Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems.

Hongjian Xiao,Danilo P. Mandic

doi:10.3390/e24010026

Abstract

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Highlights

To avoid unknown influence of control variables, time lags were set to L = 1 for all operations, to make the temporal span fully defined by the modification of the embedding dimension
The variational embedding multiscale sample entropy method has been introduced for robust structural complexity analysis of real-world data
It has been shown that variational embedding multiscale sample entropy (veMSE) is capable of assessing the complex features of the system at large scales and with higher embedding dimensions, compared to the standard multivariate multiscale sample entropy (MMSE)

Summary

Introduction

The proposed veMSE is shown to exhibit computational advantages over the existing amplitude distance-based entropy methods. It is important to note that bio-signals tend to exhibit high degrees of irregularities and complex dynamical behaviours [9], resulting from interactions between the human body (organisms) and peripheral environment, together with continuous fluctuations in time [10]. The definition of structural complexity is inconsistent in the literature [13], there are several commonly used methods for the quantification of the “degree of dynamics”, with entropy-based methodologies being the most popular ones. The estimation of complexity of nonlinear systems, through the fractal dimension [9], recurrence plots [10], and entropy analyses holds the advantage of simplicity.

Objectives

Results

Conclusion