A novel method of visualizing q-complexity-entropy curve in the multiscale fashion

Increasing reports indicated that multiscale fashion is a general and efficient approach to investigate various natural and physiological states. To this end, a generalization of the q-complexity-entropy curve in the multiscale fashion (GMCE curve) is introduced. In addition, the concept of the minimum permutation entropy and the maximum statistical complexity are proposed to simplify the visualization of entropy/complexity in the multiscale fashion, so-called generalized multiscale permutation entropy (GMPE), which is proposed to yield a spectrum of entropy and complexity. We demonstrate that the proposed GMCE curve or the GMPE method is capable of identifying an irregular oscillation is either stochastic or chaotic, highly predictable or long-term correlated. Simulations include Gaussian white noise and 1 / f noise, stationary and fractionally integrated autoregressive processes, logistic map and Hénon map. In the application of the GMCE curve and the GMPE method in real datasets, the GMCE loop of the daily streamflow of hydrologic alteration is found to be able of serving as an indicator to basin imperviousness or the level of urbanization. High basin imperviousness corresponds to narrower q-complexity-entropy loop. In the sleep analyses, both the minimum permutation entropy and the maximum statistical complexity show significant differences across sleep stages (p< 0. 0001 ^∗) , whereas all five sleep stages are differentiable in the multiple comparisons. Both the real datasets present clearer visualization and discrimination among basin imperviousness or sleep stages than the standard multiscale entropy. Our approach enables us to investigate irregular oscillations with generalization in timescales and Tsallis q-entropy.