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Brain functional network (BFN) has become an increasingly important tool to understand the inherent organization of the brain and explore informative biomarkers of neurological disorders. Pearson’s correlation (PC) is the most widely accepted method for constructing BFNs and provides a basis for designing new BFN estimation schemes. Particularly, a recent study proposes to use two sequential PC operations, namely, correlation’s correlation (CC), for constructing the high-order BFN. Despite its empirical effectiveness in identifying neurological disorders and detecting subtle changes of connections in different subject groups, CC is defined intuitively without a solid and sustainable theoretical foundation. For understanding CC more rigorously and providing a systematic BFN learning framework, in this paper, we reformulate it in the Bayesian view with a prior of matrix-variate normal distribution. As a result, we obtain a probabilistic explanation of CC. In addition, we develop a Bayesian high-order method (BHM) to automatically and simultaneously estimate the high- and low-order BFN based on the probabilistic framework. An efficient optimization algorithm is also proposed. Finally, we evaluate BHM in identifying subjects with autism spectrum disorder (ASD) from typical controls based on the estimated BFNs. Experimental results suggest that the automatically learned high- and low-order BFNs yield a superior performance over the artificially defined BFNs  via  conventional CC and PC.

Estimating High-Order Brain Functional Networks in Bayesian View for Autism Spectrum Disorder Identification