Power-Law Exponent Modulated Multiscale Entropy: A Complexity Measure Applied to Physiologic Time Series

Abstract

Quantifying the complexity of physiologic time series has long attracted interest from researchers. The multiscale entropy (MSE) algorithm is a prevailing method to quantify the complexity of signals in a variety of research fields. However, the MSE method assigns increased complexity to the mixed signal of a physiologic time series added with white noise, although the mixed signal should become less complex due to the broken correlation. In addition, the MSE method needs users to visually examine its scale dependence (shape) to better characterize the complexity of a physiologic process, which is sometimes not feasible. In this paper, we proposed a new method, namely the power-law exponent modulated multiscale entropy (pMSE), as a complexity measure for physiologic time series. We tested the pMSE method on simulated data and real-world physiologic interbeat interval time series and demonstrated that it could solve the above two difficulties of the MSE method. We expect that the proposed pMSE method or its future variants could serve as a useful complement to the MSE method for the complexity analysis of physiologic time series.

Keywords

• Time series
• multiscale entropy
• complexity
• power-law
• self-similarity