Measuring multiscale complexity in human sleep electroencephalography

Increasing reports indicated that multiscale fashion is a general and efficient approach to investigate various of natural and physiological states. In this work, 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 allow the intuitive visualizations of entropy/complexity in the multiscale fashion, so-called generalized multiscale permutation entropy (GMPE), which is proposed to yield a spectrum of entropies and complexities. The proposed GMCE curve and/or the GMPE method is shown capable of identifying if an irregular oscillation is either chaotic or randomly distributed, as well as if it is highly predictable or long-term correlated. In the sleep analyses, both the minimum permutation entropy and the maximum statistical complexity present significant differences across sleep stages (p <. 0001∗), whereas all five sleep stages are differentiable in the multiple comparisons. The proposed methods facilitated the investigations of irregular oscillations with generalization in timescales and Tsallis q-entropy.