Multi-Moment Multiscale Local Sample Entropy and Its Application to Complex Physiological Time Series

Abstract

The Multiscale Entropy (MSE) is an effective measure to quantify the dynamical complexity of complex systems, which has many successful applications in physiological and physical fields. It uses different scales to mean-coarse-grain the original series, and then calculates the sample entropy for each coarse-grained series. Inspired by the MSE, we in this paper propose the Multi-Moment Multiscale Local Sample Entropy (MMMLSE), which considers both mean-coarse-grained and standard-deviation-coarse-grained characteristics of the original series for each scale, to quantify the dynamical complexity of complex systems. We use simulated data (1/f noise, white noise and logistic map) to test the performance of our proposed method, with results showing that the MMMLSE can accurately and effectively characterize these complex systems. The ability to preserve nonlinear dynamics of the proposed method is also proved by surrogate data and nonlinearity test experiment. Furthermore, we apply the MMMLSE to analyze physiological signals, and the MMMLSE reveals that the ill individuals have lower dynamical complexity at larger scales than the healthy ones, and the elder individuals have lower dynamical complexity at larger scales than the younger ones, which are consistent with the reality.