Heterogeneous graph neural networks (HeteGNNs) have demonstrated strong abilities to learn node representations by effectively extracting complex structural and semantic information in heterogeneous graphs. Most of the prevailing HeteGNNs follow the neighborhood aggregation paradigm, leveraging meta-path based message passing to learn latent node representations. However, due to the pairwise nature of meta-paths, these models fail to capture high-order relations among nodes, resulting in suboptimal performance. Additionally, the challenge of ``over-squashing'', where long-range message passing in HeteGNNs leads to severe information distortion, further limits the efficacy of these models. To address these limitations, this paper proposes MGA-HHN, a Multi-Granular Attention based Heterogeneous Hypergraph Neural Network for heterogeneous graph representation learning. MGA-HHN introduces two key innovations: (1) a novel approach for constructing meta-path based heterogeneous hypergraphs that explicitly models higher-order semantic information in heterogeneous graphs through multiple views, and (2) a multi-granular attention mechanism that operates at both the node and hyperedge levels. This mechanism enables the model to capture fine-grained interactions among nodes sharing the same semantic context within a hyperedge type, while preserving the diversity of semantics across different hyperedge types. As such, MGA-HHN effectively mitigates long-range message distortion and generates more expressive node representations. Extensive experiments on real-world benchmark datasets demonstrate that MGA-HHN outperforms state-of-the-art models, showcasing its effectiveness in node classification, node clustering and visualization tasks.
Graph Neural Networks (GNNs) update node representations through message passing, which is primarily based on the homophily principle, assuming that adjacent nodes share similar features. However, in real-world graphs with long-tailed degree distributions, high-degree nodes dominate message passing, causing a degree bias where low-degree nodes remain under-represented due to inadequate messages. The main challenge in addressing degree bias is how to discover non-adjacent nodes to provide additional messages to low-degree nodes while reducing excessive messages for high-degree nodes. Nevertheless, exploiting non-adjacent nodes to provide valuable messages is challenging, as it could generate noisy information and disrupt the original graph structures. To solve it, we propose a novel Degree Fairness Graph Transformer, named DegFairGT, to mitigate degree bias by discovering structural similarities between non-adjacent nodes through learnable structural augmentation and structural self-attention. Our key idea is to exploit non-adjacent nodes with similar roles in the same community to generate informative edges under our augmentation, which could provide informative messages between nodes with similar roles while ensuring that the homophily principle is maintained within the community. To enable DegFairGT to learn such structural similarities, we then propose a structural self-attention to capture the similarities between node pairs. To preserve global graph structures and prevent graph augmentation from hindering graph structure, we propose a Self-Supervised Learning task to preserve p-step transition probability and regularize graph augmentation. Extensive experiments on six datasets showed that DegFairGT outperformed state-of-the-art baselines in degree fairness analysis, node classification, and node clustering tasks.
Quantification learning is the task of predicting the label distribution of a set of instances. We study this problem in the context of graph-structured data, where the instances are vertices. Previously, this problem has only been addressed via node clustering methods. In this paper, we extend the popular Adjusted Classify & Count (ACC) method to graphs. We show that the prior probability shift assumption upon which ACC relies is often not fulfilled and propose two novel graph quantification techniques: Structural importance sampling (SIS) makes ACC applicable in graph domains with covariate shift. Neighborhood-aware ACC improves quantification in the presence of non-homophilic edges. We show the effectiveness of our techniques on multiple graph quantification tasks.
Graph node clustering is a fundamental unsupervised task. Existing methods typically train an encoder through selfsupervised learning and then apply K-means to the encoder output. Some methods use this clustering result directly as the final assignment, while others initialize centroids based on this initial clustering and then finetune both the encoder and these learnable centroids. However, due to their reliance on K-means, these methods inherit its drawbacks when the cluster separability of encoder output is low, facing challenges from the Uniform Effect and Cluster Assimilation. We summarize three reasons for the low cluster separability in existing methods: (1) lack of contextual information prevents discrimination between similar nodes from different clusters; (2) training tasks are not sufficiently aligned with the downstream clustering task; (3) the cluster information in the graph structure is not appropriately exploited. To address these issues, we propose conTrastive grapH clustEring by SwApping fUsed gRomov-wasserstein coUplingS (THESAURUS). Our method introduces semantic prototypes to provide contextual information, and employs a cross-view assignment prediction pretext task that aligns well with the downstream clustering task. Additionally, it utilizes Gromov-Wasserstein Optimal Transport (GW-OT) along with the proposed prototype graph to thoroughly exploit cluster information in the graph structure. To adapt to diverse real-world data, THESAURUS updates the prototype graph and the prototype marginal distribution in OT by using momentum. Extensive experiments demonstrate that THESAURUS achieves higher cluster separability than the prior art, effectively mitigating the Uniform Effect and Cluster Assimilation issues
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning techniques to 1) work with attributed graphs, 2) enabling a mini-batch based approach, and 3) achieving scalability. Based on a multi-class tuplet loss function, we present two algorithms -- DMT for semi-supervised learning and DMAT-i for the unsupervised case. Analyzing our methods, we provide a generalization bound for the downstream node classification task and for the first time relate tuplet loss to contrastive learning. Through extensive experiments, we show high scalability of representation construction, and in applying the method for three downstream tasks (node clustering, node classification, and link prediction) better consistency over any single existing method.
Physical-Layer Authentication (PLA) offers endogenous security, lightweight implementation, and high reliability, making it a promising complement to upper-layer security methods in Edge Intelligence (EI)-empowered Industrial Internet of Things (IIoT). However, state-of-the-art Channel State Information (CSI)-based PLA schemes face challenges in recognizing mobile multi-users due to the limited reliability of CSI fingerprints in low Signal-to-Noise Ratio (SNR) environments and the constantly shifting CSI distributions with user movements. To address these issues, we propose a Temporal Dynamic Graph Convolutional Network (TDGCN)-based PLA scheme. This scheme harnesses Intelligent Reflecting Surfaces (IRSs) to refine CSI fingerprint precision and employs Graph Neural Networks (GNNs) to capture the spatio-temporal dynamics induced by user movements and IRS deployments. Specifically, we partition hierarchical CSI fingerprints into multivariate time series and utilize dynamic GNNs to capture their associations. Additionally, Temporal Convolutional Networks (TCNs) handle temporal dependencies within each CSI fingerprint dimension. Dynamic Graph Isomorphism Networks (GINs) and cascade node clustering pooling further enable efficient information aggregation and reduced computational complexity. Simulations demonstrate the proposed scheme's superior authentication accuracy compared to seven baseline schemes.
We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which necessitate calculating the distance between any two nodes, our proposed technique determines density through a propagation process, thereby making it suitable for a graph space. In DPSM, nodes are partitioned into small clusters based on propagated density. The partitioning technique has been proved to be sound and complete. We then extend the concept of spectral clustering from individual nodes to these small clusters, while introducing the CluCut measure to guide cluster merging. This measure is modified in various ways to account for cluster properties, thus provides guidance on when to terminate the merging process. Various experiments have validated the effectiveness of DOSM and the accuracy of these conclusions.
Graphs play a central role in modeling complex relationships across various domains. Most graph learning methods rely heavily on neighborhood information, raising the question of how to handle cold-start nodes - nodes with no known connections within the graph. These models often overlook the cold-start nodes, making them ineffective for real-world scenarios. To tackle this, we propose G-SPARC, a novel framework addressing cold-start nodes, that leverages generalizable spectral embedding. This framework enables extension to state-of-the-art methods making them suitable for practical applications. By utilizing a key idea of transitioning from graph representation to spectral representation, our approach is generalizable to cold-start nodes, capturing the global structure of the graph without relying on adjacency data. Experimental results demonstrate that our method outperforms existing models on cold-start nodes across various tasks like node classification, node clustering, and link prediction. G-SPARC provides a breakthrough built-in solution to the cold-start problem in graph learning. Our code will be publicly available upon acceptance.
Federated learning (FL) is a decentralized AI mechanism suitable for a large number of devices like in smart IoT. A major challenge of FL is the non-IID dataset problem, originating from the heterogeneous data collected by FL participants, leading to performance deterioration of the trained global model. There have been various attempts to rectify non-IID dataset, mostly focusing on manipulating the collected data. This paper, however, proposes a novel approach to ensure data IIDness by properly clustering and grouping mobile IoT nodes exploiting their geographical characteristics, so that each FL group can achieve IID dataset. We first provide an experimental evidence for the independence and identicalness features of IoT data according to the inter-device distance, and then propose Dynamic Clustering and Partial-Steady Grouping algorithms that partition FL participants to achieve near-IIDness in their dataset while considering device mobility. Our mechanism significantly outperforms benchmark grouping algorithms at least by 110 times in terms of the joint cost between the number of dropout devices and the evenness in per-group device count, with a mild increase in the number of groups only by up to 0.93 groups.
In the realm of graph learning, there is a category of methods that conceptualize graphs as hierarchical structures, utilizing node clustering to capture broader structural information. While generally effective, these methods often rely on a fixed graph coarsening routine, leading to overly homogeneous cluster representations and loss of node-level information. In this paper, we envision the graph as a network of interconnected node sets without compressing each cluster into a single embedding. To enable effective information transfer among these node sets, we propose the Node-to-Cluster Attention (N2C-Attn) mechanism. N2C-Attn incorporates techniques from Multiple Kernel Learning into the kernelized attention framework, effectively capturing information at both node and cluster levels. We then devise an efficient form for N2C-Attn using the cluster-wise message-passing framework, achieving linear time complexity. We further analyze how N2C-Attn combines bi-level feature maps of queries and keys, demonstrating its capability to merge dual-granularity information. The resulting architecture, Cluster-wise Graph Transformer (Cluster-GT), which uses node clusters as tokens and employs our proposed N2C-Attn module, shows superior performance on various graph-level tasks. Code is available at https://github.com/LUMIA-Group/Cluster-wise-Graph-Transformer.
Attributed networks containing entity-specific information in node attributes are ubiquitous in modeling social networks, e-commerce, bioinformatics, etc. Their inherent network topology ranges from simple graphs to hypergraphs with high-order interactions and multiplex graphs with separate layers. An important graph mining task is node clustering, aiming to partition the nodes of an attributed network into k disjoint clusters such that intra-cluster nodes are closely connected and share similar attributes, while inter-cluster nodes are far apart and dissimilar. It is highly challenging to capture multi-hop connections via nodes or attributes for effective clustering on multiple types of attributed networks. In this paper, we first present AHCKA as an efficient approach to attributed hypergraph clustering (AHC). AHCKA includes a carefully-crafted K-nearest neighbor augmentation strategy for the optimized exploitation of attribute information on hypergraphs, a joint hypergraph random walk model to devise an effective AHC objective, and an efficient solver with speedup techniques for the objective optimization. The proposed techniques are extensible to various types of attributed networks, and thus, we develop ANCKA as a versatile attributed network clustering framework, capable of attributed graph clustering (AGC), attributed multiplex graph clustering (AMGC), and AHC. Moreover, we devise ANCKA with algorithmic designs tailored for GPU acceleration to boost efficiency. We have conducted extensive experiments to compare our methods with 19 competitors on 8 attributed hypergraphs, 16 competitors on 6 attributed graphs, and 16 competitors on 3 attributed multiplex graphs, all demonstrating the superb clustering quality and efficiency of our methods.
Contrastive learning is a significant paradigm in graph self-supervised learning. However, it requires negative samples to prevent model collapse and learn discriminative representations. These negative samples inevitably lead to heavy computation, memory overhead and class collision, compromising the representation learning. Recent studies present that methods obviating negative samples can attain competitive performance and scalability enhancements, exemplified by bootstrapped graph latents (BGRL). However, BGRL neglects the inherent graph homophily, which provides valuable insights into underlying positive pairs. Our motivation arises from the observation that subtly introducing a few ground-truth positive pairs significantly improves BGRL. Although we can't obtain ground-truth positive pairs without labels under the self-supervised setting, edges in the graph can reflect noisy positive pairs, i.e., neighboring nodes often share the same label. Therefore, we propose to expand the positive pair set with node-neighbor pairs. Subsequently, we introduce a cross-attention module to predict the supportiveness score of a neighbor with respect to the anchor node. This score quantifies the positive support from each neighboring node, and is encoded into the training objective. Consequently, our method mitigates class collision from negative and noisy positive samples, concurrently enhancing intra-class compactness. Extensive experiments are conducted on five benchmark datasets and three downstream task node classification, node clustering, and node similarity search. The results demonstrate that our method generates node representations with enhanced intra-class compactness and achieves state-of-the-art performance.
Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph Transformers (GTs) for enhanced HIN representation learning. However, research on GT in HINs remains limited, with two key shortcomings in existing work: (1) A node's neighbors at different distances in HINs convey diverse semantics. Unfortunately, existing methods ignore such differences and uniformly treat neighbors within a given distance in a coarse manner, which results in semantic confusion. (2) Nodes in HINs have various types, each with unique semantics. Nevertheless, existing methods mix nodes of different types during neighbor aggregation, hindering the capture of proper correlations between nodes of diverse types. To bridge these gaps, we design an innovative structure named (k,t)-ring neighborhood, where nodes are initially organized by their distance, forming different non-overlapping k-ring neighborhoods for each distance. Within each k-ring structure, nodes are further categorized into different groups according to their types, thus emphasizing the heterogeneity of both distances and types in HINs naturally. Based on this structure, we propose a novel Hierarchical Heterogeneous Graph Transformer (HHGT) model, which seamlessly integrates a Type-level Transformer for aggregating nodes of different types within each k-ring neighborhood, followed by a Ring-level Transformer for aggregating different k-ring neighborhoods in a hierarchical manner. Extensive experiments are conducted on downstream tasks to verify HHGT's superiority over 14 baselines, with a notable improvement of up to 24.75% in NMI and 29.25% in ARI for node clustering task on the ACM dataset compared to the best baseline.
Foundation Models (FMs) serve as a general class for the development of artificial intelligence systems, offering broad potential for generalization across a spectrum of downstream tasks. Despite extensive research into self-supervised learning as the cornerstone of FMs, several outstanding issues persist in Graph Foundation Models that rely on graph self-supervised learning, namely: 1) Homogenization. The extent of generalization capability on downstream tasks remains unclear. 2) Scalability. It is unknown how effectively these models can scale to large datasets. 3) Efficiency. The training time and memory usage of these models require evaluation. 4) Training Stop Criteria. Determining the optimal stopping strategy for pre-training across multiple tasks to maximize performance on downstream tasks. To address these questions, we have constructed a rigorous benchmark that thoroughly analyzes and studies the generalization and scalability of self-supervised Graph Neural Network (GNN) models. Regarding generalization, we have implemented and compared the performance of various self-supervised GNN models, trained to generate node representations, across tasks such as node classification, link prediction, and node clustering. For scalability, we have compared the performance of various models after training using full-batch and mini-batch strategies. Additionally, we have assessed the training efficiency of these models by conducting experiments to test their GPU memory usage and throughput. Through these experiments, we aim to provide insights to motivate future research. The code for this benchmark is publicly available at https://github.com/NYUSHCS/GraphFM.
Clustering nodes in heterophilous graphs presents unique challenges due to the asymmetric relationships often overlooked by traditional methods, which moreover assume that good clustering corresponds to high intra-cluster and low inter-cluster connectivity. To address these issues, we introduce HeNCler - a novel approach for Heterophilous Node Clustering. Our method begins by defining a weighted kernel singular value decomposition to create an asymmetric similarity graph, applicable to both directed and undirected graphs. We further establish that the dual problem of this formulation aligns with asymmetric kernel spectral clustering, interpreting learned graph similarities without relying on homophily. We demonstrate the ability to solve the primal problem directly, circumventing the computational difficulties of the dual approach. Experimental evidence confirms that HeNCler significantly enhances performance in node clustering tasks within heterophilous graph contexts.
Graph Convolution Networks (GCNs) have significantly succeeded in learning user and item representations for recommendation systems. The core of their efficacy is the ability to explicitly exploit the collaborative signals from both the first- and high-order neighboring nodes. However, most existing GCN-based methods overlook the multiple interests of users while performing high-order graph convolution. Thus, the noisy information from unreliable neighbor nodes (e.g., users with dissimilar interests) negatively impacts the representation learning of the target node. Additionally, conducting graph convolution operations without differentiating high-order neighbors suffers the over-smoothing issue when stacking more layers, resulting in performance degradation. In this paper, we aim to capture more valuable information from high-order neighboring nodes while avoiding noise for better representation learning of the target node. To achieve this goal, we propose a novel GCN-based recommendation model, termed Cluster-based Graph Collaborative Filtering (ClusterGCF). This model performs high-order graph convolution on cluster-specific graphs, which are constructed by capturing the multiple interests of users and identifying the common interests among them. Specifically, we design an unsupervised and optimizable soft node clustering approach to classify user and item nodes into multiple clusters. Based on the soft node clustering results and the topology of the user-item interaction graph, we assign the nodes with probabilities for different clusters to construct the cluster-specific graphs. To evaluate the effectiveness of ClusterGCF, we conducted extensive experiments on four publicly available datasets. Experimental results demonstrate that our model can significantly improve recommendation performance.
Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.
Graph Neural Networks (GNNs) can be trained to detect communities within a graph by learning from the duality of feature and connectivity information. Currently, the common approach for optimisation of GNNs is to use comparisons to ground-truth for hyperparameter tuning and model selection. In this work, we show that nodes can be clustered into communities with GNNs by solely optimising for modularity, without any comparison to ground-truth. Although modularity is a graph partitioning quality metric, we show that this can be used to optimise GNNs that also encode features without a drop in performance. We take it a step further and also study whether the unsupervised metric performance can predict ground-truth performance. To investigate why modularity can be used to optimise GNNs, we design synthetic experiments that show the limitations of this approach. The synthetic graphs are created to highlight current capabilities in distinct, random and zero information space partitions in attributed graphs. We conclude that modularity can be used for hyperparameter optimisation and model selection on real-world datasets as well as being a suitable proxy for predicting ground-truth performance, however, GNNs fail to balance the information duality when the spaces contain conflicting signals.
Variational Graph Auto-Encoders (VGAEs) have been widely used to solve the node clustering task. However, the state-of-the-art methods have numerous challenges. First, existing VGAEs do not account for the discrepancy between the inference and generative models after incorporating the clustering inductive bias. Second, current models are prone to degenerate solutions that make the latent codes match the prior independently of the input signal (i.e., Posterior Collapse). Third, existing VGAEs overlook the effect of the noisy clustering assignments (i.e., Feature Randomness) and the impact of the strong trade-off between clustering and reconstruction (i.e., Feature Drift). To address these problems, we formulate a variational lower bound in a contrastive setting. Our lower bound is a tighter approximation of the log-likelihood function than the corresponding Evidence Lower BOund (ELBO). Thanks to a newly identified term, our lower bound can escape Posterior Collapse and has more flexibility to account for the difference between the inference and generative models. Additionally, our solution has two mechanisms to control the trade-off between Feature Randomness and Feature Drift. Extensive experiments show that the proposed method achieves state-of-the-art clustering results on several datasets. We provide strong evidence that this improvement is attributed to four aspects: integrating contrastive learning and alleviating Feature Randomness, Feature Drift, and Posterior Collapse.
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.