Assessing multiscale permutation entropy for short electroencephalogram recordings

Electroencephalogram (EEG) has been a standard tool to monitor the status of the brain. For a quantification of EEG recordings, permutation entropy (PE) has been of interest due to simplicity and robustness to noise. A multiscale extension of PE, called multiscale PE (MPE), has been promising for describing the dynamical characteristics of EEG over multiple temporal scales. However, an imprecise estimation of MPE at large scales limits its application for analyzing of short EEG recordings. Here, with the aim of estimating MPE accurately, a modified MPE (MMPE) measure is presented. The proposed MMPE consists of two processes: (1) computation of PE values of all possible coarse-grained EEG time-series, (2) averaging of PE values at each scale. Through simulations with two synthetic signals, i.e., white and 1 / f noises, MMPE proves its capability over MPE in terms of accuracy. Experimental results using the actual EEG recordings indicate that MMPE is an improved quantifier in the sense that MMPE reduces variance of entropy estimation in comparison with MPE.