A Modified Multivariate Permutation Entropy Algorithm - Pukenas, Kazimieras (Discontinuity, Nonlinearity, and Complexity, 2026)
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}