Abstract
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.
Highlights
Multivariate techniques are needed to analyse data consisting of more than one time series [1,2,3].The majority of physiological and pathophysiological activities, and even many non-physiological signals, include interactions between different kinds of single processes
Our results indicate that multivariate MDE (mvMDE) is noticeably faster than the existing methods, leads to more stable results, better discriminates different kinds of biomedical time series, does not lead to undefined values for short multivariate time series, and needs to store a considerably smaller number of elements in comparison with Multivariate multiscale entropy (mvMSE)
The number of sample points for each of the 1/ f noise and white Gaussian noise (WGN) signals were 15,000. mvMSE and multivariate multiscale fuzzy entropy (mvMFE) are based on conditional entropy [2,8,17]
Summary
Multivariate techniques are needed to analyse data consisting of more than one time series [1,2,3].The majority of physiological and pathophysiological activities, and even many non-physiological signals, include interactions between different kinds of single processes. Multivariate techniques are needed to analyse data consisting of more than one time series [1,2,3]. Advances on information theory and non-linear dynamical approaches have recently allowed the study of different kinds of multivariate time series [3,7,8,9]. Due to the intrinsic non-linearity of diverse physiological and non-physiological processes, non-linear analysis of multivariate time series has been broadly used in biomedical signal processing with the aim of studying the relationship between simultaneously recorded signals [3,7,8]. P are mapped to c classes with integer indices from 1 to c To this aim, there are a number of linear and nonlinear mapping approaches [30]. The simple linear mapping technique may lead to the problem of assigning the majority of xk,i to limited classes when maximum or minimum values are noticeably larger or smaller than the mean/median value of the image [30].
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