Complex Tensor Factorization With PARAFAC2 for the Estimation of Brain Connectivity From the EEG

Area of Science:

• Neuroscience
• Signal Processing
• Biomedical Engineering

Background:

• Functional brain connectivity estimation is crucial for clinical applications.
• Electroencephalography (EEG) and cross-spectrum analysis are common methods for assessing brain connectivity.
• Traditional tensor analysis methods have limitations in accurately estimating complex brain network dynamics.

Purpose of the Study:

• To evaluate the efficacy of tensor factorization, specifically the PARAFAC2 model, for estimating functional brain connectivity using EEG data.
• To develop and validate a novel connectivity metric based on complex tensor factorization of EEG signals.
• To compare the performance of the proposed PARAFAC2 method against traditional tensor analysis (PARAFAC) and MVAR-ICA.

Main Methods:

• A complex domain EEG model was derived to justify the use of the PARAFAC2 model.
• Complex tensor factorization based on PARAFAC2 was applied to decompose EEG data into spatial, spectral, and complex trial profiles.
• A connectivity metric was derived from the complex trial profiles of the extracted components.
• The method was validated on a benchmark EEG dataset and applied to EEG data from patients with mild cognitive impairment or Alzheimer's disease.

Main Results:

• PARAFAC2 demonstrated superior performance in estimating brain connectivity compared to PARAFAC across various signal-to-noise ratios.
• MVAR-ICA outperformed PARAFAC2 only at very low signal-to-noise ratios but lacked trial-to-trial information estimation.
• Analysis of patient data revealed that PARAFAC2 successfully identified loss of brain connectivity consistent with known pathology in mild cognitive impairment and Alzheimer's disease.

Conclusions:

• Complex PARAFAC2 is a suitable algorithm for EEG connectivity estimation, enabling the extraction of meaningful coupled sources.
• The proposed complex tensor factorization paradigm offers improved connectivity estimates over PARAFAC and MVAR-ICA.
• This novel approach successfully identifies brain connectivity and coupled sources in both benchmark and real-world EEG datasets, with potential for future clinical applications.