Functional brain network analysis has become one principled way of revealing informative organization architectures in healthy brains, and providing sensitive biomarkers for diagnosis of neurological disorders. Prior to any post hoc analysis, however, a natural issue is how to construct “ideal” brain networks given, for example, a set of functional magnetic resonance imaging (fMRI) time series associated with different brain regions. Although many methods have been developed, it is currently still an open field to estimate biologically meaningful and statistically robust brain networks due to our limited understanding of the human brain as well as complex noises in the observed data. Motivated by the fact that the brain is organized with modular structures, in this paper, we propose a novel functional brain network modeling scheme by encoding a modularity prior under a matrix-regularized network learning framework, and further formulate it as a sparse low-rank graph learning problem, which can be solved by an efficient optimization algorithm. Then, we apply the learned brain networks to identify patients with mild cognitive impairment (MCI) from normal controls. We achieved 89.01% classification accuracy even with a simple feature selection and classification pipeline, which significantly outperforms the conventional brain network construction methods. Moreover, we further explore brain network features that contributed to MCI identification, and discovered potential biomarkers for personalized diagnosis.

High-order correlation has recently been proposed to model brain functional connectivity network (FCN) for identifying neurological disorders, such as mild cognitive impairment (MCI) and autism spectrum disorder (ASD). In practice, the high-order FCN (HoFCN) can be derived from multiple low-order FCNs that are estimated separately in a series of sliding windows, and thus it in fact provides a way of integrating dynamic information encoded in a sequence of low-order FCNs. However, the estimation of low-order FCN may be unreliable due to the fact that the use of limited volumes/samples in a sliding window can significantly reduce the statistical power, which in turn affects the reliability of the resulted HoFCN. To address this issue, we propose to enhance HoFCN based on a regularized learning framework. More specifically, we first calculate an initial HoFCN using a recently developed method based on maximum likelihood estimation. Then, we learn an optimal neighborhood network of the initially estimated HoFCN with sparsity and modularity priors as regularizers. Finally, based on the improved HoFCNs, we conduct experiments to identify MCI and ASD patients from their corresponding normal controls. Experimental results show that the proposed methods outperform the baseline methods, and the improved HoFCNs with modularity prior consistently achieve the best performance.

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