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Entropy metrics are nonlinear measures to quantify the complexity of timeseries. Among them, permutation entropy is a common metric due to itsrobustness and fast computation. Multivariate entropy metrics techniques areneeded to analyse data consisting of more than one time series. To this end, wepresent a multivariate permutation entropy, $MPE_G$, using a graph-basedapproach.  Given a multivariate signal, the algorithm $MPE_G$ involves two main steps:1) we construct an underlying graph G as the Cartesian product of two graphs G1and G2, where G1 preserves temporal information of each times series togetherwith G2 that models the relations between different channels, and 2) weconsider the multivariate signal as samples defined on the regular graph G andapply the recently introduced permutation entropy for graphs.  Our graph-based approach gives the flexibility to consider diverse types ofcross channel relationships and signals, and it overcomes with the limitationsof current multivariate permutation entropy.

Multivariate permutation entropy, a Cartesian graph product approach