Refined scale-dependent permutation entropy to analyze systems complexity

Multiscale entropy (MSE) has become a prevailing method to quantify the complexity of systems. Unfortunately, MSE has a temporal complexity in O(N-2), 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. (C) 2016 Elsevier B.V. All rights reserved.