Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detection

Graph anomaly detection (GAD) aims to identify irregular nodes or structures in attributed graphs. Neighbor information, which reflects both structural connectivity and attribute consistency with surrounding nodes, is essential for distinguishing anomalies from normal patterns. Although recent graph neural network (GNN)-based methods incorporate such information through message passing, they often fail to explicitly model its effect or interaction with attributes, limiting detection performance. This work introduces NeiGAD, a novel plug-and-play module that captures neighbor information through spectral graph analysis. Theoretical insights demonstrate that eigenvectors of the adjacency matrix encode local neighbor interactions and progressively amplify anomaly signals. Based on this, NeiGAD selects a compact set of eigenvectors to construct efficient and discriminative representations. Experiments on eight real-world datasets show that NeiGAD consistently improves detection accuracy and outperforms state-of-the-art GAD methods. These results demonstrate the importance of explicit neighbor modeling and the effectiveness of spectral analysis in anomaly detection. Code is available at: https://github.com/huafeihuang/NeiGAD.

Graph anomaly detection (GAD) aims to identify nodes that deviate from normal patterns in structure or features. While recent GNN-based approaches have advanced this task, they struggle with two major challenges: 1) homophily disparity, where nodes exhibit varying homophily at both class and node levels; and 2) limited scalability, as many methods rely on costly whole-graph operations. To address them, we propose SAGAD, a Scalable and Adaptive framework for GAD. SAGAD precomputes multi-hop embeddings and applies reparameterized Chebyshev filters to extract low- and high-frequency information, enabling efficient training and capturing both homophilic and heterophilic patterns. To mitigate node-level homophily disparity, we introduce an Anomaly Context-Aware Adaptive Fusion, which adaptively fuses low- and high-pass embeddings using fusion coefficients conditioned on Rayleigh Quotient-guided anomalous subgraph structures for each node. To alleviate class-level disparity, we design a Frequency Preference Guidance Loss, which encourages anomalies to preserve more high-frequency information than normal nodes. SAGAD supports mini-batch training, achieves linear time and space complexity, and drastically reduces memory usage on large-scale graphs. Theoretically, SAGAD ensures asymptotic linear separability between normal and abnormal nodes under mild conditions. Extensive experiments on 10 benchmarks confirm SAGAD's superior accuracy and scalability over state-of-the-art methods.

Graph anomaly detection aims to identify nodes that deviate from normal behavioral patterns within graphs. However, existing methods largely rely on the homophily assumption, which makes it difficult to distinguish spurious affinities and to capture the diverse behaviors of normal nodes,limiting their robustness in complex real-world scenarios. To address this problem, we propose RagGAD, an unsupervised graph anomaly detection framework based on rationale-aware conditional Gaussian mixture normalizing flow. RagGAD introduces an adaptive rationale disentangler to disentangle stable rationales from spurious correlations within node interrelationships, and further decomposes stable rationales into robust and fragile components. The learned rationales capture underlying interaction patterns that characterize normal behaviors under varying conditions, while anomalies emerge as deviations associated with unstable or spurious correlations. To model the intricate distributions of normal and abnormal nodes, RagGAD integrates rationale-non-rationale Gaussian mixture modeling with a robust-fragile rationale mixture learning strategy. By mitigating spurious homophilic correlations and embracing the heterogeneity of normal patterns, RagGAD identifies anomalies as low-density regions within a structure-aware distribution space. Extensive experiments on multiple benchmark datasets demonstrate that RagGAD outperforms state-of-the-art methods.