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

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.

Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

“…The technique we developed has a precise mathematical formulation and can be used to optimize entropy parameters, such in as the particle swarm optimization method. In this sense, the problem of classification based on entropy-based features has a more rigorous solution than assessing the magnitude of chaos and irregularity, which is often based on intuitive premises [58].…”

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

“…While this approach offers an interesting and modular configuration of analysis, it faces challenges that limit its applicability. These are the potential mismatch of each channel's data length with the optimal scale values, the limitation of multiscale analysis to specific scales for each channel resulting in an incomplete multiscale output, [48], the instability of the method for increased number of channels [49], and the potential for overshadowing to occur even at optimal scale combinations.…”

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

“…While this approach offers an interesting and modular configuration of analysis for multi-channel time-series, assuming that an optimal combination of scales is succesfully determined, it faces multiple challenges that limit the range of its applicability. These are the potential mismatch of each channel's data length with the optimal scale values, the limitation of multiscale analysis to specific scales for each channel resulting in an incomplete multiscale output, [43], the instability of the method for increased number of channels [44] and the potential for overshadowing to occur even at optimal scale combinations.…”