Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detection

Xiang Wang; Zhijun Cheng; Zhenyu Meng

cs.AIAug 27, 2026

Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detection

Authors: Xiang Wang, Zhijun Cheng, Zhenyu Meng

Organizations: School of Artificial Intelligence and Transportation Engineering, Fujian University of Technology, Fuzhou, China · Institute of Artificial Intelligence, Fujian University of Technology, Fuzhou, China

Abstract

In recent years, graph anomaly detection (GAD) based on frequency-domain filtering have achieved promising results. However, existing approaches still face three major challenges: First, they use static basic function to constructed graph filter which cannot effectively adapt to the frequency-domain distribution of graph data. Second, they fail to adequately consider the importance information of each attribute in the node feature vector, leading to the loss of fine-grained information. Third, they insufficiently utilize node labels for GAD. To address these issues, this paper proposes a novel graph anomaly detection method called JPGFN (Feature Transformation Enhanced Jacobi Polynomial Graph Filtering Network). First, a Feature Separation Transformation Network (FSTNN) is developed to better learn fine-grained node features by feature separation and applying nonlinear transformations to node features across different dimensions. Second, an adaptive Jacobi polynomial graph filtering module is constructed based on Jacobi polynomials to adaptively capture complex frequency-domain features of graph signals. Finally, a node label constraint module is developed to facilitate the use of node labels and enhance the performance of GAD. Experimental results on multiple real-world datasets demonstrate that the proposed method significantly outperforms mainstream approaches.

Figures & tables

Figure 1: Graph data and its corresponding frequency domain distribution.

Figure 2: Architecture diagram of JPGFN model.

Figure 3: Signal density functions of different datasets and frequency-domain fitting results for different polynomial basis functions.

Dataset	Nodes	Edges	Anomaly(%)	Features
Amazon	11,944	4,398,392	6.87	25
YelpChi	45,954	3,846,979	14.53	32
T-Finance	39,357	21,222,543	4.58	10
Elliptic	46,564	73,248	9.76	93
Weibo	8,405	407,963	10.33	400

Table 1: Statistical information of five datasets.

Model	Amazon		YelpChi		T-Finance		Elliptic		Weibo
	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR
GCN	$82.39_{\pm 0.41}$	$35.13_{\pm 1.30}$	$58.02_{\pm 0.33}$	$21.33_{\pm 0.37}$	$92.34_{\pm 2.33}$	$73.84_{\pm 5.24}$	$82.17_{\pm 0.59}$	$21.94_{\pm 2.73}$	$97.96_{\pm 0.48}$	$94.4_{\pm 1.04}$
GAT	$96.66_{\pm 0.95}$	$86.67_{\pm 1.38}$	$79.50_{\pm 1.93}$	$42.41_{\pm 4.55}$	$92.76_{\pm 1.47}$	$63.08_{\pm 10.95}$	$84.44_{\pm 1.73}$	$25.16_{\pm 4.82}$	$95.47_{\pm 1.07}$	$91.06_{\pm 1.53}$
GraphSAGE	$89.35_{\pm 3.80}$	$67.50_{\pm 13.19}$	$84.82_{\pm 1.47}$	$53.19_{\pm 3.47}$	$77.63_{\pm 4.46}$	$30.19_{\pm 11.89}$	$84.31_{\pm 1.24}$	$31.43_{\pm 4.54}$	$93.94_{\pm 1.50}$	$84.65_{\pm 3.17}$
GIN	$93.82_{\pm 1.33}$	$79.22_{\pm 1.51}$	$77.02_{\pm 0.86}$	$36.50_{\pm 1.47}$	$88.07_{\pm 4.13}$	$63.70_{\pm 4.72}$	$82.49_{\pm 1.88}$	$24.73_{\pm 4.52}$	$95.50_{\pm 0.76}$	$90.53_{\pm 1.32}$
GAS	$95.90_{\pm 0.95}$	$85.14_{\pm 1.23}$	$78.31_{\pm 1.13}$	$37.55_{\pm 1.97}$	$92.06_{\pm 3.42}$	$72.84_{\pm 3.18}$	$85.24_{\pm 0.96}$	$49.46_{\pm 5.73}$	$94.29_{\pm 1.23}$	$90.32_{\pm 1.43}$

Table 2: Performance comparison of different methods on five real-life datasets. Boldface indicates the best performance, and underlining indicates the second-best performance.

Model	Amazon		YelpChi		T-Finance		Elliptic		Weibo
	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR	AUC-ROC	AUC-PR
w/o FSTNN	$95.54_{\pm 1.26}$	$84.70_{\pm 2.16}$	$82.82_{\pm 0.99}$	$52.12_{\pm 3.04}$	$92.78_{\pm 1.22}$	$73.16_{\pm 4.89}$	$87.41_{\pm 0.47}$	$61.39_{\pm 6.23}$	$96.18_{\pm 0.55}$	$91.87_{\pm 0.63}$
w/ MLP	$98.20_{\pm 0.17}$	$89.17_{\pm 0.56}$	$86.06_{\pm 0.29}$	$60.01_{\pm 0.64}$	$95.19_{\pm 0.25}$	$82.21_{\pm 1.12}$	$88.28_{\pm 0.41}$	$67.21_{\pm 3.59}$	$98.27_{\pm 0.18}$	$94.78_{\pm 0.59}$
w/o Jacobi	$97.60_{\pm 0.41}$	$88.43_{\pm 1.08}$	$89.58_{\pm 0.33}$	$67.88_{\pm 1.17}$	$93.51_{\pm 0.19}$	$74.33_{\pm 0.63}$	$92.05_{\pm 1.39}$	$75.93_{\pm 2.29}$	$95.90_{\pm 0.55}$	$88.51_{\pm 0.72}$
w/ Chebyshev	$98.07_{\pm 0.31}$	$89.35_{\pm 0.90}$	$89.60_{\pm 0.24}$	$68.70_{\pm 0.54}$	$96.33_{\pm 0.12}$	$84.76_{\pm 0.69}$	$87.16_{\pm 1.69}$	$62.83_{\pm 4.76}$	$\mathbf{98.99}_{\mathbf{\pm 0.33}}$	$95.47_{\pm 0.55}$
w/ Legendre	$98.28_{\pm 0.22}$	$89.55_{\pm 0.59}$	$91.71_{\pm 0.33}$	$73.73_{\pm 0.74}$	$96.65_{\pm 0.20}$	$86.25_{\pm 0.36}$	$88.96_{\pm 2.09}$	$67.30_{\pm 4.06}$	$98.73_{\pm 0.42}$	$95.05_{\pm 0.40}$

Table 3: The ablation study of JPGFN. Here, w/o denotes without this module and w/ denotes with this module

Figure 4: Experimental results of parameter analysis. The figure shows the trends of the AUC-PR metric changing with the parameters $a$ , $b$ , the polynomial order $K$ , and the hidden layer dimension $hid\text{-}dim$ .

Panel of Figure 5 — Figure 5: Visualization results on YelpChi.

Model	Calculation time		Time complexity
Model	Training [-2pt] (ms/epoch)	Inference [-2pt] (ms)	Time complexity
GAT	96	42	$O\left(MNd^{2}+MEd\right)$
AHFAN	197	94	$O\left(Nd^{2}+Ed\right)$
SEC-GFD	42	78	$O\left(Nd^{2}+K^{2}Ed\right)$
DSGAD	61	32	$O\left(LNd^{2}+LKEd\right)$
JPGFN	116	95	$O\left(Nnd^{2}+KEd\right)$

Table 4: Comparison of Time Complexity for Different Methods.

Explore similar work

NeiGAD: Augmenting Graph Anomaly Detection via Spectral Neighbor Information
Mar 30, 2026Qing Qing, Huafei Huang, Mingliang Hou +2Anomaly Detection Graph Neural Networks
College of Computer Science and Technology, Jilin University, Changchun 130012, China · School of Computer Science and Information Technology, Adelaide University, SA 5095, Australia · Guangdong Institute of Smart Education, Jinan University, Guangzhou 510632, China +1
Mitigating Homophily Disparity in Graph Anomaly Detection: A Scalable and Adaptive Approach
Mar 9, 2026Yunhui Liu, Qizhuo Xie, Yinfeng Chen +4Anomaly Detection Graph Neural Networks
State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China
RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detection
Aug 17, 2026Junxin Lu, Jing Zhao, Shiliang SunUnsupervised Anomaly Detection Anomaly Detection
School of Computer Science and Technology, East China Normal University, Shanghai 200062, China · State Key Laboratory of Submarine Geoscience, School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Mar 30, 2026J/K move · Enter open · S save

NeiGAD: Augmenting Graph Anomaly Detection via Spectral Neighbor Information

Qing Qing, Huafei Huang, Mingliang Hou, Renqiang Luo+1

College of Computer Science and Technology, Jilin University, Changchun 130012, China · School of Computer Science and Information Technology, Adelaide University, SA 5095, Australia · Guangdong Institute of Smart Education, Jinan University, Guangzhou 510632, China+1

Anomaly Detection Graph Neural Networks Spectral Methods

Open paper AskPDF arXiv

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.

Abstract

Explore similar work

NeiGAD: Augmenting Graph Anomaly Detection via Spectral Neighbor Information

Mitigating Homophily Disparity in Graph Anomaly Detection: A Scalable and Adaptive Approach

RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detection