During recent decades, functional magnetic resonance imaging (fMRI)-derived functional connectivity network (FCN) or functional connectome, characterized by functional connectivity (FC) between every pair of human brain regions of interest (ROIs), has been extensively investigated to discover potential neuro-imaging biomarkers for automated diagnosis of psychiatric and neurological disorders, such as autism, schizophrenia, and depression (Van Den Heuvel and Pol, 2010, Fornito et al., 2015, Park and Friston, 2013). Compared with the conventional symptom-based diagnostic criteria that are subjective and therefore most likely to lead to misdiagnosis and missed diagnosis, the FCN provides an objective, reliable, and noninvasive diagnostic modality to examine the pathophysiological mechanisms underlying such brain diseases (Wang et al., 2021, Li et al., 2022). Specifically, the FCN is naturally delineated as a graph, for which vertexes represent the spatially distributed but functionally linked ROIs, and edges indicate the between-ROI FCs that are quantified as the dependence between blood oxygenation level-dependent (BOLD) time series of paired ROIs. Abnormalities in FC at the level of the whole brain are expected to result in disease-related biomarker signatures.

A massive number of machine/deep learning models have recently attracted considerable attention to FCN analysis for automated diagnosis of brain diseases, such as support vector machine (SVM) for discrimination between multiple system atrophy and Parkinson’s disease (Baggio et al., 2019), logistic regression for Alzheimer’s disease early detection (Zhang et al., 2015), and deep neural networks (DNNs) for schizophrenia identification (Chen et al., 2021), among others. However, the FCN, as a matrix consisting of all FCs, is straightforwardly vectorized as input into the aforementioned models, such that significant topological structure information among ROIs is overlooked. In order to uncover the discriminative patterns in brain network, FCN should be regarded as irregular graph-structured data and fed into one diagnostic model as a whole, where each ROI represents a vertex and its associated FC profile serves as the vertex features.

To this end, as graph convolutional network (GCN) can well handle irregular graph structures with the graph convolution to propagate features of adjacent vertexes (Scarselli et al., 2008), GCN based models have achieved greater successes in learning FCN feature representation (namely FCN embedding), and consequently have improved the diagnostic performance for brain diseases (Ktena et al., 2018, Qin et al., 2022, Chu et al., 2022, Xu et al., 2023, Yang et al., 2023, Huang et al., 2022). A systematic study of GCN-based brain network analysis with models, examples and out-of-box Python package has been presented (Cui et al., 2022). For example, a Siamese GCN model was proposed to learn a graph similarity metric between FCNs for identifying autism patients from healthy controls (Ktena et al., 2018). A graph embedding learning (GEL) model was investigated for diagnosis of major depressive disorder, where FCN embeddings were first learned via GCN and then fed into one fully connected layer activated by a soft-max function for final classification (Qin et al., 2022). Moreover, a multiview graph embedding learning (MGEL) model was developed to leverage complementary information of FCNs constructed on multiple atlases, resulting in a multiatlas-based FCN embedding with better performance in downstream autism diagnosis than only using FCN on any single atlas (Chu et al., 2022).

Current GCNs, although effective, still suffer from three main deficiencies when applied to FCN analysis, particularly in multisite fMRI studies. First, we know that in GCNs, the vertex features are propagated along between-ROI connections on a simple graph. However, brain network is likely more complex than can be wholly represented by pairwise relations between ROIs (Yu et al., 2011). In other words, there shall exist complicated interactions among multiple (more than two) ROIs. Second, the FCN embedding is considered for each subject individually in the learning process of GCNs, failing to manage the between-subject association of intra- and inter-classes that can quantify compactness within each class and separation between classes. Third, most previous GCN based multisite FCN studies typically assume that fMRI data collected from different sites share the same or similar distributions, yet the between-site heterogeneity arising from differences in imaging scanners and/or scanning protocols is often ignored. This may lead to biased modeling of FCNs for disease diagnosis (Guan and Liu, 2021).

To address the above issues, in this paper we propose a class-consistency and site-independence multiview hyperedge-aware hypergraph embedding learning (CcSi-MHAHGEL) framework to accommodate multiatlas-based FCNs for diagnosis of brain diseases in a multisite fMRI study, as illustrated in Fig. 2. It is basically comprised of the following three components. (1) We first develop a multiview hyperedge-aware hypergraph convolutional network (HGCN) to integrate FCNs constructed on multiple atlases for each subject. To do this, for each subject, we learn an FCN embedding vector with respect to every atlas via a hyperedge-aware HGCN followed by a combination of max and average poolings, and the multiatlas-based FCN embedding is then a weighted concatenation of the learned FCN embedding vectors for all the atlases. Note here that by modeling brain network as a hypergraph, we employ HGCN instead of GCN to capture more complex relations among ROIs, due to the fact that an edge of a hypergraph (Berge, 1985) (called a hyperedge) can connect more than two vertexes (i.e., ROIs) which makes HGCN involve vertex feature propagation both within and across hyperedges at two levels. Moreover, in contrast with predefining the hyperedge weights and maintaining them constant throughout all the hypergraph convolution layers in traditional HGCNs, we adaptively learn more flexible hyperedge weights in each hypergraph convolution layer of our hyperedge-aware HGCN. (2) In addition, we impose two modules for jointly learning of the multiatlas-based FCN embeddings to take into account the between-subject associations across classes and sites, respectively. Specifically, a class-consistency module is utilized to simultaneously minimize the intra-class dissimilarities and inter-class similarities of the embeddings, and in the meantime, a site-independence module is adopted to minimize the statistical dependence between the embeddings and acquisition sites for mitigating undesired site influences. (3) Finally, the learned multiatlas-based FCN embeddings are input into a few fully connected layers followed by the soft-max classifier to detect brain diseases.

To validate the efficiency of our CcSi-MHAHGEL, we conduct extensive experiments on the automated anatomical labeling (AAL) (Tzourio-Mazoyer et al., 2002) and Harvard-Oxford (HO) (Desikan et al., 2006) atlas-based FCNs of 355 subjects (167 autism spectrum disorder (ASD) patients and 188 healthy controls) from the top four sites with the largest sample sizes in the ABIDE database (Di Martino et al., 2014). The experimental results on ASD identification demonstrate the superiority of our CcSi-MHAHGEL over several other methods. We also exploit gradient-weighted class activation mapping (Grad-CAM) (Selvaraju et al., 2017) in our CcSi-MHAHGEL to uncover discriminative ROIs associated with ASD, and our findings are in line with previous reports.

To summarize, the contribution of this paper is threefold.

We introduce a novel multiview hyperedge-aware HGCN based FCN embedding learning approach to integrate FCNs constructed on multiple brain atlases at different spatial scales, where the multiatlas-based FCNs provide multiple views of brain network, and within each view, brain network is modeled as a hypergraph (not a simple graph) and hyperedge-aware HGCN instead of GCN or HGCN is developed to capture more complex information in brain network.

Class-consistency and site-independence modules are formulated to account for the between-subject association of intra- and inter-classes and the between-site heterogeneity in the embedding space, respectively, which can promote the learning of multiatlas-based FCN embeddings discriminative across classes and sites.

The extensive experiments on the multisite, multiatlas fMRI from the ABIDE demonstrate that the proposed CcSi-MHAHGEL outperforms several other methods for ASD identification.

The remainder of this paper is organized as follows. Section 2 reviews the details of hypergraphs and HGCN, and presents the proposed CcSi-MHAHGEL. Section 3 provides the experimental results for autism identification, followed by discussions on the experiment related analysis, the limitations of this current study, and future research directions in Section 4. Section 5 concludes this paper. As a remark, this paper is the extension of our previous work (Wang and Xiao, 2023) by presenting progress in all the above three components (i.e., multiview hyperedge-aware HGCN, and class-consistency and site-independence modules) of CcSi-MHAHGEL.

Notation

Throughout this paper, we use uppercase boldface, lowercase boldface, and normal italic letters to denote matrices, vectors, and scalars, respectively. Let I be the identity matrix, and 1 be the vector of ones. The element at the ith row and jth column of a matrix A is denoted as Ai,j. The superscript T denotes the vector/matrix transpose, tr(⋅) denotes the trace of a matrix, and |⋅| denotes the cardinality of a set.