Coupled CP Decomposition of Simultaneous MEG-EEG Signals for Differentiating Oscillators During Photic Driving.

Kristina Naskovska,Jens Haueisen,Stephan Lau,Martin Haardt,Alexey A Korobkov

doi:10.3389/fnins.2020.00261

Abstract

Magnetoencephalography (MEG) and electroencephalography (EEG) are contemporary methods to investigate the function and organization of the brain. Simultaneously acquired MEG-EEG data are inherently multi-dimensional and exhibit coupling. This study uses a coupled tensor decomposition to extract the signal sources from MEG-EEG during intermittent photic stimulation (IPS). We employ the Coupled Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization (C-SECSI). After comparing its performance with alternative methods using simulated benchmark data, we apply it to MEG-EEG recordings of 12 participants during IPS with fractions of the individual alpha frequency between 0.4 and 1.3. In the benchmark tests, C-SECSI is more accurate than SECSI and alternative methods, especially in ill-conditioned scenarios, e.g., involving collinear factors or noise sources with different variances. The component field-maps allow us to separate physiologically meaningful oscillations of visually evoked brain activity from background signals. The frequency signatures of the components identify either an entrainment to the respective stimulation frequency or its first harmonic, or an oscillation in the individual alpha band or theta band. In the group analysis of both, MEG and EEG data, we observe a reciprocal relationship between alpha and theta band oscillations. The coupled tensor decomposition using C-SECSI is a robust, powerful method for the extraction of physiologically meaningful sources from multidimensional biomedical data. Unsupervised signal source extraction is an essential solution for rendering advanced multi-modal signal acquisition technology accessible to clinical diagnostics, pre-surgical planning, and brain computer interface applications.

Highlights

Magnetoencephalography (MEG) and electroencephalography (EEG) are contemporary methods to investigate the function and organization of the brain
In order to systematically compare the C-SECSI decomposition approach with other methods (Roemer and Haardt, 2008, 2013; Cichocki et al, 2015) on the algorithmic level, we use a set of simulations covering a broad range of tensor properties
These curves result from Monte Carlo simulations with 1,000 realizations, for real valued tensors of dimensions 8 × 8 × 8, which spans open a tensor space with sufficient points per dimension to include complex multidimensional patterns

Summary

Introduction

Magnetoencephalography (MEG) and electroencephalography (EEG) are contemporary methods to investigate the function and organization of the brain. They, respectively, measure the magnetic flux and the electric potential at the head surface that are generated by simultaneous neuronal activity inside the brain. Acquired MEG and EEG signals capture aspects of the same electric activity over time and can, exhibit coupling. Tensor algebra has applications in signal processing, data analysis, blind source separation, and many more (Cichocki et al, 2015). Roemer and Haardt (2008, 2013) present a Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization (SECSI) for the efficient and robust computation of the an approximate low-rank CP decomposition of noise corrupted data The multidimensional signals are decomposed into rank one components according to the Canonical Polyadic (CP) decomposition (Kolda and Bader, 2009). Roemer and Haardt (2008, 2013) present a Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization (SECSI) for the efficient and robust computation of the an approximate low-rank CP decomposition of noise corrupted data

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