Multiscale multivariate fuzzy entropy analysis

Multiscale multivariate sample entropy can test the multivariate complexity, which is accepted as a kind of reflection of nonlinear dynamical interactions in multichannel data. It is however relatively unstable due to the rigid ranking scheme used in comparison among different patterns. It is not applicable to the nonlinear and non-stationary data because the multiscale framework used is in fact handled by moving average succeeded by down-sampling, which actually has a premise of stationary data. We substitute a fuzzy membership function for the original rigid one and compare the performances of different kinds of fuzzy membership functions. In addition, we employ the multivariate empirical mode decomposition (MEMD) to capture different scales. Results show that the substitution of fuzzy membership function brings in significant stability. It is much more obvious by using the introduced physical fuzzy membership function (PFMF). Also MEMD could capture scales more robustly. In conclusion, the introduced PFMF- and MEMD-based MMFE perform best. Final analysis on the interactions between heart rate variability (HRV) and heart diastolic time interval variability (DIV) validates it. In addition, the results show that the multivariate complexity between HRV and DIV decreases in aging or heart failure group but in a distinctly different decreasing manner–it deceased at low scales with aging, indicating a loss of short-range correlation but both at low and high scales with heart failure, which shows the losses of both short- and long-range correlations. Studies in noninvasive detection of cardiovascular diseases should benefit from the above conclusions.