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This article is part of the series Recent Advances in Theory and Methods for Nonstationary Signal Analysis.

Open Access Open Badges Research Article

Multivariate Empirical Mode Decomposition for Quantifying Multivariate Phase Synchronization

Ali Yener Mutlu and Selin Aviyente*

Author Affiliations

Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA

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EURASIP Journal on Advances in Signal Processing 2011, 2011:615717  doi:10.1155/2011/615717

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2011/1/615717

Received:3 August 2010
Accepted:8 November 2010
Published:23 November 2010

© 2011 Ali Yener Mutlu and Selin Aviyente.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Quantifying the phase synchrony between signals is important in many different applications, including the study of the chaotic oscillators in physics and the modeling of the joint dynamics between channels of brain activity recorded by electroencephalogram (EEG). Current measures of phase synchrony rely on either the wavelet transform or the Hilbert transform of the signals and suffer from constraints such as the limit on time-frequency resolution in the wavelet analysis and the prefiltering requirement in Hilbert transform. Furthermore, the current phase synchrony measures are limited to quantifying bivariate relationships and do not reveal any information about multivariate synchronization patterns, which are important for understanding the underlying oscillatory networks. In this paper, we address these two issues by employing the recently introduced multivariate empirical mode decomposition (MEMD) for quantifying multivariate phase synchrony. First, an MEMD-based bivariate phase synchrony measure is defined for a more robust description of time-varying phase synchrony across frequencies. Second, the proposed bivariate phase synchronization index is used to quantify multivariate synchronization within a network of oscillators using measures of multiple correlation and complexity. Finally, the proposed measures are applied to both simulated networks of chaotic oscillators and real EEG data.

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