Multivariate Empirical Mode Decomposition for Quantifying Multivariate Phase Synchronization

Ali Yener Mutlu,Selin Aviyente

doi:10.1155/2011/615717

Ali Yener Mutlu, Selin Aviyente

Open Access

https://doi.org/10.1155/2011/615717

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Abstract

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.

Highlights

Studying the dynamics of complex systems is relevant in many scientific fields, from meteorology and geophysics to economics and neuroscience
Phase synchronization of chaotic oscillators occurs in many complex systems including the human brain, where synchronization of neural oscillators measured by means of noninvasive measurements such as multichannel electroencephalography (EEG) and magnetoencephalography (MEG) recordings (e.g., [3, 4]) is of crucial importance for visual pattern recognition and motor control
The proposed approach is based on the application of multivariate empirical mode decomposition for extracting time- and frequencydependent phase information, and adapting measures of correlation from statistics to multivariate analysis

Summary

Introduction

Studying the dynamics of complex systems is relevant in many scientific fields, from meteorology and geophysics to economics and neuroscience. We propose to use a recently developed transform, multivariate empirical mode decomposition (MEMD), for quantifying the phase synchrony between multiple time series. Multivariate EMD will be used for the first time to define pairwise synchrony between multiple time series across the same frequency This approach will allow us to quantify the synchrony across data-driven modes/frequencies that are consistent across all of the signals. This paper will extend the notion of bivariate synchrony to multivariate synchronization by employing measures of multivariate correlation and complexity to quantify the synchronization within and across groups of signals rather than between pairs This approach will be useful for applications such as EEG signals, where the synchronization within or across regions is more important than individual pairwise synchrony

Background

Multivariate EMD-Based Multivariate Synchrony Measures

Results

Conclusions