Optimizing non-uniform multivariate embedding for multiscale entropy analysis of complex systems

Multivariate signals are ubiquitous in various complex systems. There has been substantial interest in measuring the complexity of them to describe the target system. Traditional entropy-based methods are applicable only to univariate time series and cannot properly assess the structural complexity as a whole. The recently proposed multivariate multiscale entropy is capable of evaluating the complexity of a complex system of multi-channel data, but it is based on uniform time delay embedding and not able to account for multiple time scales structure. To this end, we develop the non-uniform multivariate multiscale entropy based on a non-uniform multivariate embedding which is optimized by solving the proposed algorithm. Experimental results on both synthetic chaotic systems and real-world brain systems of multivariate physiological signals demonstrate that the nonuniform multivariate multiscale entropy outperforms the multivariate multiscale entropy in measuring the complexity of multivariate complex systems, which is potentially applied for critical transition detection and pattern recognition problems.