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Open AccessArticle

A Novel Multivariate Sample Entropy Algorithm for Modeling Time Series Synchronization

Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK
Author to whom correspondence should be addressed.
Entropy 2018, 20(2), 82;
Received: 29 November 2017 / Revised: 15 January 2018 / Accepted: 19 January 2018 / Published: 24 January 2018
Approximate and sample entropy (AE and SE) provide robust measures of the deterministic or stochastic content of a time series (regularity), as well as the degree of structural richness (complexity), through operations at multiple data scales. Despite the success of the univariate algorithms, multivariate sample entropy (mSE) algorithms are still in their infancy and have considerable shortcomings. Not only are existing mSE algorithms unable to analyse within- and cross-channel dynamics, they can counter-intuitively interpret increased correlation between variates as decreased regularity. To this end, we first revisit the embedding of multivariate delay vectors (DVs), critical to ensuring physically meaningful and accurate analysis. We next propose a novel mSE algorithm and demonstrate its improved performance over existing work, for synthetic data and for classifying wake and sleep states from real-world physiological data. It is furthermore revealed that, unlike other tools, such as the correlation of phase synchrony, synchronized regularity dynamics are uniquely identified via mSE analysis. In addition, a model for the operation of this novel algorithm in the presence of white Gaussian noise is presented, which, in contrast to the existing algorithms, reveals for the first time that increasing correlation between different variates reduces entropy. View Full-Text
Keywords: multivariate sample entropy; time series synchronization; structural complexity multivariate sample entropy; time series synchronization; structural complexity
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Looney, D.; Adjei, T.; Mandic, D.P. A Novel Multivariate Sample Entropy Algorithm for Modeling Time Series Synchronization. Entropy 2018, 20, 82.

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