Multivariate distance dispersion entropy: a complexity analysis method capturing intra- and inter-channel signal variations for multichannel data - Niu, Yan; Ding, Runan; Zhou, Mengni; Sun, Jie; Dou, Mingliang; Wen, Xin; Cui, Xiaohong; Yao, Rong; Wei, Jing; Xiang, Jie (Nonlinear dynamics, 2025)
Complexity analysis of multichannel signals provides valuable insight into complex nonlinear dynamic systems. Several multivariate entropy algorithms have been proposed by extending univariate entropy measures. However, there is a lack of multivariate entropy algorithms that simultaneously capture intra- and inter-channel signal variations. In this study, a novel entropy-based approach called multivariate distance dispersion entropy (mvDDE) was proposed. Simulated and real data were used to analyze the performance of the mvDDE algorithm. Using white Gaussian and 1/f noise, we found mvDDE to be more reliable and stable, especially for short signals, compared to multivariate sample entropy (mvSE) and multivariate dispersion entropy (mvDE). In addition, mvDDE was observed to have better anti-noise performance and lower computational cost using signals simulated by the MIX model. Finally, when mvDDE was applied to the complexity analysis of electrocardiogram data from 47 different subjects, significant differences were found between two of the three types of heartbeat signals using mvDDE, and a triple classification accuracy of 80.19% was achieved, outperforming mvSE and mvDE. Analysis of electroencephalogram data from Parkinson's patients and normal subjects was performed using mvDDE, with a classification accuracy of 99.74%. In addition, significant differences were found in the central region with mvDDE, but not with mvSE and mvDE. These results showed that mvDDE exhibited good diagnostic and detection performance. Thus, mvDDE is a valuable method for detecting the nonlinear dynamics and complexity of multivariate signals.