Multivariate permutation entropy, a Cartesian graph product approach

John Stewart Fabila Carrasco*, Chao Tan, Javier Escudero

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a commonly used 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, MPEG, using a graph-based approach. Given a multivariate signal, the algorithm to compute MPEG 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 and G2 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.
Original languageEnglish
Title of host publication2022 30th European Signal Processing Conference (EUSIPCO)
PublisherEuropean Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Electronic)978-90-827970-9-1, 978-90-827970-8-4
ISBN (Print)978-1-6654-6799-5
Publication statusE-pub ahead of print - 18 Oct 2022
Event30th European Signal Processing Conference - Belgrade , Serbia
Duration: 29 Aug 20222 Sep 2022

Publication series

NameEuropean Signal Processing Conference (EUSIPCO)
ISSN (Print)2219-5491
ISSN (Electronic)2076-1465


Conference30th European Signal Processing Conference
Abbreviated titleEUSIPCO 2022
Internet address


  • Computational modeling
  • time series analyses
  • signal processing algorithms
  • Europe
  • Signal processing
  • Time measurement
  • Permutation entropy
  • graph signals
  • entropy metrics
  • complexity
  • Multivariate Time Series


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