Cryptocurrency transaction fraud detection faces the dual challenges of increasingly complex transaction patterns and severe class imbalance. Traditional methods rely on manual feature engineering and struggle to capture temporal and structural dependencies in transaction networks. This paper proposes an Augmented Temporal-aware Graph Attention Network (ATGAT) that enhances detection performance through three modules: (1) designing an advanced temporal embedding module that fuses multi-scale time difference features with periodic position encoding; (2) constructing a temporal-aware triple attention mechanism that jointly optimizes structural, temporal, and global context attention; (3) employing weighted BCE loss to address class imbalance. Experiments on the Elliptic++ cryptocurrency dataset demonstrate that ATGAT achieves an AUC of 0.9130, representing a 9.2% improvement over the best traditional method XGBoost, 12.0% over GCN, and 10.0% over standard GAT. This method not only validates the enhancement effect of temporal awareness and triple attention mechanisms on graph neural networks, but also provides financial institutions with more reliable fraud detection tools, with its design principles generalizable to other temporal graph anomaly detection tasks.
Nowadays, Graph Fraud Detection (GFD) in financial scenarios has become an urgent research topic to protect online payment security. However, as organized crime groups are becoming more professional in real-world scenarios, fraudsters are employing more sophisticated camouflage strategies. Specifically, fraudsters disguise themselves by mimicking the behavioral data collected by platforms, ensuring that their key characteristics are consistent with those of benign users to a high degree, which we call Adaptive Camouflage. Consequently, this narrows the differences in behavioral traits between them and benign users within the platform's database, thereby making current GFD models lose efficiency. To address this problem, we propose a relation diffusion-based graph augmentation model Grad. In detail, Grad leverages a supervised graph contrastive learning module to enhance the fraud-benign difference and employs a guided relation diffusion generator to generate auxiliary homophilic relations from scratch. Based on these, weak fraudulent signals would be enhanced during the aggregation process, thus being obvious enough to be captured. Extensive experiments have been conducted on two real-world datasets provided by WeChat Pay, one of the largest online payment platforms with billions of users, and three public datasets. The results show that our proposed model Grad outperforms SOTA methods in both various scenarios, achieving at most 11.10% and 43.95% increases in AUC and AP, respectively.
Graph anomaly detection aims to identify unusual patterns in graph-based data, with wide applications in fields such as web security and financial fraud detection. Existing methods typically rely on contrastive learning, assuming that a lower similarity between a node and its local subgraph indicates abnormality. However, these approaches overlook a crucial limitation: the presence of interfering edges invalidates this assumption, since it introduces disruptive noise that compromises the contrastive learning process. Consequently, this limitation impairs the ability to effectively learn meaningful representations of normal patterns, leading to suboptimal detection performance. To address this issue, we propose a Clean-View Enhanced Graph Anomaly Detection framework (CVGAD), which includes a multi-scale anomaly awareness module to identify key sources of interference in the contrastive learning process. Moreover, to mitigate bias from the one-step edge removal process, we introduce a novel progressive purification module. This module incrementally refines the graph by iteratively identifying and removing interfering edges, thereby enhancing model performance. Extensive experiments on five benchmark datasets validate the effectiveness of our approach.
In this paper, we propose HLSAD, a novel method for detecting anomalies in time-evolving simplicial complexes. While traditional graph anomaly detection techniques have been extensively studied, they often fail to capture changes in higher-order interactions that are crucial for identifying complex structural anomalies. These higher-order interactions can arise either directly from the underlying data itself or through graph lifting techniques. Our approach leverages the spectral properties of Hodge Laplacians of simplicial complexes to effectively model multi-way interactions among data points. By incorporating higher-dimensional simplicial structures into our method, our method enhances both detection accuracy and computational efficiency. Through comprehensive experiments on both synthetic and real-world datasets, we demonstrate that our approach outperforms existing graph methods in detecting both events and change points.
Graph Anomaly Detection (GAD) in heterogeneous networks presents unique challenges due to node and edge heterogeneity. Existing Graph Neural Network (GNN) methods primarily focus on homogeneous GAD and thus fail to address three key issues: (C1) Capturing abnormal signal and rich semantics across diverse meta-paths; (C2) Retaining high-frequency content in HIN dimension alignment; and (C3) Learning effectively from difficult anomaly samples with class imbalance. To overcome these, we propose ChiGAD, a spectral GNN framework based on a novel Chi-Square filter, inspired by the wavelet effectiveness in diverse domains. Specifically, ChiGAD consists of: (1) Multi-Graph Chi-Square Filter, which captures anomalous information via applying dedicated Chi-Square filters to each meta-path graph; (2) Interactive Meta-Graph Convolution, which aligns features while preserving high-frequency information and incorporates heterogeneous messages by a unified Chi-Square Filter; and (3) Contribution-Informed Cross-Entropy Loss, which prioritizes difficult anomalies to address class imbalance. Extensive experiments on public and industrial datasets show that ChiGAD outperforms state-of-the-art models on multiple metrics. Additionally, its homogeneous variant, ChiGNN, excels on seven GAD datasets, validating the effectiveness of Chi-Square filters. Our code is available at https://github.com/HsipingLi/ChiGAD.
Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by $k$-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility.
Graph anomaly detection is a popular and vital task in various real-world scenarios, which has been studied for several decades. Recently, many studies extending deep learning-based methods have shown preferable performance on graph anomaly detection. However, existing methods are lack of efficiency that is definitely necessary for embedded devices. Towards this end, we propose an Efficient Anomaly detection model on heterogeneous Graphs via contrastive LEarning (EAGLE) by contrasting abnormal nodes with normal ones in terms of their distances to the local context. The proposed method first samples instance pairs on meta path-level for contrastive learning. Then, a graph autoencoder-based model is applied to learn informative node embeddings in an unsupervised way, which will be further combined with the discriminator to predict the anomaly scores of nodes. Experimental results show that EAGLE outperforms the state-of-the-art methods on three heterogeneous network datasets.
Graph anomaly detection (GAD) has garnered increasing attention in recent years, yet remains challenging due to two key factors: (1) label scarcity stemming from the high cost of annotations and (2) homophily disparity at node and class levels. In this paper, we introduce Anomaly-Aware Pre-Training and Fine-Tuning (APF), a targeted and effective framework to mitigate the above challenges in GAD. In the pre-training stage, APF incorporates node-specific subgraphs selected via the Rayleigh Quotient, a label-free anomaly metric, into the learning objective to enhance anomaly awareness. It further introduces two learnable spectral polynomial filters to jointly learn dual representations that capture both general semantics and subtle anomaly cues. During fine-tuning, a gated fusion mechanism adaptively integrates pre-trained representations across nodes and dimensions, while an anomaly-aware regularization loss encourages abnormal nodes to preserve more anomaly-relevant information. Furthermore, we theoretically show that APF tends to achieve linear separability under mild conditions. Comprehensive experiments on 10 benchmark datasets validate the superior performance of APF in comparison to state-of-the-art baselines.
Graph Anomaly Detection (GAD) is critical in security-sensitive domains, yet faces reliability challenges: miscalibrated confidence estimation (underconfidence in normal nodes, overconfidence in anomalies), adversarial vulnerability of derived confidence score under structural perturbations, and limited efficacy of conventional calibration methods for sparse anomaly patterns. Thus we propose CRC-SGAD, a framework integrating statistical risk control into GAD via two innovations: (1) A Dual-Threshold Conformal Risk Control mechanism that provides theoretically guaranteed bounds for both False Negative Rate (FNR) and False Positive Rate (FPR) through providing prediction sets; (2) A Subgraph-aware Spectral Graph Neural Calibrator (SSGNC) that optimizes node representations through adaptive spectral filtering while reducing the size of prediction sets via hybrid loss optimization. Experiments on four datasets and five GAD models demonstrate statistically significant improvements in FNR and FPR control and prediction set size. CRC-SGAD establishes a paradigm for statistically rigorous anomaly detection in graph-structured security applications.
Graph Anomaly Detection (GAD) plays a vital role in various data mining applications such as e-commerce fraud prevention and malicious user detection. Recently, Graph Neural Network (GNN) based approach has demonstrated great effectiveness in GAD by first encoding graph data into low-dimensional representations and then identifying anomalies under the guidance of supervised or unsupervised signals. However, existing GNN-based approaches implicitly follow the homophily principle (i.e., the "like attracts like" phenomenon) and fail to learn discriminative embedding for anomalies that connect vast normal nodes. Moreover, such approaches identify anomalies in a unified global perspective but overlook diversified abnormal patterns conditioned on local graph context, leading to suboptimal performance. To overcome the aforementioned limitations, in this paper, we propose a Multi-hypersphere Heterophilic Graph Learning (MHetGL) framework for unsupervised GAD. Specifically, we first devise a Heterophilic Graph Encoding (HGE) module to learn distinguishable representations for potential anomalies by purifying and augmenting their neighborhood in a fully unsupervised manner. Then, we propose a Multi-Hypersphere Learning (MHL) module to enhance the detection capability for context-dependent anomalies by jointly incorporating critical patterns from both global and local perspectives. Extensive experiments on ten real-world datasets show that MHetGL outperforms 14 baselines. Our code is publicly available at https://github.com/KennyNH/MHetGL.
Graph Neural Networks (GNNs) have achieved significant success in machine learning, with wide applications in social networks, bioinformatics, knowledge graphs, and other fields. Most research assumes ideal closed-set environments. However, in real-world open-set environments, graph learning models face challenges in robustness and reliability due to unseen classes. This highlights the need for Graph Open-Set Recognition (GOSR) methods to address these issues and ensure effective GNN application in practical scenarios. Research in GOSR is in its early stages, with a lack of a comprehensive benchmark spanning diverse tasks and datasets to evaluate methods. Moreover, traditional methods, Graph Out-of-Distribution Detection (GOODD), GOSR, and Graph Anomaly Detection (GAD) have mostly evolved in isolation, with little exploration of their interconnections or potential applications to GOSR. To fill these gaps, we introduce \textbf{G-OSR}, a comprehensive benchmark for evaluating GOSR methods at both the node and graph levels, using datasets from multiple domains to ensure fair and standardized comparisons of effectiveness and efficiency across traditional, GOODD, GOSR, and GAD methods. The results offer critical insights into the generalizability and limitations of current GOSR methods and provide valuable resources for advancing research in this field through systematic analysis of diverse approaches.
Graph Anomaly Detection (GAD) has demonstrated great effectiveness in identifying unusual patterns within graph-structured data. However, while labeled anomalies are often scarce in emerging applications, existing supervised GAD approaches are either ineffective or not applicable when moved across graph domains due to distribution shifts and heterogeneous feature spaces. To address these challenges, we present AdaGraph-T3, a novel test-time training framework for cross-domain GAD. AdaGraph-T3 combines supervised and self-supervised learning during training while adapting to a new domain during test time using only self-supervised learning by leveraging a homophily-based affinity score that captures domain-invariant properties of anomalies. Our framework introduces four key innovations to cross-domain GAD: an effective self-supervision scheme, an attention-based mechanism that dynamically learns edge importance weights during message passing, domain-specific encoders for handling heterogeneous features, and class-aware regularization to address imbalance. Experiments across multiple cross-domain settings demonstrate that AdaGraph-T3 significantly outperforms existing approaches, achieving average improvements of over 6.6% in AUROC and 7.9% in AUPRC compared to the best competing model.
Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on structural and attribute-level anomalies. To this end, we propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies. CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability: (1) Curvature-equivariant geometry reconstruction, which focuses exclusively on reconstructing the edge curvatures using a mixed-curvature, Riemannian encoder and Gaussian kernel-based decoder; and (2) Curvature-invariant structure and attribute reconstruction, which decouples structural and attribute anomalies from geometric irregularities by regularizing graph curvature under discrete Ollivier-Ricci flow, thereby isolating the non-geometric anomalies. By leveraging curvature, CurvGAD refines the existing anomaly classifications and identifies new curvature-driven anomalies. Extensive experimentation over 10 real-world datasets (both homophilic and heterophilic) demonstrates an improvement of up to 6.5% over state-of-the-art GAD methods.
Graph machine learning has witnessed rapid growth, driving advancements across diverse domains. However, the in-distribution assumption, where training and testing data share the same distribution, often breaks in real-world scenarios, leading to degraded model performance under distribution shifts. This challenge has catalyzed interest in graph out-of-distribution (GOOD) detection, which focuses on identifying graph data that deviates from the distribution seen during training, thereby enhancing model robustness. In this paper, we provide a rigorous definition of GOOD detection and systematically categorize existing methods into four types: enhancement-based, reconstruction-based, information propagation-based, and classification-based approaches. We analyze the principles and mechanisms of each approach and clarify the distinctions between GOOD detection and related fields, such as graph anomaly detection, outlier detection, and GOOD generalization. Beyond methodology, we discuss practical applications and theoretical foundations, highlighting the unique challenges posed by graph data. Finally, we discuss the primary challenges and propose future directions to advance this emerging field. The repository of this survey is available at https://github.com/ca1man-2022/Awesome-GOOD-Detection.
Graph anomaly detection (GAD) aims to identify abnormal nodes that differ from the majority of the nodes in a graph, which has been attracting significant attention in recent years. Existing generalist graph models have achieved remarkable success in different graph tasks but struggle to generalize to the GAD task. This limitation arises from their difficulty in learning generalized knowledge for capturing the inherently infrequent, irregular and heterogeneous abnormality patterns in graphs from different domains. To address this challenge, we propose AnomalyGFM, a GAD-oriented graph foundation model that supports zero-shot inference and few-shot prompt tuning for GAD in diverse graph datasets. One key insight is that graph-agnostic representations for normal and abnormal classes are required to support effective zero/few-shot GAD across different graphs. Motivated by this, AnomalyGFM is pre-trained to align data-independent, learnable normal and abnormal class prototypes with node representation residuals (i.e., representation deviation of a node from its neighbors). The residual features essentially project the node information into a unified feature space where we can effectively measure the abnormality of nodes from different graphs in a consistent way. This provides a driving force for the learning of graph-agnostic, discriminative prototypes for the normal and abnormal classes, which can be used to enable zero-shot GAD on new graphs, including very large-scale graphs. If there are few-shot labeled normal nodes available in the new graphs, AnomalyGFM can further support prompt tuning to leverage these nodes for better adaptation. Comprehensive experiments on 11 widely-used GAD datasets with real anomalies, demonstrate that AnomalyGFM significantly outperforms state-of-the-art competing methods under both zero- and few-shot GAD settings.
Semi-supervised graph anomaly detection (GAD) has recently received increasing attention, which aims to distinguish anomalous patterns from graphs under the guidance of a moderate amount of labeled data and a large volume of unlabeled data. Although these proposed semi-supervised GAD methods have achieved great success, their superior performance will be seriously degraded when the provided labels are extremely limited due to some unpredictable factors. Besides, the existing methods primarily focus on anomaly detection in static graphs, and little effort was paid to consider the continuous evolution characteristic of graphs over time (dynamic graphs). To address these challenges, we propose a novel GAD framework (EL$^{2}$-DGAD) to tackle anomaly detection problem in dynamic graphs with extremely limited labels. Specifically, a transformer-based graph encoder model is designed to more effectively preserve evolving graph structures beyond the local neighborhood. Then, we incorporate an ego-context hypersphere classification loss to classify temporal interactions according to their structure and temporal neighborhoods while ensuring the normal samples are mapped compactly against anomalous data. Finally, the above loss is further augmented with an ego-context contrasting module which utilizes unlabeled data to enhance model generalization. Extensive experiments on four datasets and three label rates demonstrate the effectiveness of the proposed method in comparison to the existing GAD methods.
Graph anomaly detection (GAD) aims to identify nodes from a graph that are significantly different from normal patterns. Most previous studies are model-driven, focusing on enhancing the detection effect by improving the model structure. However, these approaches often treat all nodes equally, neglecting the different contributions of various nodes to the training. Therefore, we introduce graph curriculum learning as a simple and effective plug-and-play module to optimize GAD methods. The existing graph curriculum learning mainly focuses on the homogeneity of graphs and treats nodes with high homogeneity as easy nodes. In fact, GAD models can handle not only graph homogeneity but also heterogeneity, which leads to the unsuitability of these existing methods. To address this problem, we propose an innovative Bi-directional Curriculum Learning strategy (BCL), which considers nodes with higher and lower similarity to neighbor nodes as simple nodes in the direction of focusing on homogeneity and focusing on heterogeneity, respectively, and prioritizes their training. Extensive experiments show that BCL can be quickly integrated into existing detection processes and significantly improves the performance of ten GAD anomaly detection models on seven commonly used datasets.
Self-supervised learning (SSL) is an emerging paradigm that exploits supervisory signals generated from the data itself, and many recent studies have leveraged SSL to conduct graph anomaly detection. However, we empirically found that three important factors can substantially impact detection performance across datasets: 1) the specific SSL strategy employed; 2) the tuning of the strategy's hyperparameters; and 3) the allocation of combination weights when using multiple strategies. Most SSL-based graph anomaly detection methods circumvent these issues by arbitrarily or selectively (i.e., guided by label information) choosing SSL strategies, hyperparameter settings, and combination weights. While an arbitrary choice may lead to subpar performance, using label information in an unsupervised setting is label information leakage and leads to severe overestimation of a method's performance. Leakage has been criticized as "one of the top ten data mining mistakes", yet many recent studies on SSL-based graph anomaly detection have been using label information to select hyperparameters. To mitigate this issue, we propose to use an internal evaluation strategy (with theoretical analysis) to select hyperparameters in SSL for unsupervised anomaly detection. We perform extensive experiments using 10 recent SSL-based graph anomaly detection algorithms on various benchmark datasets, demonstrating both the prior issues with hyperparameter selection and the effectiveness of our proposed strategy.
Graph anomaly detection (GAD) is a critical task in graph machine learning, with the primary objective of identifying anomalous nodes that deviate significantly from the majority. This task is widely applied in various real-world scenarios, including fraud detection and social network analysis. However, existing GAD methods still face two major challenges: (1) They are often limited to detecting anomalies in single-type interaction graphs and struggle with multiple interaction types in multiplex heterogeneous graphs; (2) In unsupervised scenarios, selecting appropriate anomaly score thresholds remains a significant challenge for accurate anomaly detection. To address the above challenges, we propose a novel Unsupervised Multiplex Graph Anomaly Detection method, named UMGAD. We first learn multi-relational correlations among nodes in multiplex heterogeneous graphs and capture anomaly information during node attribute and structure reconstruction through graph-masked autoencoder (GMAE). Then, to further weaken the influence of noise and redundant information on abnormal information extraction, we generate attribute-level and subgraph-level augmented-view graphs respectively, and perform attribute and structure reconstruction through GMAE. Finally, We learn to optimize node attributes and structural features through contrastive learning between original-view and augmented-view graphs to improve the model's ability to capture anomalies. Meanwhile, we also propose a new anomaly score threshold selection strategy, which allows the model to be independent of the ground truth in real unsupervised scenarios. Extensive experiments on four datasets show that our \model significantly outperforms state-of-the-art methods, achieving average improvements of 13.48% in AUC and 11.68% in Macro-F1 across all datasets.
Graph Anomaly Detection (GAD) aims to identify uncommon, deviated, or suspicious objects within graph-structured data. Existing methods generally focus on a single graph object type (node, edge, graph, etc.) and often overlook the inherent connections among different object types of graph anomalies. For instance, a money laundering transaction might involve an abnormal account and the broader community it interacts with. To address this, we present UniGAD, the first unified framework for detecting anomalies at node, edge, and graph levels jointly. Specifically, we develop the Maximum Rayleigh Quotient Subgraph Sampler (MRQSampler) that unifies multi-level formats by transferring objects at each level into graph-level tasks on subgraphs. We theoretically prove that MRQSampler maximizes the accumulated spectral energy of subgraphs (i.e., the Rayleigh quotient) to preserve the most significant anomaly information. To further unify multi-level training, we introduce a novel GraphStitch Network to integrate information across different levels, adjust the amount of sharing required at each level, and harmonize conflicting training goals. Comprehensive experiments show that UniGAD outperforms both existing GAD methods specialized for a single task and graph prompt-based approaches for multiple tasks, while also providing robust zero-shot task transferability. All codes can be found at https://github.com/lllyyq1121/UniGAD.