A graph structure is a mathematical model composed of nodes edges connecting these nodes (10), used to represent objects and their relationships. Graph neural networks (GNNs) leverage neural network techniques applied to the nodes and edges of the graph to effectively learn and extract features of individual nodes, edges, and the entire graph. This enables GNN and its variants variants (11–13) to achieve strong performance in tasks node classification, graph classification, and link prediction.

GNN-based methods treat brain regions as nodes and their connections as edges. Mapping fMRI data into a graph structure allows researchers to capture functional associations between brain regions. For example, Li et al. (4) introduced BrainGNN, which uses ROI-aware graph convolutional layers and ROI-selection pooling layers to identify key brain regions related to autism disease. Wang et al. (14) proposed adaptive multi-channel graph convolutional networks, which focus on integrating node features and topological structures to improve the performance of semi-supervised node classification tasks. These methods extend the traditional graph convolutional network paradigm and offer valuable tools for efficient modeling and analysis of brain network data.

To address the limitations of traditional graph representations, researchers introduced hypergraphs. A hypergraph uses hyperedges that can connect any number of nodes, allowing for the natural modeling of high-order interactions among multiple brain regions (15). Hypergraph neural networks (HGNNs) can capture more complex patterns by aggregating and updating features from hyperedges and their associated nodes nodes (8, 16). This approach supports a more detailed analysis of high-order networks in the brain.

Hypergraphs and HGNNs have also been introduced to the analysis of brain networks (6, 7). For example, Greenspan et al. (17) introduced the BrainHGNN model, which uses ROI identity encoding and random-walk strategies to build a hypergraph. A self-learned weighted hypergraph convolution updates node and hyperedge features, revealing AD-related propagation patterns. Ji et al. (18) proposed a hypergraph attention network to model functional brain networks with kNN and k-means, by using node and hyperedge attention layers. However, the current hypergraph structure modeling method often relies on fixed data-driven strategies, resulting in fixed sets of nodes and edges. This rigid approach does not fully reflect the complex and multi-scale high-order interactions in real brain networks and ignores valuable domain knowledge. Combining domain knowledge with data-driven strategies to adaptively model high-order relationships from a global to a local scale remains a key challenge in brain network analysis.

As shown in Figure 1, the proposed UMHL framework has three key modules. In the knowledge-driven branch, a hypergraph is constructed using prior knowledge of eight functional brain subnetworks subnetworks (19) to capture high-order associations within each region. In the data-driven branch, global-local hypergraph modeling method that adapts the granularity of interactions. Both branches are combined through soft voting for brain disease classification.

Consider a hypergraph H=(V,E), where V is the set of vertices and E is the set of hyperedges. The incidence matrix can be defined as H∈ℝ|V|×|E|, whose elements are determined as follows:

where w_e(v) denotes the weight of vertex v in the hyperedge e. Unlike the adjacency matrix of a traditional graph, which is square, the incidence matrix of a hypergraph is not necessarily square. When |V|≠|E|, H forms a rectangular matrix. For the same dataset with fixed nodes, this characteristic enables the direct concatenation of different types of hyperedges, thereby creating fused hyperedges and a fused hypergraph structure (20).

Initially, preprocessed fMRI data comprising blood oxygenation level-dependent (BOLD) signals are registered to a standardized brain template (21). Subsequently, Pearson's correlation coefficients are computed to derive the functional connectivity (FC) matrix representing pairwise associations between regions of interest (ROIs). This FC matrix serves as input to both computational branches.

Within the knowledge-driven hypergraph neural network (HGNN) branch, we integrate the derived FC features with a priori knowledge pertaining to eight pivotal functional brain regions. This integration facilitates the construction of a biologically grounded hypergraph structure, which explicitly models higher-order functional associations among these specialized subnetworks. Previous studies (19) have established that distinct brain regions subserve specialized cognitive and neural functions through collaborative interactions. By embedding these well-established neurobiological insights into the feature extraction framework, our model enhances the capacity to identify complex connectivity patterns and detect disease-associated alterations specific to individual subnetworks.

Formally, given the FC matrix F∈ℝ^N×N, where N represents the number of ROIs, i.e., brain regions. Each ROI is treated as a node in the hypergraph, and its feature vector is defined as the row vector of F corresponding to that node. For a node v_i (corresponding to the i-th ROI), its feature vector is xi=[Fi1,Fi2,…,FiN]⊤∈ℝN, where F_ij denotes the functional connectivity strength between ROI v_i and ROI v_j. Based on the prior knowledge of eight functional brain subnetworks, all N ROIs are partitioned into eight mutually exclusive functional brain subnetworks. Each subset is treated as a hyperedge e_m, connecting all ROIs within that brain subnetwork. Thus, the hypergraph is constructed as:

We introduce two modeling strategies to enrich multi-scale feature representations, i.e., the granularity-adaptive local modeling and the kNN-based global modeling. By leveraging the inherent characteristics of the data, the former constructs non-overlapping, fine-grained local topology hyperedges, and the latter constructs overlapping, global semantic hyperedges.

To summarize, we construct three types of hypergraph structures for each individual: a knowledge-driven hypergraph Hprior=(V,Eprior), a granularity-adaptive local hypergraph Hlocal=(V,Elocal), and a kNN based global semantic hypergraph Hglobal=(V,Eglobal). Since all three hypergraphs are built upon the same individual, they share the same node set V, i.e., brain regions).

For a hypergraph H=(V,E), where H∈{Hprior,Hlocal,Hglobal}, it can be denoted as a combination of a feature matrix and an incidence matrix, i.e., (X⁽⁰⁾, H). The hypergraph convolution process can be formally expressed as Gao et al. (8): (4)X(l+1)=δ(H(Mask(H⊤X(l)Θ(l)))), where δ(·) denotes the nonlinear activation function, Mask(·) represents the hyperedge feature masking, and Θ^(l) is the learnable parameters. After several layers of hypergraph convolution, the learned node features X^(L+1) is obtained.

Next, we perform feature embedding on the three sets of node features. Since Xprior(L+1) and Xlocal(L+1) consist of mutually exclusive functional brain regions and fine-grained subnetworks respectively, a local pooling strategy is applied to these two representations. Specifically, for each subnetwork, the node feature vectors are mean pooled to generate the feature representation of the subnetwork, and the feature representations of all subnetworks are then concatenated to form the final feature representations f_prior and f_local. For Xglobal(L+1), a global pooling is applied to obtain f_global, where all node features are pooled using both max pooling and mean pooling, and the results are concatenated.

Finally, f_prior, f_local, and f_global are separately passed through multi-layer perceptrons (MLPs) and Softmax layers to generate logits for classification. The final classification decision is obtained through soft voting, where the logits are summed and a final softmax operation is applied: (5)Logitsfinal=Softmax(Logitsprior+Logitslocal+Logitsglobal). In summary, the knowledge-driven hypergraph focuses on capturing higher-order relationships within the predefined functional brain networks. In contrast, the data-driven hypergraphs (global and local) capture semantic relevance at the global scale and fine-grained topological structures at the local scale of the brain network, respectively. Consequently, the feature representations from these three distinct perspectives are inherently complementary rather than redundant. During the feature fusion stage, the use of soft voting further mitigates detrimental interference between branches, effectively ensuring model performance and robustness.

We used the Autism Brain Imaging Data Exchange (ABIDE) dataset (24) and the ADHD-200 dataset (25) in this work. The ABIDE dataset consists of 403 autism spectrum disorder (ASD) patients and 468 normal controls (NC). The ADHD-200 dataset consists of 362 ADHD patients and 585 NCs. Each subject contains at least one rs-fMRI scan. All the rs-fMRI are processed via the Data Processing Assistant for Resting-State fMRI (DPARSF) Tool with standard steps¹. Subsequently, each subject's brain was parcellated into 200 regions of interest (ROIs) based on the CC200 atlas (21).

All experiments were performed on an NVIDIA RTX 3090 GPU using PyTorch. The Adam optimizer was employed with a learning rate of 0.0005 and a weight decay of 0.00001. For hypergraph construction, the default parameter k of the global branch was set to 5. The model comprises two hypergraph convolutional layers and was trained for 100 epochs with early stopping.

The proposed method was evaluated to CNN-based method [BrainNetCNN (26)], GNN-based methods [BrainGNN (4), MVS-GCN (27), PLSNet (28), and BrainIB (5)], HGNN-based methods [HGNN (29) and HH-GF (30)].

The 5-fold cross-validation was used for all methods. The following metrics were selected for evaluation: accuracy, sensitivity, specificity, F1 score, and AUC. The final results are presented as the mean and standard error obtained during the 5-fold cross-validation process.

The experimental results on the ABIDE dataset are shown in Table 1, which demonstrates that our proposed UMHL method outperforms existing graph-based and hypergraph-based methods. The main limitation of graph-based methods lies in their ability to capture only pairwise low-order correlations, which are insufficient to represent the complex multi-region interactions and higher-order correlations in brain networks. While hypergraph-based methods attempt to address this limitation by connecting multiple nodes with hyperedges, their reliance on data-driven strategies often fails to precisely capture the fine-grained, disease-specific higher-order relationships between brain regions. Our method combines both knowledge-driven and data-driven strategies, utilizing prior knowledge to guide the construction of hypergraphs while flexibly modeling both local and global relationships. As shown in Table 2, on the ADHD dataset, the results reveal that all methods exhibit higher specificity than sensitivity, which reflects the inherent characteristics and imbalance of the dataset. Despite this, our UMHL method shows remarkable performance, indicating its strong robustness and flexibility in handling imbalanced datasets.

Furthermore, the key hyperparameter k can highly affect the performance. Specifically, setting k too large increases the number of neighbor nodes connected to each brain region, potentially leading to an overly complex hypergraph structure that incorporates numerous irrelevant or weakly correlated regions. This redundancy could dilute genuinely pathological signals and reduce model precision. Conversely, setting k too small results in overly sparse connections between brain region nodes, potentially failing to adequately capture important disease-specific inter-regional interaction patterns, leading to insufficient sensitivity to key pathological features. Therefore, the k value needs to be judiciously selected within a moderate range based on specific data characteristics to achieve precise and effective feature capture.

Table 3 shows the ablation study results. The prior knowledge-driven model does not capture the complex inter-region relationships, leading to lower performance. The global interaction model improves the results by modeling large-scale associations, but it still lacks the fine-grained details provided by local interactions. When both local and global models are combined, the performance significantly improves, demonstrating that detailed, region-specific interactions are essential for accurate brain disease diagnosis. The full UMHL model leverages the strengths of each component, showing that combining prior knowledge, global, and local interactions provides a more robust and effective approach. As shown in Figure 2, we have visualized the significant hyperedges of different hypergraph modeling methods, where the hyperedges of the eight brain subnetworks are distinguished by color. Additionally, the stark contrast in significance between the two data-driven modeling approaches further underscores the importance of incorporating both global and local information to achieve a more comprehensive understanding.