Abstract
Multiscale entropy (MSE) was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i) a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii) the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE)—based on the same steps as MSE—also exists. Compared to MSE, rcMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy for short time series. The multivariate versions of MSE (MMSE) and rcMSE (MrcMSE) have also been introduced. In the coarse-graining step used in MSE, rcMSE, MMSE, and MrcMSE, the mean value is used to derive representations of the original data at different resolutions. A generalization of MSE was recently published, using the computation of different moments in the coarse-graining procedure. However, so far, this generalization only exists for univariate signals. We therefore herein propose an extension of this generalized MSE to multivariate data. The multivariate generalized algorithms of MMSE and MrcMSE presented herein (MGMSE and MGrcMSE, respectively) are first analyzed through the processing of synthetic signals. We reveal that MGrcMSE shows better performance than MGMSE for short multivariate data. We then study the performance of MGrcMSE on two sets of short multivariate electroencephalograms (EEG) available in the public domain. We report that MGrcMSE may show better performance than MrcMSE in distinguishing different types of multivariate EEG data. MGrcMSE could therefore supplement MMSE or MrcMSE in the processing of multivariate datasets.
Highlights
Multiscale entropy (MSE) was proposed in the 2000s to quantify the degree of unpredictability of systems across multiple scales [1,2]
If we focus on the decrease rate observed for MGMSEσ2 and MGrcMSEσ2, we can say that the results are consistent with what was expected: the more the multivariate data contain
We observe that MGrcMSEμ, MGrcMSEσ2, and MGrcMSEskewness show different patterns for each of the five cases
Summary
Multiscale entropy (MSE) was proposed in the 2000s to quantify the degree of unpredictability of systems across multiple scales [1,2]. The coarse-graining procedure for scale τ is obtained by averaging the samples of the time series inside consecutive but non-overlapping windows of length τ. The length of a coarse-grained time series at a scale factor τ is equal to N/τ, where N is the number of samples in the original signal. (ii) Computation of the sample entropy for each coarse-grained time series. To increase the accuracy of entropy estimation, and to reduce the probability of inducing undefined entropy for short time series, a refined composite multiscale entropy (rcMSE) has recently been proposed [5]. To increase the accuracy of entropy estimation, and to reduce the probability of inducing undefined entropy for short time series, a refined composite multiscale entropy (rcMSE) has recently been proposed [5]. rcMSE is based on the same steps as MSE (see below)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
