Refined scale-dependent permutation entropy to analyze systems complexity

• Published in: Physica A 2016-05, Vol.450, p.454-461
• Main Authors: Wu, Shuen-De, Wu, Chiu-Wen, Humeau-Heurtier, Anne
• Format: Article
• Language: English
• Subjects: Complexity; Computation; Computational efficiency; Engineering Sciences; Entropy; Multiscale entropy; Nonlinear dynamics; Permutation entropy; Permutations; Sample entropy; Samples; Signal and Image processing; Statistical mechanics; Time series
• ISSN: 0378-4371; 1873-2119; 0378-4371
• DOI: 10.1016/j.physa.2016.01.044

Multiscale entropy (MSE) has become a prevailing method to quantify the complexity of systems. Unfortunately, MSE has a temporal complexity in O(N2), which is unrealistic for long time series. Moreover, MSE relies on the sample entropy computation which is length-dependent and which leads to large variance and possible undefined entropy values for short time series. Here, we propose and introduce a new multiscale complexity measure, the refined scale-dependent permutation entropy (RSDPE). Through the processing of different kinds of synthetic data and real signals, we show that RSDPE has a behavior close to the one of MSE. Furthermore, RSDPE has a temporal complexity in O(N). Finally, RSDPE has the advantage of being much less length-dependent than MSE. From all this, we conclude that RSDPE over-performs MSE in terms of computational cost and computational accuracy. •Multiscale entropy (MSE) is a prevailing complexity measure, but it has drawbacks.•A new multiscale complexity measure is introduced: RSDPE.•RSDPE has a behavior close to the one MSE.•RSDPE over-performs MSE in terms of computational cost.•RSDPE over-performs MSE in terms of computational accuracy.