Parallel Factorization to Implement Group Analysis in Brain Networks Estimation

When dealing with complex functional brain networks, group analysis still represents an open issue. In this paper, we investigated the potential of an innovative approach based on PARAllel FActorization (PARAFAC) for the extraction of the grand average connectivity matrices from both simulated and real datasets. The PARAFAC approach was solved using three different numbers of rank-one tensors (PAR-FACT). Synthetic data were parametrized according to different levels of three parameters: network dimension (NODES), number of observations (SAMPLE-SIZE), and noise (SWAP-CON) in order to investigate the way they affect the grand average estimation. PARAFAC was then tested on a real connectivity dataset, derived from EEG data of 17 healthy subjects performing wrist extension with left and right hand separately. Findings on both synthetic and real data revealed the potential of the PARAFAC algorithm as a useful tool for grand average extraction. As expected, the best performances in terms of FPR, FNR, and AUC were achieved for great values of sample size and low noise level. A crucial role has been revealed for the PAR-FACT parameter, revealing that an increase in the number of rank-one tensors solving the PARAFAC problem leads to an increase in FPR values and, thus, to a worse grand average estimation.