Multivariate permutation entropy, a Cartesian graph product approach

TL;DR

This paper introduces a novel multivariate permutation entropy method, MPE_G, using a graph-based approach to analyze complex multichannel time series data by constructing a Cartesian product graph that captures temporal and inter-channel relationships.

Contribution

The paper presents a new multivariate permutation entropy method based on Cartesian product graphs, allowing flexible modeling of temporal and inter-channel relationships in multichannel signals.

Findings

The method effectively captures diverse cross-channel relationships.

It overcomes limitations of existing multivariate permutation entropy methods.

The approach is applicable to complex multichannel time series analysis.

Abstract

Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse data consisting of more than one time series. To this end, we present a multivariate permutation entropy, $MPE_G$, using a graph-based approach. 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 G1 and G2, where G1 preserves temporal information of each times series together with G2 that models the relations between different channels, and 2) we consider the multivariate signal as samples defined on the regular graph G and apply the recently introduced permutation entropy for graphs. Our graph-based approach gives the flexibility to consider diverse types of cross channel relationships and signals, and it overcomes with the limitations of current multivariate permutation entropy.