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Updated: Jul 16, 2025

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Measuring multivariate phase synchronization with symbolization and permutation.

Zhaohui Li1, Xinyan Wang2, Yanyu Xing2

  • 1School of Information Science and Engineering, Yanshan University, Qinhuangdao, 066004, China; Hebei Key Laboratory of information transmission and signal processing, Yanshan University, Qinhuangdao, 066004, China.

Neural Networks : the Official Journal of the International Neural Network Society
|September 23, 2023
PubMed
Summary

We developed a new method, symbolic phase difference and permutation entropy (SPDPE), to measure global phase synchronization in neural networks. SPDPE accurately quantifies brain network interactions and outperforms existing techniques, even with noisy data.

Keywords:
Global phase synchronizationMultivariate neural signalPermutationSeizure classificationSymbolization

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Signal Processing

Background:

  • Phase synchronization is crucial for neural information processing.
  • Existing bivariate measures fail to capture global interactions in neural systems.
  • Multivariate neural signal analysis necessitates advanced global phase synchronization (GPS) quantification.

Purpose of the Study:

  • To introduce a novel method, symbolic phase difference and permutation entropy (SPDPE), for estimating GPS in neural networks.
  • To address the limitations of bivariate measures in capturing complex neural interactions.
  • To provide a robust tool for multivariate neural signal analysis.

Main Methods:

  • Developed SPDPE by symbolizing phase differences in multivariate neural signals.
  • Estimated GPS using permutation patterns of symbolic sequences.
  • Validated SPDPE with simulated data (Kuramoto and Rössler models) and real SEEG data.

Main Results:

  • SPDPE accurately characterizes GPS and effectively resists noise.
  • The method shows low sensitivity to data length.
  • SPDPE successfully classified seizures and non-seizures using SEEG data.

Conclusions:

  • SPDPE offers a significant advancement in quantifying global phase synchronization.
  • The method has broad applicability in brain-computer interfaces, brain modeling, and EEG-fMRI analysis.
  • SPDPE enhances the understanding of neural network dynamics and information processing.