The brain is an information-processing system with many complicated and precise computations when dealing with various daily activities [1]. Daily physiological activities are always associated with the interaction between multiple neurons, neuronal clusters, or multiple brain regions. This interaction is called brain functional network (BFN), which describes the relationship between temporal blood-oxygen-level-dependent (BOLD) signals from distant brain areas [2]. Dementia (i.e., Alzheimer’s Disease, AD) is a typical kind of neuropathic disorder where patients usually show abnormal functional connections between brain regions [3]. It can result in a series of cognitive symptoms: memory impairment, poor language expression, and changes in vision [4,5]. Functional magnetic resonance imaging (fMRI) can easily capture these abnormal features using the non-intrusive scanning technology [6]. The BFN can bring a new way for the diagnosis and analysis of neurodegenerative disorders [7]. Therefore, analysis of BFNs is important to mine complex brain connectivity features and help detect dementia-related biomarkers. It is further important to understand the pathogenic mechanism and the drug discovery for neurodegenerative disorders [8].

The BFN is usually constructed through a software toolbox by splitting the human brain into predefined Region-of-Interests (ROIs) [9]. The element in the BFN matrix indicates the functional correlation between two ROIs. Many approaches based on machine learning were utilized to diagnose neurological disease in an end-to-end scheme [10–16]. For example, Meier et al. [17] applied the support vector machine (SVM) classifier to distinguish older adults from younger adults using functional connectivity data. To boost the Mild Cognitive Impairment (MCI) prediction performance, Yu et al. [18] designed a sparse graph representation learning method with a weighting scheme to generate sparse BFNs. Bi et al. [19] combined convolutional learning and recurrent learning to extract regional connectivity and adjacent positional features, which proves its learning ability in AD diagnosis. More advanced techniques are proposed to explore the complex connectivity-based features [20–22]. Ji et al. [23] devised novel convolutional kernels to capture hierarchical topological characteristics by element-wise weighting brain networks and achieved more accurate classification performance. The work in [24] applied the graph convolutional network (GCN) method to improve the classification accuracy by jointly using the functional time series and connectivity-based matrices. Nevertheless, the limited medical data makes data-driven models challenging to achieve good prediction results.

The straightforward way to improve classification performance is to synthesize more similar medical data and feed it to data-driven models [25,26]. Numerous data-augmented methods have been developed to solve the small data problem in the field of brain imaging analysis. For example, Hong et al. [27] augmented the routine brain magnetic resonance (MR) imaging with scaling, rotation, translation, and gamma correction and achieved accurate results predicting children’s brain age through a deep learning model. Hu et al. [28] synthesized the positron emission tomography (PET) from MR using generative models, which can handle the problem of incomplete modalities and is promising for multimodal fusion. However, the above methods cannot be applied to BFN augmentation, because it only considers the local features between adjacent pixels and ignores the topological information between distant pixels. Many efforts have been tried to generate new graph data in the graph domain. Meszlényi et al. [29] created some simulated connectivity-based datasets by applying noise weights (NW) to improve the classification performance. The study of [30] solved the problem of small-size data by employing the synthetic minority over-sampling technique (SMOTE) algorithm and achieved a good classification accuracy of non-tumorous facial pigmentation disorders. However, these methods do not directly generate new graph data but interpolate existing brain networks to augment the data, which brings some noise and may have some side effects on the model’s classification performance.

The generative adversarial networks (GANs) [31] is a two-player game that can produce quite good results by mutual game learning [32]. It has gained broad applications in analyzing medical imaging because of its strong ability in distribution fitting [33]. These applications cover the image-related fields, including cross-modal synthesis [34], point cloud generation [35], image super-resolution [36], disease classification [37–39], regression task [40,41], and organ segmentation [42]. Besides, the prior distribution can guide the model’s optimization and thus stabilize the representation learning in the GAN’s training [43]. Reference [44] introduced a Gaussian distribution to constrain the graph embedding in adversarial learning and achieved good performance in graph analytics. The GAN-based model has been applied in the BFN augmentation. For example, Tan et al. [45] utilized the Gaussian noise to synthesize BFNs by applying a semi-positive definite manifold constraint. Also, the transformer network [46] can greatly improve image classification performance by combining adversarial strategy, which can model a strong relationship between distant ROIs.

Motivated by these observations, in this study, a novel distribution-regularized adversarial graph autoencoder (DAGAE) model is proposed to generate BFNs for dementia diagnosis. The main works of this paper are as follows: (1) The label distribution is estimated to regularize the latent space learned by the graph encoder, which can make the learning process stable and deduce a robust representation. (2) The transformer-based network in the generator is introduced to map the node representations into node-to-node connections by exploring the global connectivity information between distant ROIs. It preserves the main topological properties and more discriminative features. (3) The generated BFNs enhance disease prediction using different classifiers, which can be applied to analyze other related brain diseases.

The proposed DAGAE model can generate new BFNs for improving classification performance. Each module in the model contributes to the generation quality of BFNs. To analyze the influence of different modules, we remove the encoder, discriminator, and classifier from the DAGAE model and evaluate the final classification performance. Fig. 10 demonstrates that the encoder significantly impacts the whole model. It drops by 16% in terms of ACC by removing the encoder module. The discriminator ensures the latent node representation in a prior distribution, which also influences the quality of the generated BFNs. This suggests the usefulness of prior label distribution can regularize the latent representation with a stable learning strategy and enhance the BFN classification. Furthermore, we study the dimension p of the latent node representation H in the prediction performance. As shown in Fig. 11, the value of ACC and AUC shows relatively stable fluctuation when p exceeds 32. Considering the computation efficiency, we select p=32 in the experiment. The transformer generator is essential for the generated BFN quality. We study two variations of the designed transformer generator to test its effectiveness. (1) Remove the DU layer in the generator (No-DU), which means the input and output dimension is the same as the dimension of latent representation H; (2) remove the connectivity transformer (No-CT), which simplifies the generator into two layer perceptrons. The results are illustrated in Table 2; it can be seen that the combination of DU and CT achieves the best prediction performance. The classification results demonstrate the effectiveness of the transformer generator in the model. This can be explained by that the transformer-based network in the generator preserves the main topological properties and captures more discriminative features.

Data-driven models achieve better performance by using large amounts of data. To investigate how much generated data influences the prediction performance, we generate k∈{1,2,...,8} times the original training set, combine the original BFNs and generated BFNs to train the SVM-based and GCN-based classifier. The mean ACC is estimated by predicting five-fold original test sets separately. The metric DeltaACC is defined as ACCk−ACC0. Here, ACC0 refers to the predicted results of the classifier trained using the original train set, and the ACCk refers to the predicted results of the classifier trained using the original and generated data. Fig. 12 gives the different quantities of generated BFNs that maximizes classification performance in both classifiers. The best quantity of generated data is about five times the original data, with the largest DeltaACC value of 19.3% and 13.3% for the SVM and GCN classifier, respectively. The reason why more data degrades classification performance may be that the generated BFNs bring a lot of noise. Besides, compared with the SVM classifier, the GCN-based classifier increases by 5.3% on the best ACC value. This marginal increase may be explained by considering the topological information among the brain regions, which can characterize the disease-related features of the BFNs. Thus, in the BFN augmentation experiment, it is better to choose the GCN-based classifier to evaluate the prediction performance, and different quantities of generated BFNs should be explored to maximize the effect of data augmentation.

Although the proposed DAGAE is promising in augmenting the BFN data for disease prediction, there are still two limitations that have not been considered. (1) The label distribution is estimated using the limited training data, which can not add other prior knowledge. We will introduce disease-related anatomical brain knowledge into the model for performance evaluation. (2) The data in this work are deliberately picked out to maintain category balance. The real condition in the category distribution is always imbalanced. In the following study, we will try to apply the proposed DAGAE in category-imbalanced datasets for other brain disorder diagnosis.

This study proposes a novel DAGAE model to augment new BFNs for dementia diagnosis. The BFN augmentation is different from traditional image synthesis, where the latter only extracts local patterns and ignores the topological information buried in the brain network. Our model is novel in two aspects. One is that the estimated label distribution can regularize the latent space and make the learning process stable. Another one is that the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions, which preserves the main topological properties and more discriminative features. Testing on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) public dataset, the proposed DAGAE can generate similar and high-quality BFNs. The classification results show that adding generated data can achieve higher accuracy values of 85.33%, 83.33%, and 80.67% than the original method using GCN, DNN, and SVM classifiers, respectively. The proposed model also performs better than related augmented models, providing new insight for improving cognitive disease diagnosis accuracy.