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

The coupling between neuronal populations and its magnitude have been shown to be informative for various clinical applications. One method to estimate functional brain connectivity is with electroencephalography (EEG) from which the cross spectrum between different sensor locations is derived. We wish to test the efficacy of tensor factorization in the estimation of brain connectivity. An EEG model in the complex domain is derived that shows the suitability of the PARAFAC2 model. Complex tensor factorization based on PARAFAC2 is used to decompose the EEG into scalp components described by the spatial, spectral, and complex trial profiles. A connectivity metric is also derived on the complex trial profiles of the extracted components. Results on a benchmark EEG dataset confirmed that the PARAFAC2 can estimate connectivity better than traditional tensor analysis such as PARAFAC within a range of signal-to-noise ratios. MVAR-ICA outperformed PARAFAC2 for very low signal-to-noise ratios while being inferior in most of the range, and in contrast to our method, MVAR-ICA does not allow the estimation of trial to trial information. The analysis of the EEG from patients with mild cognitive impairment or Alzheimer's disease showed that the PARAFAC2 identifies loss of brain connectivity agreeing with prior pathological knowledge. The complex PARAFAC2 algorithm is suitable for the EEG connectivity estimation since it allows to extract meaningful-coupled sources and provides better estimates than complex PARAFAC and MVAR-ICA. A new paradigm that employs complex tensor factorization has demonstrated to be successful in identifying brain connectivity and the location of couples sources for both a benchmark and a real-world EEG dataset. This can enable future applications and has the potential to solve some the issues that deteriorate the performance of traditional connectivity metrics.