Estimating sparse functional connectivity networks via hyperparameter-free learning model

Functional connectivity networks (FCNs) provide a potential way for understanding the brain organizational patterns and diagnosing neurological diseases. Currently, researchers have proposed many methods for FCN construction, among which the most classic example is Pearson's correlation (PC). Despite its simplicity and popularity, PC always results in dense FCNs, and thus a thresholding strategy is usually needed in practice to sparsify the estimated FCNs prior to the network analysis, which undoubtedly causes the problem of threshold parameter selection. As an alternative to PC, sparse representation (SR) can directly generate sparse FCNs due to the l₁ regularizer in the estimation model. However, similar to the thresholding scheme used in PC, it is also challenging to determine suitable values for the regularization parameter in SR. To circumvent the difficulty of parameter selection involved in these traditional methods, we propose a hyperparameter-free method for FCN construction based on the global representation among fMRI time courses. Interestingly, the proposed method can automatically generate sparse FCNs, without any thresholding or regularization parameters. To verify the effectiveness of the proposed method, we conduct experiments to identify subjects with mild cognitive impairment (MCI) and Autism spectrum disorder (ASD) from normal controls (NCs) based on the estimated FCNs. Experimental results on two benchmark databases demonstrate that the achieved classification performance of our proposed scheme is comparable to four conventional methods.