Graph Neural Networks (GNNs) excel in delineating graph structures in diverse domains, including community analysis and recommendation systems. As the interpretation of GNNs becomes increasingly important, the demand for robust baselines and expansive graph datasets is accentuated, particularly in the context of Heterogeneous Information Networks (HIN). Addressing this, we introduce SynHING, a novel framework for Synthetic Heterogeneous Information Network Generation aimed at enhancing graph learning and explanation. SynHING systematically identifies major motifs in a target HIN and employs a bottom-up generation process with intra-cluster and inter-cluster merge modules. This process, supplemented by post-pruning techniques, ensures the synthetic HIN closely mirrors the original graph's structural and statistical properties. Crucially, SynHING provides ground-truth motifs for evaluating GNN explainer models, setting a new standard for explainable, synthetic HIN generation and contributing to the advancement of interpretable machine learning in complex networks.
Graph Neural Networks (GNNs) are a class of deep learning models capable of processing graph-structured data, and they have demonstrated significant performance in a variety of real-world applications. Recent studies have found that GNN models are vulnerable to backdoor attacks. When specific patterns (called backdoor triggers, e.g., subgraphs, nodes, etc.) appear in the input data, the backdoor embedded in the GNN models is activated, which misclassifies the input data into the target class label specified by the attacker, whereas when there are no backdoor triggers in the input, the backdoor embedded in the GNN models is not activated, and the models work normally. Backdoor attacks are highly stealthy and expose GNN models to serious security risks. Currently, research on backdoor attacks against GNNs mainly focus on tasks such as graph classification and node classification, and backdoor attacks against link prediction tasks are rarely studied. In this paper, we propose a backdoor attack against the link prediction tasks based on GNNs and reveal the existence of such security vulnerability in GNN models, which make the backdoored GNN models to incorrectly predict unlinked two nodes as having a link relationship when a trigger appear. The method uses a single node as the trigger and poison selected node pairs in the training graph, and then the backdoor will be embedded in the GNN models through the training process. In the inference stage, the backdoor in the GNN models can be activated by simply linking the trigger node to the two end nodes of the unlinked node pairs in the input data, causing the GNN models to produce incorrect link prediction results for the target node pairs.
Local neighborhoods play a crucial role in embedding generation in graph-based learning. It is commonly believed that nodes ought to have embeddings that resemble those of their neighbors. In this research, we try to carefully expand the concept of similarity from nearby neighborhoods to the entire graph. We provide an extension of similarity that is based on transitivity relations, which enables Graph Neural Networks (GNNs) to capture both global similarities and local similarities over the whole graph. We introduce Transitivity Graph Neural Network (TransGNN), which more than local node similarities, takes into account global similarities by distinguishing strong transitivity relations from weak ones and exploiting them. We evaluate our model over several real-world datasets and showed that it considerably improves the performance of several well-known GNN models, for tasks such as node classification.
Backdoor attacks in the traditional graph neural networks (GNNs) field are easily detectable due to the dilemma of confusing labels. To explore the backdoor vulnerability of GNNs and create a more stealthy backdoor attack method, a clean-label graph backdoor attack method(CGBA) in the node classification task is proposed in this paper. Differently from existing backdoor attack methods, CGBA requires neither modification of node labels nor graph structure. Specifically, to solve the problem of inconsistency between the contents and labels of the samples, CGBA selects poisoning samples in a specific target class and uses the label of sample as the target label (i.e., clean-label) after injecting triggers into the target samples. To guarantee the similarity of neighboring nodes, the raw features of the nodes are elaborately picked as triggers to further improve the concealment of the triggers. Extensive experiments results show the effectiveness of our method. When the poisoning rate is 0.04, CGBA can achieve an average attack success rate of 87.8%, 98.9%, 89.1%, and 98.5%, respectively.
Despite the success of graph neural networks (GNNs) in various domains, they exhibit susceptibility to adversarial attacks. Understanding these vulnerabilities is crucial for developing robust and secure applications. In this paper, we investigate the impact of test time adversarial attacks through edge perturbations which involve both edge insertions and deletions. A novel explainability-based method is proposed to identify important nodes in the graph and perform edge perturbation between these nodes. The proposed method is tested for node classification with three different architectures and datasets. The results suggest that introducing edges between nodes of different classes has higher impact as compared to removing edges among nodes within the same class.
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the need for more effective and specialized approaches grows with the production of graph data with diverse characteristics. In particular, real-world multiplex graphs may exhibit a high number of dimensions, making it difficult to construct a single consensus representation. Furthermore, important information can be hidden in complex latent structures scattered in multiple dimensions. To address these issues, we propose HMGE, a novel embedding method based on hierarchical aggregation for high-dimensional multiplex graphs. Hierarchical aggregation consists of learning a hierarchical combination of the graph dimensions and refining the embeddings at each hierarchy level. Non-linear combinations are computed from previous ones, thus uncovering complex information and latent structures hidden in the multiplex graph dimensions. Moreover, we leverage mutual information maximization between local patches and global summaries to train the model without supervision. This allows to capture of globally relevant information present in diverse locations of the graph. Detailed experiments on synthetic and real-world data illustrate the suitability of our approach to downstream supervised tasks, including link prediction and node classification.
This study utilizes community structures to address node degree biases in message-passing (MP) via learnable graph augmentations and novel graph transformers. Recent augmentation-based methods showed that MP neural networks often perform poorly on low-degree nodes, leading to degree biases due to a lack of messages reaching low-degree nodes. Despite their success, most methods use heuristic or uniform random augmentations, which are non-differentiable and may not always generate valuable edges for learning representations. In this paper, we propose Community-aware Graph Transformers, namely CGT, to learn degree-unbiased representations based on learnable augmentations and graph transformers by extracting within community structures. We first design a learnable graph augmentation to generate more within-community edges connecting low-degree nodes through edge perturbation. Second, we propose an improved self-attention to learn underlying proximity and the roles of nodes within the community. Third, we propose a self-supervised learning task that could learn the representations to preserve the global graph structure and regularize the graph augmentations. Extensive experiments on various benchmark datasets showed CGT outperforms state-of-the-art baselines and significantly improves the node degree biases. The source code is available at https://github.com/NSLab-CUK/Community-aware-Graph-Transformer.
Graph convolution networks (GCNs) are extensively utilized in various graph tasks to mine knowledge from spatial data. Our study marks the pioneering attempt to quantitatively investigate the GCN robustness over omnipresent heterophilic graphs for node classification. We uncover that the predominant vulnerability is caused by the structural out-of-distribution (OOD) issue. This finding motivates us to present a novel method that aims to harden GCNs by automatically learning Latent Homophilic Structures over heterophilic graphs. We term such a methodology as LHS. To elaborate, our initial step involves learning a latent structure by employing a novel self-expressive technique based on multi-node interactions. Subsequently, the structure is refined using a pairwisely constrained dual-view contrastive learning approach. We iteratively perform the above procedure, enabling a GCN model to aggregate information in a homophilic way on heterophilic graphs. Armed with such an adaptable structure, we can properly mitigate the structural OOD threats over heterophilic graphs. Experiments on various benchmarks show the effectiveness of the proposed LHS approach for robust GCNs.
Graph summarization as a preprocessing step is an effective and complementary technique for scalable graph neural network (GNN) training. In this work, we propose the Coarsening Via Convolution Matching (CONVMATCH) algorithm and a highly scalable variant, A-CONVMATCH, for creating summarized graphs that preserve the output of graph convolution. We evaluate CONVMATCH on six real-world link prediction and node classification graph datasets, and show it is efficient and preserves prediction performance while significantly reducing the graph size. Notably, CONVMATCH achieves up to 95% of the prediction performance of GNNs on node classification while trained on graphs summarized down to 1% the size of the original graph. Furthermore, on link prediction tasks, CONVMATCH consistently outperforms all baselines, achieving up to a 2x improvement.
Heterogeneous graph neural networks (HGNs) are prominent approaches to node classification tasks on heterogeneous graphs. Despite the superior performance, insights about the predictions made from HGNs are obscure to humans. Existing explainability techniques are mainly proposed for GNNs on homogeneous graphs. They focus on highlighting salient graph objects to the predictions whereas the problem of how these objects affect the predictions remains unsolved. Given heterogeneous graphs with complex structures and rich semantics, it is imperative that salient objects can be accompanied with their influence paths to the predictions, unveiling the reasoning process of HGNs. In this paper, we develop xPath, a new framework that provides fine-grained explanations for black-box HGNs specifying a cause node with its influence path to the target node. In xPath, we differentiate the influence of a node on the prediction w.r.t. every individual influence path, and measure the influence by perturbing graph structure via a novel graph rewiring algorithm. Furthermore, we introduce a greedy search algorithm to find the most influential fine-grained explanations efficiently. Empirical results on various HGNs and heterogeneous graphs show that xPath yields faithful explanations efficiently, outperforming the adaptations of advanced GNN explanation approaches.
Knowledge Graphs (KGs) such as Resource Description Framework (RDF) data represent relationships between various entities through the structure of triples (<subject, predicate, object>). Knowledge graph embedding (KGE) is crucial in machine learning applications, specifically in node classification and link prediction tasks. KGE remains a vital research topic within the semantic web community. RDF-star introduces the concept of a quoted triple (QT), a specific form of triple employed either as the subject or object within another triple. Moreover, RDF-star permits a QT to act as compositional entities within another QT, thereby enabling the representation of recursive, hyper-relational KGs with nested structures. However, existing KGE models fail to adequately learn the semantics of QTs and entities, primarily because they do not account for RDF-star graphs containing multi-leveled nested QTs and QT-QT relationships. This study introduces RDF-star2Vec, a novel KGE model specifically designed for RDF-star graphs. RDF-star2Vec introduces graph walk techniques that enable probabilistic transitions between a QT and its compositional entities. Feature vectors for QTs, entities, and relations are derived from generated sequences through the structured skip-gram model. Additionally, we provide a dataset and a benchmarking framework for data mining tasks focused on complex RDF-star graphs. Evaluative experiments demonstrated that RDF-star2Vec yielded superior performance compared to recent extensions of RDF2Vec in various tasks including classification, clustering, entity relatedness, and QT similarity.
Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly.
When handling streaming graphs, existing graph representation learning models encounter a catastrophic forgetting problem, where previously learned knowledge of these models is easily overwritten when learning with newly incoming graphs. In response, Continual Graph Learning (CGL) emerges as a novel paradigm enabling graph representation learning from streaming graphs. Our prior work, Condense and Train (CaT) is a replay-based CGL framework with a balanced continual learning procedure, which designs a small yet effective memory bankn for replaying. Although the CaT alleviates the catastrophic forgetting problem, there exist three issues: (1) The graph condensation only focuses on labelled nodes while neglecting abundant information carried by unlabelled nodes; (2) The continual training scheme of the CaT overemphasises on the previously learned knowledge, limiting the model capacity to learn from newly added memories; (3) Both the condensation process and replaying process of the CaT are time-consuming. In this paper, we propose a PsUdo-label guided Memory bAnk (PUMA) CGL framework, extending from the CaT to enhance its efficiency and effectiveness by overcoming the above-mentioned weaknesses and limits. To fully exploit the information in a graph, PUMA expands the coverage of nodes during graph condensation with both labelled and unlabelled nodes. Furthermore, a training-from-scratch strategy is proposed to upgrade the previous continual learning scheme for a balanced training between the historical and the new graphs. Besides, PUMA uses a one-time prorogation and wide graph encoders to accelerate the graph condensation and the graph encoding process in the training stage to improve the efficiency of the whole framework. Extensive experiments on six datasets for the node classification task demonstrate the state-of-the-art performance and efficiency over existing methods.
The Adam optimizer is a popular choice in contemporary deep learning, due to its strong empirical performance. However we observe that in privacy sensitive scenarios, the traditional use of Differential Privacy (DP) with the Adam optimizer leads to sub-optimal performance on several tasks. We find that this performance degradation is due to a DP bias in Adam's second moment estimator, introduced by the addition of independent noise in the gradient computation to enforce DP guarantees. This DP bias leads to a different scaling for low variance parameter updates, that is inconsistent with the behavior of non-private Adam. We propose DP-AdamBC, an optimization algorithm which removes the bias in the second moment estimation and retrieves the expected behaviour of Adam. Empirically, DP-AdamBC significantly improves the optimization performance of DP-Adam by up to 3.5% in final accuracy in image, text, and graph node classification tasks.
Recently, many carefully crafted graph representation learning methods have achieved impressive performance on either strong heterophilic or homophilic graphs, but not both. Therefore, they are incapable of generalizing well across real-world graphs with different levels of homophily. This is attributed to their neglect of homophily in heterophilic graphs, and vice versa. In this paper, we propose a two-fold filtering mechanism to extract homophily in heterophilic graphs and vice versa. In particular, we extend the graph heat equation to perform heterophilic aggregation of global information from a long distance. The resultant filter can be exactly approximated by the Possion-Charlier (PC) polynomials. To further exploit information at multiple orders, we introduce a powerful graph convolution PC-Conv and its instantiation PCNet for the node classification task. Compared with state-of-the-art GNNs, PCNet shows competitive performance on well-known homophilic and heterophilic graphs. Our implementation is available at https://github.com/uestclbh/PC-Conv.
Graph Neural Networks (GNNs) have become mainstream methods for solving the semi-supervised node classification problem. However, due to the uneven location distribution of labeled nodes in the graph, labeled nodes are only accessible to a small portion of unlabeled nodes, leading to the \emph{under-reaching} issue. In this study, we firstly reveal under-reaching by conducting an empirical investigation on various well-known graphs. Then, we demonstrate that under-reaching results in unsatisfactory distribution alignment between labeled and unlabeled nodes through systematic experimental analysis, significantly degrading GNNs' performance. To tackle under-reaching for GNNs, we propose an architecture-agnostic method dubbed NodeMixup. The fundamental idea is to (1) increase the reachability of labeled nodes by labeled-unlabeled pairs mixup, (2) leverage graph structures via fusing the neighbor connections of intra-class node pairs to improve performance gains of mixup, and (3) use neighbor label distribution similarity incorporating node degrees to determine sampling weights for node mixup. Extensive experiments demonstrate the efficacy of NodeMixup in assisting GNNs in handling under-reaching. The source code is available at \url{https://github.com/WeigangLu/NodeMixup}.
Hierarchy is an important and commonly observed topological property in real-world graphs that indicate the relationships between supervisors and subordinates or the organizational behavior of human groups. As hierarchy is introduced as a new inductive bias into the Graph Neural Networks (GNNs) in various tasks, it implies latent topological relations for attackers to improve their inference attack performance, leading to serious privacy leakage issues. In addition, existing privacy-preserving frameworks suffer from reduced protection ability in hierarchical propagation due to the deficiency of adaptive upper-bound estimation of the hierarchical perturbation boundary. It is of great urgency to effectively leverage the hierarchical property of data while satisfying privacy guarantees. To solve the problem, we propose the Poincar\'e Differential Privacy framework, named PoinDP, to protect the hierarchy-aware graph embedding based on hyperbolic geometry. Specifically, PoinDP first learns the hierarchy weights for each entity based on the Poincar\'e model in hyperbolic space. Then, the Personalized Hierarchy-aware Sensitivity is designed to measure the sensitivity of the hierarchical structure and adaptively allocate the privacy protection strength. Besides, the Hyperbolic Gaussian Mechanism (HGM) is proposed to extend the Gaussian mechanism in Euclidean space to hyperbolic space to realize random perturbations that satisfy differential privacy under the hyperbolic space metric. Extensive experiment results on five real-world datasets demonstrate the proposed PoinDP's advantages of effective privacy protection while maintaining good performance on the node classification task.
There has been significant progress in improving the performance of graph neural networks (GNNs) through enhancements in graph data, model architecture design, and training strategies. For fairness in graphs, recent studies achieve fair representations and predictions through either graph data pre-processing (e.g., node feature masking, and topology rewiring) or fair training strategies (e.g., regularization, adversarial debiasing, and fair contrastive learning). How to achieve fairness in graphs from the model architecture perspective is less explored. More importantly, GNNs exhibit worse fairness performance compared to multilayer perception since their model architecture (i.e., neighbor aggregation) amplifies biases. To this end, we aim to achieve fairness via a new GNN architecture. We propose \textsf{F}air \textsf{M}essage \textsf{P}assing (FMP) designed within a unified optimization framework for GNNs. Notably, FMP \textit{explicitly} renders sensitive attribute usage in \textit{forward propagation} for node classification task using cross-entropy loss without data pre-processing. In FMP, the aggregation is first adopted to utilize neighbors' information and then the bias mitigation step explicitly pushes demographic group node presentation centers together. In this way, FMP scheme can aggregate useful information from neighbors and mitigate bias to achieve better fairness and prediction tradeoff performance. Experiments on node classification tasks demonstrate that the proposed FMP outperforms several baselines in terms of fairness and accuracy on three real-world datasets. The code is available in {\url{https://github.com/zhimengj0326/FMP}}.
This paper introduces a new approach to address the issue of class imbalance in graph neural networks (GNNs) for learning on graph-structured data. Our approach integrates imbalanced node classification and Bias-Variance Decomposition, establishing a theoretical framework that closely relates data imbalance to model variance. We also leverage graph augmentation technique to estimate the variance, and design a regularization term to alleviate the impact of imbalance. Exhaustive tests are conducted on multiple benchmarks, including naturally imbalanced datasets and public-split class-imbalanced datasets, demonstrating that our approach outperforms state-of-the-art methods in various imbalanced scenarios. This work provides a novel theoretical perspective for addressing the problem of imbalanced node classification in GNNs.
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering remarkable performance across various tasks, e.g., hypergraph node classification. However, these models struggle to capture global structural information due to their reliance on local message passing. To address this challenge, we propose a novel hypergraph learning framework, HyperGraph Transformer (HyperGT). HyperGT uses a Transformer-based neural network architecture to effectively consider global correlations among all nodes and hyperedges. To incorporate local structural information, HyperGT has two distinct designs: i) a positional encoding based on the hypergraph incidence matrix, offering valuable insights into node-node and hyperedge-hyperedge interactions; and ii) a hypergraph structure regularization in the loss function, capturing connectivities between nodes and hyperedges. Through these designs, HyperGT achieves comprehensive hypergraph representation learning by effectively incorporating global interactions while preserving local connectivity patterns. Extensive experiments conducted on real-world hypergraph node classification tasks showcase that HyperGT consistently outperforms existing methods, establishing new state-of-the-art benchmarks. Ablation studies affirm the effectiveness of the individual designs of our model.