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Entropy 2018, 20(2), 138; https://doi.org/10.3390/e20020138

Coarse-Graining Approaches in Univariate Multiscale Sample and Dispersion Entropy

School of Engineering, Institute for Digital Communications, The University of Edinburgh, Edinburgh EH9 3FB, UK
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Received: 1 December 2017 / Revised: 15 February 2018 / Accepted: 16 February 2018 / Published: 22 February 2018
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Abstract

The evaluation of complexity in univariate signals has attracted considerable attention in recent years. This is often done using the framework of Multiscale Entropy, which entails two basic steps: coarse-graining to consider multiple temporal scales, and evaluation of irregularity for each of those scales with entropy estimators. Recent developments in the field have proposed modifications to this approach to facilitate the analysis of short-time series. However, the role of the downsampling in the classical coarse-graining process and its relationships with alternative filtering techniques has not been systematically explored yet. Here, we assess the impact of coarse-graining in multiscale entropy estimations based on both Sample Entropy and Dispersion Entropy. We compare the classical moving average approach with low-pass Butterworth filtering, both with and without downsampling, and empirical mode decomposition in Intrinsic Multiscale Entropy, in selected synthetic data and two real physiological datasets. The results show that when the sampling frequency is low or high, downsampling respectively decreases or increases the entropy values. Our results suggest that, when dealing with long signals and relatively low levels of noise, the refine composite method makes little difference in the quality of the entropy estimation at the expense of considerable additional computational cost. It is also found that downsampling within the coarse-graining procedure may not be required to quantify the complexity of signals, especially for short ones. Overall, we expect these results to contribute to the ongoing discussion about the development of stable, fast and robust-to-noise multiscale entropy techniques suited for either short or long recordings. View Full-Text
Keywords: complexity; multiscale dispersion and sample entropy; refined composite technique; intrinsic mode dispersion and sample entropy; moving average; Butterworth filter; empirical mode decomposition; downsampling complexity; multiscale dispersion and sample entropy; refined composite technique; intrinsic mode dispersion and sample entropy; moving average; Butterworth filter; empirical mode decomposition; downsampling
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Azami, H.; Escudero, J. Coarse-Graining Approaches in Univariate Multiscale Sample and Dispersion Entropy. Entropy 2018, 20, 138.

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