A Modified Multivariate Permutation Entropy Algorithm
This paper proposes a modified multivariate permutation entropy (MPE) algorithm to quantify the complexity of the multi-dimensional time series. The novelty of the algorithm lies in a multivariate ordinal pattern representation which requires a significantly smaller number of combinations of obtained multivariate d-order permutations for m-dimensional time series, comparing the direct application of a univariate permutation entropy to the multi-dimensional time series and resulting in the value of d!^m combinations. More specifically, the number of combinations of multivariate ordinal patterns is reduced to d!^k with k, number=1, journal=Discontinuity, Nonlinearity, and Complexity, author=Pukenas, Kazimieras, year=2026, month=Aug., pages=15–22