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Open AccessFeature PaperArticle

Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

School of Engineering, Institute for Digital Communications, University of Edinburgh, King’s Buildings, Edinburgh EH9 3FB, UK
Department of Neurology and Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA
Departamento de Psiquiatría y Psicología Médica, Universidad Complutense de Madrid, 28040 Madrid, Spain
Laboratorio de Neurociencia Cognitiva y Computacional, Centro de Tecnología Biomédica, Universidad Politecnica de Madrid and Universidad Complutense de Madrid, 28040 Madrid, Spain
Author to whom correspondence should be addressed.
Entropy 2019, 21(9), 913;
Received: 22 July 2019 / Revised: 10 September 2019 / Accepted: 12 September 2019 / Published: 19 September 2019
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications)
Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals. View Full-Text
Keywords: complexity; multivariate multiscale dispersion entropy; multivariate time series; electroencephalogram; magnetoencephalogram complexity; multivariate multiscale dispersion entropy; multivariate time series; electroencephalogram; magnetoencephalogram
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Azami, H.; Fernández, A.; Escudero, J. Multivariate Multiscale Dispersion Entropy of Biomedical Times Series. Entropy 2019, 21, 913.

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