  Data fusion refers to the joint analysis of multiple datasets which provide
complementary views of the same task. In this preprint, the problem of jointly
analyzing electroencephalography (EEG) and functional Magnetic Resonance
Imaging (fMRI) data is considered. Jointly analyzing EEG and fMRI measurements
is highly beneficial for studying brain function because these modalities have
complementary spatiotemporal resolution: EEG offers good temporal resolution
while fMRI is better in its spatial resolution. The fusion methods reported so
far ignore the underlying multi-way nature of the data in at least one of the
modalities and/or rely on very strong assumptions about the relation of the two
datasets. In this preprint, these two points are addressed by adopting for the
first time tensor models in the two modalities while also exploring double
coupled tensor decompositions and by following soft and flexible coupling
approaches to implement the multi-modal analysis. To cope with the Event
Related Potential (ERP) variability in EEG, the PARAFAC2 model is adopted. The
results obtained are compared against those of parallel Independent Component
Analysis (ICA) and hard coupling alternatives in both simulated and real data.
Our results confirm the superiority of tensorial methods over methods based on
ICA. In scenarios that do not meet the assumptions underlying hard coupling,
the advantage of soft and flexible coupled decompositions is clearly
demonstrated.
