Functional connectivity networks (FCNs) are important in the diagnosis of neurological diseases and the understanding of brain tissue patterns. Recently, many methods, such as Pearson’s correlation (PC), Sparse representation (SR), and Sparse low-rank representation have been proposed to estimate FCNs. Despite their popularity, they only capture the low-order connections of the brain regions, failing to encode more complex relationships (i.e. , high-order relationships). Although researchers have proposed high-order methods, like PC + PC and SR + SR, aiming to build FCNs that can reflect more real state of the brain. However, such methods only consider the relationships between brain regions during the FCN construction process, neglecting the potential shared topological structure information between FCNs of different subjects. In addition, the low-order relationships are always neglected during the construction of high-order FCNs. To address these issues, in this paper we proposed a novel method, namely Ho-FCNTops, towards estimating high-order FCNs based on brain topological structure. Specifically, inspired by the Group-constrained sparse representation (GSR), we first introduced a prior assumption that all subjects share the same topological structure in the construction of the low-order FCNs. Subsequently, we employed the Correlation-reserved embedding (COPE) to eliminate noise and redundancy from the low-order FCNs. Meanwhile, we retained the original low-order relationships during the embedding process to obtain new node representations. Finally, we utilized the SR method on the obtained new node representations to construct the Ho-FCNTops required for disease identification. To validate the effectiveness of the proposed method, experiments were conducted on 137 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database to identify Mild Cognitive Impairment (MCI) patients from the normal controls. The experimental results demonstrate superior performance compared to baseline methods.
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