Journal
BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES
Volume 60, Issue 3, Pages 433-445Publisher
POLSKA AKAD NAUK, POLISH ACAD SCI, DIV IV TECHNICAL SCIENCES PAS
DOI: 10.2478/v10175-012-0055-0
Keywords
multivariate sample entropy; multivariate empirical mode decomposition (MEMD); multivariate multiscale entropy; complexity analysis; multivariate complexity; postural sway analysis; stride interval analysis; brain consciousness analysis; alpha-attenuated EEG data
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Established complexity measures typically operate at a single scale and thus fail to quantify inherent long-range correlations in real-world data, a key feature of complex systems. The recently introduced multiscale entropy (MSE) method has the ability to detect fractal correlations and has been used successfully to assess the complexity of univariate data. However, multivariate observations are common in many real-world scenarios and a simultaneous analysis of their structural complexity is a prerequisite for the understanding of the underlying signal-generating mechanism. For this purpose, based on the notion of multivariate sample entropy, the standard MSE method is extended to the multivariate case, whereby for rigor, the intrinsic multivariate scales of the input data are generated adaptively via the multivariate empirical mode decomposition (MEMD) algorithm. This allows us to gain better understanding of the complexity of the underlying multivariate real-world process, together with more degrees of freedom and physical interpretation in the analysis. Simulations on both synthetic and real-world biological multivariate data sets support the analysis.
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