructed vectors. The complexity of different chaotic systems is analyzed. As with the PE algorithm, the NPE algorithm-based analysis results are also reliable for chaotic systems. Finally, the NPE is applied to estimate the complexity of EEG signals of normal healthy persons and epileptic patients. It is shown that the normal healthy persons have the largest NPE values, while the EEG signals of epileptic patients are lower during both seizure-free intervals and seizure activity. Hence, NPE could be used as an alternative to PE for the nonlinear characteristics of chaotic systems and EEG signal-based physiological and biomedical analysis.
Highlights
Measuring the nature of the complexity of obtained time series can provide a better understanding of nonlinear systems
We investigated the complexity of these EEG signals by employing the fractional FuzzyEn algorithm [11] and the multiscale permutation Rényi entropy [29]
Let us take the given periodic time series {1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, ...} of length 20,480 as an example to show the superiority of the network PE (NPE) algorithm for the periodic time series
Summary
Measuring the nature of the complexity of obtained time series can provide a better understanding of nonlinear systems This has aroused much interest from researches. In 2002, Bandt and Pompe [23] proposed the PE algorithm based on the patterns deduced from constructed vectors It was indicated in many literature works that the PE algorithm has some drawbacks that cannot always measure complexity effectively. Approaches for complexity analysis of nonlinear time series using networks is a hot topic [36,37,38,39,40]. It could provide many possibilities for further investigation of the complexity algorithms.
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