Brain Function Network: Higher Order vs. More Discrimination

Brain functional network (BFN) has become an increasingly important tool to explore individual differences and identify neurological/mental diseases. For estimating a “good” BFN (with more discriminative information for example), researchers have developed various methods, in which the most popular and simplest is Pearson's correlation (PC). Despite its empirical effectiveness, PC only encodes the low-order (second-order) statistics between brain regions. To model high-order statistics, researchers recently proposed to estimate BFN by conducting two sequential PCs (denoted as PC(2) in this paper), and found that PC(2)-based BFN can provide additional information for group difference analysis. This inspires us to think about (1) what will happen if continuing the correlation operation to construct much higher-order BFN by PC(n) (n>2), and (2) whether the higher-order correlation will result in stronger discriminative ability. To answer these questions, we use PC(n)-based BFNs to predict individual differences (Female vs. Male) as well as identify subjects with mild cognitive impairment (MCI) from healthy controls (HCs). Through experiments, we have the following findings: (1) with the increase of n, the discriminative ability of PC(n)-based BFNs tends to decrease; (2) fusing the PC(n)-based BFNs (n>1) with the PC(1)-based BFN can generally improve the sensitivity for MCI identification, but fail to help the classification accuracy. In addition, we empirically find that the sequence of BFN adjacency matrices estimated by PC(n) (n = 1,2,3,⋯ ) will converge to a binary matrix with elements of ± 1.