Learning graph embeddings is a crucial task in graph mining tasks. An effective graph embedding model can learn low-dimensional representations from graph-structured data for data publishing benefiting various downstream applications such as node classification, link prediction, etc. However, recent studies have revealed that graph embeddings are susceptible to attribute inference attacks, which allow attackers to infer private node attributes from the learned graph embeddings. To address these concerns, privacy-preserving graph embedding methods have emerged, aiming to simultaneously consider primary learning and privacy protection through adversarial learning. However, most existing methods assume that representation models have access to all sensitive attributes in advance during the training stage, which is not always the case due to diverse privacy preferences. Furthermore, the commonly used adversarial learning technique in privacy-preserving representation learning suffers from unstable training issues. In this paper, we propose a novel approach called Private Variational Graph AutoEncoders (PVGAE) with the aid of independent distribution penalty as a regularization term. Specifically, we split the original variational graph autoencoder (VGAE) to learn sensitive and non-sensitive latent representations using two sets of encoders. Additionally, we introduce a novel regularization to enforce the independence of the encoders. We prove the theoretical effectiveness of regularization from the perspective of mutual information. Experimental results on three real-world datasets demonstrate that PVGAE outperforms other baselines in private embedding learning regarding utility performance and privacy protection.
Existing studies for applying the mixup technique on graphs mainly focus on graph classification tasks, while the research in node classification is still under-explored. In this paper, we propose a novel mixup augmentation for node classification called Structural Mixup (S-Mixup). The core idea is to take into account the structural information while mixing nodes. Specifically, S-Mixup obtains pseudo-labels for unlabeled nodes in a graph along with their prediction confidence via a Graph Neural Network (GNN) classifier. These serve as the criteria for the composition of the mixup pool for both inter and intra-class mixups. Furthermore, we utilize the edge gradient obtained from the GNN training and propose a gradient-based edge selection strategy for selecting edges to be attached to the nodes generated by the mixup. Through extensive experiments on real-world benchmark datasets, we demonstrate the effectiveness of S-Mixup evaluated on the node classification task. We observe that S-Mixup enhances the robustness and generalization performance of GNNs, especially in heterophilous situations. The source code of S-Mixup can be found at \url{https://github.com/SukwonYun/S-Mixup}
Recently, Graph Neural Networks (GNNs) have shown promising performance in tasks on dynamic graphs such as node classification, link prediction and graph regression. However, few work has studied the temporal edge regression task which has important real-world applications. In this paper, we explore the application of GNNs to edge regression tasks in both static and dynamic settings, focusing on predicting food and agriculture trade values between nations. We introduce three simple yet strong baselines and comprehensively evaluate one static and three dynamic GNN models using the UN Trade dataset. Our experimental results reveal that the baselines exhibit remarkably strong performance across various settings, highlighting the inadequacy of existing GNNs. We also find that TGN outperforms other GNN models, suggesting TGN is a more appropriate choice for edge regression tasks. Moreover, we note that the proportion of negative edges in the training samples significantly affects the test performance. The companion source code can be found at: https://github.com/scylj1/GNN_Edge_Regression.
Semi-Supervised image classification is one of the most fundamental problem in computer vision, which significantly reduces the need for human labor. In this paper, we introduce a new semi-supervised learning algorithm - SimMatchV2, which formulates various consistency regularizations between labeled and unlabeled data from the graph perspective. In SimMatchV2, we regard the augmented view of a sample as a node, which consists of a label and its corresponding representation. Different nodes are connected with the edges, which are measured by the similarity of the node representations. Inspired by the message passing and node classification in graph theory, we propose four types of consistencies, namely 1) node-node consistency, 2) node-edge consistency, 3) edge-edge consistency, and 4) edge-node consistency. We also uncover that a simple feature normalization can reduce the gaps of the feature norm between different augmented views, significantly improving the performance of SimMatchV2. Our SimMatchV2 has been validated on multiple semi-supervised learning benchmarks. Notably, with ResNet-50 as our backbone and 300 epochs of training, SimMatchV2 achieves 71.9\% and 76.2\% Top-1 Accuracy with 1\% and 10\% labeled examples on ImageNet, which significantly outperforms the previous methods and achieves state-of-the-art performance. Code and pre-trained models are available at \href{https://github.com/mingkai-zheng/SimMatchV2}{https://github.com/mingkai-zheng/SimMatchV2}.
Textual graphs (TGs) are graphs whose nodes correspond to text (sentences or documents), which are widely prevalent. The representation learning of TGs involves two stages: (i) unsupervised feature extraction and (ii) supervised graph representation learning. In recent years, extensive efforts have been devoted to the latter stage, where Graph Neural Networks (GNNs) have dominated. However, the former stage for most existing graph benchmarks still relies on traditional feature engineering techniques. More recently, with the rapid development of language models (LMs), researchers have focused on leveraging LMs to facilitate the learning of TGs, either by jointly training them in a computationally intensive framework (merging the two stages), or designing complex self-supervised training tasks for feature extraction (enhancing the first stage). In this work, we present SimTeG, a frustratingly Simple approach for Textual Graph learning that does not innovate in frameworks, models, and tasks. Instead, we first perform supervised parameter-efficient fine-tuning (PEFT) on a pre-trained LM on the downstream task, such as node classification. We then generate node embeddings using the last hidden states of finetuned LM. These derived features can be further utilized by any GNN for training on the same task. We evaluate our approach on two fundamental graph representation learning tasks: node classification and link prediction. Through extensive experiments, we show that our approach significantly improves the performance of various GNNs on multiple graph benchmarks.
Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and their well-designed variants, on some commonly used benchmark graphs and hypergraphs, they are outperformed by even a simple Multi-Layer Perceptron. This observation motivates a reexamination of the design paradigm of the current GNNs and HGNNs and poses challenges of extracting graph features effectively. In this work, a universal feature encoder for both graph and hypergraph representation learning is designed, called UniG-Encoder. The architecture starts with a forward transformation of the topological relationships of connected nodes into edge or hyperedge features via a normalized projection matrix. The resulting edge/hyperedge features, together with the original node features, are fed into a neural network. The encoded node embeddings are then derived from the reversed transformation, described by the transpose of the projection matrix, of the network's output, which can be further used for tasks such as node classification. The proposed architecture, in contrast to the traditional spectral-based and/or message passing approaches, simultaneously and comprehensively exploits the node features and graph/hypergraph topologies in an efficient and unified manner, covering both heterophilic and homophilic graphs. The designed projection matrix, encoding the graph features, is intuitive and interpretable. Extensive experiments are conducted and demonstrate the superior performance of the proposed framework on twelve representative hypergraph datasets and six real-world graph datasets, compared to the state-of-the-art methods. Our implementation is available online at https://github.com/MinhZou/UniG-Encoder.
Node classification is one of the core tasks on attributed graphs, but successful graph learning solutions require sufficiently labeled data. To keep annotation costs low, active graph learning focuses on selecting the most qualitative subset of nodes that maximizes label efficiency. However, deciding which heuristic is best suited for an unlabeled graph to increase label efficiency is a persistent challenge. Existing solutions either neglect aligning the learned model and the sampling method or focus only on limited selection aspects. They are thus sometimes worse or only equally good as random sampling. In this work, we introduce a novel active graph learning approach called DiffusAL, showing significant robustness in diverse settings. Toward better transferability between different graph structures, we combine three independent scoring functions to identify the most informative node samples for labeling in a parameter-free way: i) Model Uncertainty, ii) Diversity Component, and iii) Node Importance computed via graph diffusion heuristics. Most of our calculations for acquisition and training can be pre-processed, making DiffusAL more efficient compared to approaches combining diverse selection criteria and similarly fast as simpler heuristics. Our experiments on various benchmark datasets show that, unlike previous methods, our approach significantly outperforms random selection in 100% of all datasets and labeling budgets tested.
Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including semi-supervised node classification, link prediction, and graph generation. However, it is important to acknowledge that the majority of state-of-the-art GNN models are built upon the assumption of an in-distribution setting, which hinders their performance on real-world graphs with dynamic structures. In this article, we aim to assess the impact of training GNNs on localized subsets of the graph. Such restricted training data may lead to a model that performs well in the specific region it was trained on but fails to generalize and make accurate predictions for the entire graph. In the context of graph-based semi-supervised learning (SSL), resource constraints often lead to scenarios where the dataset is large, but only a portion of it can be labeled, affecting the model's performance. This limitation affects tasks like anomaly detection or spam detection when labeling processes are biased or influenced by human subjectivity. To tackle the challenges posed by localized training data, we approach the problem as an out-of-distribution (OOD) data issue by by aligning the distributions between the training data, which represents a small portion of labeled data, and the graph inference process that involves making predictions for the entire graph. We propose a regularization method to minimize distributional discrepancies between localized training data and graph inference, improving model performance on OOD data. Extensive tests on popular GNN models show significant performance improvement on three citation GNN benchmark datasets. The regularization approach effectively enhances model adaptation and generalization, overcoming challenges posed by OOD data.
Graph domain adaptation models are widely adopted in cross-network learning tasks, with the aim of transferring labeling or structural knowledge. Currently, there mainly exist two limitations in evaluating graph domain adaptation models. On one side, they are primarily tested for the specific cross-network node classification task, leaving tasks at edge-level and graph-level largely under-explored. Moreover, they are primarily tested in limited scenarios, such as social networks or citation networks, lacking validation of model's capability in richer scenarios. As comprehensively assessing models could enhance model practicality in real-world applications, we propose a benchmark, known as OpenGDA. It provides abundant pre-processed and unified datasets for different types of tasks (node, edge, graph). They originate from diverse scenarios, covering web information systems, urban systems and natural systems. Furthermore, it integrates state-of-the-art models with standardized and end-to-end pipelines. Overall, OpenGDA provides a user-friendly, scalable and reproducible benchmark for evaluating graph domain adaptation models. The benchmark experiments highlight the challenges of applying GDA models to real-world applications with consistent good performance, and potentially provide insights to future research. As an emerging project, OpenGDA will be regularly updated with new datasets and models. It could be accessed from https://github.com/Skyorca/OpenGDA.
Despite a surge in interest in GNN development, homogeneity in benchmarking datasets still presents a fundamental issue to GNN research. GraphWorld is a recent solution which uses the Stochastic Block Model (SBM) to generate diverse populations of synthetic graphs for benchmarking any GNN task. Despite its success, the SBM imposed fundamental limitations on the kinds of graph structure GraphWorld could create. In this work we examine how two additional synthetic graph generators can improve GraphWorld's evaluation; LFR, a well-established model in the graph clustering literature and CABAM, a recent adaptation of the Barabasi-Albert model tailored for GNN benchmarking. By integrating these generators, we significantly expand the coverage of graph space within the GraphWorld framework while preserving key graph properties observed in real-world networks. To demonstrate their effectiveness, we generate 300,000 graphs to benchmark 11 GNN models on a node classification task. We find GNN performance variations in response to homophily, degree distribution and feature signal. Based on these findings, we classify models by their sensitivity to the new generators under these properties. Additionally, we release the extensions made to GraphWorld on the GitHub repository, offering further evaluation of GNN performance on new graphs.
We present PolyGNN, a polyhedron-based graph neural network for 3D building reconstruction from point clouds. PolyGNN learns to assemble primitives obtained by polyhedral decomposition via graph node classification, achieving a watertight and compact reconstruction. To effectively represent arbitrary-shaped polyhedra in the neural network, we propose a skeleton-based sampling strategy to generate polyhedron-wise queries. These queries are then incorporated with inter-polyhedron adjacency to enhance the classification. PolyGNN is end-to-end optimizable and is designed to accommodate variable-size input points, polyhedra, and queries with an index-driven batching technique. To address the abstraction gap between existing city-building models and the underlying instances, and provide a fair evaluation of the proposed method, we develop our method on a large-scale synthetic dataset with well-defined ground truths of polyhedral labels. We further conduct a transferability analysis across cities and on real-world point clouds. Both qualitative and quantitative results demonstrate the effectiveness of our method, particularly its efficiency for large-scale reconstructions. The source code and data are available at https://github.com/chenzhaiyu/polygnn.
Utilizing long-range dependency, a concept extensively studied in homogeneous graphs, remains underexplored in heterogeneous graphs, especially on large ones, posing two significant challenges: Reducing computational costs while maximizing effective information utilization in the presence of heterogeneity, and overcoming the over-smoothing issue in graph neural networks. To address this gap, we investigate the importance of different meta-paths and introduce an automatic framework for utilizing long-range dependency on heterogeneous graphs, denoted as Long-range Meta-path Search through Progressive Sampling (LMSPS). Specifically, we develop a search space with all meta-paths related to the target node type. By employing a progressive sampling algorithm, LMSPS dynamically shrinks the search space with hop-independent time complexity. Through a sampling evaluation strategy, LMSPS conducts a specialized and effective meta-path selection, leading to retraining with only effective meta-paths, thus mitigating costs and over-smoothing. Extensive experiments across diverse heterogeneous datasets validate LMSPS's capability in discovering effective long-range meta-paths, surpassing state-of-the-art methods. Our code is available at https://github.com/JHL-HUST/LMSPS.
Graph neural networks have shown great ability in representation (GNNs) learning on graphs, facilitating various tasks. Despite their great performance in modeling graphs, recent works show that GNNs tend to inherit and amplify the bias from training data, causing concerns of the adoption of GNNs in high-stake scenarios. Hence, many efforts have been taken for fairness-aware GNNs. However, most existing fair GNNs learn fair node representations by adopting statistical fairness notions, which may fail to alleviate bias in the presence of statistical anomalies. Motivated by causal theory, there are several attempts utilizing graph counterfactual fairness to mitigate root causes of unfairness. However, these methods suffer from non-realistic counterfactuals obtained by perturbation or generation. In this paper, we take a causal view on fair graph learning problem. Guided by the casual analysis, we propose a novel framework CAF, which can select counterfactuals from training data to avoid non-realistic counterfactuals and adopt selected counterfactuals to learn fair node representations for node classification task. Extensive experiments on synthetic and real-world datasets show the effectiveness of CAF. Our code is available at https://github.com/TimeLovercc/CAF-GNN.
Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring the implicit higher-order correlations when training the embedding space of the graph. In this paper, we propose a hypergraph learning framework named LFH that is capable of dynamic hyperedge construction and attentive embedding update utilizing the heterogeneity attributes of the graph. Specifically, in our framework, the high-quality features are first generated by the pairwise fusion strategy that utilizes explicit graph structure information when generating initial node embedding. Afterwards, a hypergraph is constructed through the dynamic grouping of implicit hyperedges, followed by the type-specific hypergraph learning process. To evaluate the effectiveness of our proposed framework, we conduct comprehensive experiments on several popular datasets with eleven state-of-the-art models on both node classification and link prediction tasks, which fall into categories of homogeneous pairwise graph learning, heterogeneous pairwise graph learning, and hypergraph learning. The experiment results demonstrate a significant performance gain (average 12.5% in node classification and 13.3% in link prediction) compared with recent state-of-the-art methods.
Learning on Graphs has attracted immense attention due to its wide real-world applications. The most popular pipeline for learning on graphs with textual node attributes primarily relies on Graph Neural Networks (GNNs), and utilizes shallow text embedding as initial node representations, which has limitations in general knowledge and profound semantic understanding. In recent years, Large Language Models (LLMs) have been proven to possess extensive common knowledge and powerful semantic comprehension abilities that have revolutionized existing workflows to handle text data. In this paper, we aim to explore the potential of LLMs in graph machine learning, especially the node classification task, and investigate two possible pipelines: LLMs-as-Enhancers and LLMs-as-Predictors. The former leverages LLMs to enhance nodes' text attributes with their massive knowledge and then generate predictions through GNNs. The latter attempts to directly employ LLMs as standalone predictors. We conduct comprehensive and systematical studies on these two pipelines under various settings. From comprehensive empirical results, we make original observations and find new insights that open new possibilities and suggest promising directions to leverage LLMs for learning on graphs. Our codes and datasets are available at https://github.com/CurryTang/Graph-LLM.
Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state ($t$) and previous context (over timestamps [$t-1, t-l$], $l$ is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp $t$. We consider diverse benchmarks with varying levels of ``novelty" as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.
Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture long-range dependencies and global patterns in graphs. To address this, we propose a new inductive bias based on variational analysis, drawing inspiration from the Brachistochrone problem. Our framework establishes a mapping between discrete GNN models and continuous diffusion functionals. This enables the design of application-specific objective functions in the continuous domain and the construction of discrete deep models with mathematical guarantees. To tackle over-smoothing in GNNs, we analyze the existing layer-by-layer graph embedding models and identify that they are equivalent to l2-norm integral functionals of graph gradients, which cause over-smoothing. Similar to edge-preserving filters in image denoising, we introduce total variation (TV) to align the graph diffusion pattern with global community topologies. Additionally, we devise a selective mechanism to address the trade-off between model depth and over-smoothing, which can be easily integrated into existing GNNs. Furthermore, we propose a novel generative adversarial network (GAN) that predicts spreading flows in graphs through a neural transport equation. To mitigate vanishing flows, we customize the objective function to minimize transportation within each community while maximizing inter-community flows. Our GNN models achieve state-of-the-art (SOTA) performance on popular graph learning benchmarks such as Cora, Citeseer, and Pubmed.
High-order Graph Neural Networks (HO-GNNs) have been developed to infer consistent latent spaces in the heterophilic regime, where the label distribution is not correlated with the graph structure. However, most of the existing HO-GNNs are hop-based, i.e., they rely on the powers of the transition matrix. As a result, these architectures are not fully reactive to the classification loss and the achieved structural filters have static supports. In other words, neither the filters' supports nor their coefficients can be learned with these networks. They are confined, instead, to learn combinations of filters. To address the above concerns, we propose Diffusion-jump GNNs a method relying on asymptotic diffusion distances that operates on jumps. A diffusion-pump generates pairwise distances whose projections determine both the support and coefficients of each structural filter. These filters are called jumps because they explore a wide range of scales in order to find bonds between scattered nodes with the same label. Actually, the full process is controlled by the classification loss. Both the jumps and the diffusion distances react to classification errors (i.e. they are learnable). Homophiliation, i.e., the process of learning piecewise smooth latent spaces in the heterophilic regime, is formulated as a Dirichlet problem: the known labels determine the border nodes and the diffusion-pump ensures a minimal deviation of the semi-supervised grouping from a canonical unsupervised grouping. This triggers the update of both the diffusion distances and, consequently, the jumps in order to minimize the classification error. The Dirichlet formulation has several advantages. It leads to the definition of structural heterophily, a novel measure beyond edge heterophily. It also allows us to investigate links with (learnable) diffusion distances, absorbing random walks and stochastic diffusion.
We propose Unsupervised Episode Generation method called Neighbors as Queries (NaQ) to solve the Few-Shot Node-Classification (FSNC) task by unsupervised Graph Meta-learning. Doing so enables full utilization of the information of all nodes in a graph, which is not possible in current supervised meta-learning methods for FSNC due to the label-scarcity problem. In addition, unlike unsupervised Graph Contrastive Learning (GCL) methods that overlook the downstream task to be solved at the training phase resulting in vulnerability to class imbalance of a graph, we adopt the episodic learning framework that allows the model to be aware of the downstream task format, i.e., FSNC. The proposed NaQ is a simple but effective unsupervised episode generation method that randomly samples nodes from a graph to make a support set, followed by similarity-based sampling of nodes to make the corresponding query set. Since NaQ is model-agnostic, any existing supervised graph meta-learning methods can be trained in an unsupervised manner, while not sacrificing much of their performance or sometimes even improving them. Extensive experimental results demonstrate the effectiveness of our proposed unsupervised episode generation method for graph meta-learning towards the FSNC task. Our code is available at: https://github.com/JhngJng/NaQ-PyTorch.
Few-shot node classification, which aims to predict labels for nodes on graphs with only limited labeled nodes as references, is of great significance in real-world graph mining tasks. Particularly, in this paper, we refer to the task of classifying nodes in classes with a few labeled nodes as the few-shot node classification problem. To tackle such a label shortage issue, existing works generally leverage the meta-learning framework, which utilizes a number of episodes to extract transferable knowledge from classes with abundant labeled nodes and generalizes the knowledge to other classes with limited labeled nodes. In essence, the primary aim of few-shot node classification is to learn node embeddings that are generalizable across different classes. To accomplish this, the GNN encoder must be able to distinguish node embeddings between different classes, while also aligning embeddings for nodes in the same class. Thus, in this work, we propose to consider both the intra-class and inter-class generalizability of the model. We create a novel contrastive meta-learning framework on graphs, named COSMIC, with two key designs. First, we propose to enhance the intra-class generalizability by involving a contrastive two-step optimization in each episode to explicitly align node embeddings in the same classes. Second, we strengthen the inter-class generalizability by generating hard node classes via a novel similarity-sensitive mix-up strategy. Extensive experiments on few-shot node classification datasets verify the superiority of our framework over state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/COSMIC.