Healthcare Insurance Fraud Detection via Continual Fiedler Vector Graph Model
Authors: Yehan Zhang
Huaidong Zhang
Xuandi Luo
Shengfeng He
Venue: ICLR 2026 Poster (2026)
Keywords: online learning
semi-supervised
fraud detection
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: an online learning method for real world scenario in medical insurance fraud detection

Abstract: Healthcare insurance fraud detection presents unique machine learning challenges: labeled data are scarce due to delayed verification processes, and fraudulent behaviors evolve rapidly, often manifesting in complex, graph-structured interactions. Existing methods struggle in such settings. Pretraining routines typically overlook structural anomalies under limited supervision, while online models often fail to adapt to changing fraud patterns without labeled updates.
To address these issues, we propose the Continual Fiedler Vector Graph model (ConFVG), a fraud detection framework designed for label-scarce and non-stationary environments. The framework comprises two key components. To mitigate label scarcity, we develop a Fiedler Vector-guided graph autoencoder that leverages spectral graph properties to learn structure-aware node representations. The Fiedler Vector, derived from the second smallest eigenvalue of the graph Laplacian, captures global topological signals such as community boundaries and connectivity bottlenecks, which are patterns frequently associated with collusive fraud. This enables the model to identify structurally anomalous nodes without relying on labels. To handle evolving graph streams, we propose a Subgraph Attention Fusion (SAF) module that constructs neighborhood subgraphs and applies attention-based reweighting to emphasize emerging high-risk structures. This design allows the model to adapt to new fraud patterns in real time. A Mean Teacher mechanism further stabilizes online updates and prevents forgetting of previously acquired knowledge.
Experiments on real-world medical fraud datasets demonstrate that the Continual Fiedler Vector Graph model outperforms state-of-the-art baselines in both low-label and distribution-shift scenarios, offering a scalable and structure-sensitive solution for real-time fraud detection.

Published as a conference paper at ICLR 2026
HEALTHCARE INSURANCE FRAUD DETECTION VIA CONTINUAL FIEDLER VECTOR GRAPH MODEL
Yehan Zhang' Huaidong Zhang Xuandi Luo' Shengfeng He²
'South China University of Technology, 'Singapore Management University fyehanzhang, ftxuandi. 1uo @mmail sout edu. en, huaidongz3scut. .du.. en, shengfenghe@smi edu.sg
ABSTRACT
Healthcare insurance fraud detection presents unique machine learning chal- lenges: labeled data are scarce due to delayed verification processes, and fraud- ulent behaviors evolve rapidly, often manifesting in complex, graph-structured interactions. Existing methods struggle in such settings. Pretraining routines typically overlook structural anomalies under limited supervision, while online models often fail to adapt changing fraud patterns without labeled updates. To address these issues, we propose the Continual Fiedler Vector Graph model (Con- FVG). a fraud detection framework designed for label-scarce and non-stationary environments. The framework comprises two key components. To mitigate la- bel scarcity, we develop a Fiedler fector-guided graph autoencoder that lever- ages spectral graph properties to learn structure-aware node representations, The Fiedler Vector, derived from the second smallest eigenvalue of the graph Lapla- cian, captures global topological signals such as community boundaries and con- nectivity bottlenecks, which are patterns frequently associated with collusive fraud. This enables the model to identify structurally anomalous nodes without relying on labels. To handle evolving graph streams, we propose a Subgraph At- tention Fusion (SAF) module that constructs neighborhood subgraphs and applies attention-basee reweighting to emphasize emerging high-risk structures. This de- sign allows the model to adapt to new fraud patterns real time. A Mean Teacher mechanism further stabilizes online updates and prevents forgetting of previously acquired knowledge. Experiments strate that the Continual Fiedler Vector Graph model outperforms state-of-the-wee baselines in both low-label and distribution- and structure-sensitive solution for real-time fraud detection. Codes are available httpt::t////. //g com ywwhanggzaggg 309 CVG.VG.
real-world medical fraud datasets demon-
scenarios. offering scalable
INTRODUCTION
Healthcare insurance fraud has become a critical issue in social healthcare systems, with increasingly sophisticated and large-scale fraudulent schemes causing substantial financial losses. According to the 2024 Medicaid Fraud Control Units Annual Report (U.S. Department of Health and Human Ser- vices, Office of Inspector General, 2024), Federal Medicare fraud in the U.S. reached approximately S61 billion, accounting for around 7% of total federal healthcare spending. These fraudulent claims not only undermine patients' access to rightful medical services but also strain healthcare budgets and obstruct the path toward universal healthcare. This pressing societal issue calls for more intelli- gent and scalable fraud detection solutions.
Machine learning has shown promise in identifying fraud patterns by leveraging the complex rela- tionships between entities such as patients, providers, and claims. In particular, graph-based meth- ods have demonstrated strong performance in capturing structural dependencies within healthcare data. For instance, Dou et al. (2020) introduced graph neural network (GNN) model with selective neighbor aggregation for offline fraud detection. Building this, Sadreddin and Sadaoui (2022)
"Corresponding Author.

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Published as a conference paper at ICLR 2026
Dhe tedee Ditritutioon
Day 388 Hode Dattitdien
Day Hode Britsbatton
The visualization of fraud pattern evolution in the medical insurance fraud dataset. We use I-SNE to visualize the node distribution of features. The red node denotes fraudulent nodes, whereas blue denotes normal nodes
Figure 1:
developed an adaptive learning method that combines transfer and incremental learning, In the on- line setting, Zhang et al. (2024) applied contrastive learning with parameter-level continual updates to mitigate knowledge forgetting.
Despite these advancements, existing methods remain limited in real-world fraud detection scenar- ios due to two major challenges: 1) Label scarcity during model pretraining. In practice, labeled fraud cases are rare due to the high cost and time required for manual verification (Palacio, 2019), especially in health care systems in some cases where only 0.062% are identified as fraud (Bauder et al., 2018). Most prior methods assume access to fully labeled data during pretraining or rely on supervised objectives, which suffer decline in performance when labeled supervision is limited. Although some self-supervised approaches employ the autoencoder to catch inner semantic repre- iillatiins(Houu et al., 2022), they often fail to emphasize structurally meaningful fraud patterns such as collusive groups or community anomalies.
2) Lack of adaptability non-stationary graph streams. Fraud patterns are not static as shown in Figure 1. They evolve over time, often emerging in new relational structures. Traditional static fraud detection cannot catch the progressive evolution of fraudulent behaviors, causing performance degradation over time. Meanwhile, labeled data are rarely available in online testing (Pereira and Silveira, 2019), which makes supervised updates impractical. Models based on static presentations or ground-truth label update strategies struggle to detect new fraudulent patterns.
To address these challenges, we propose the Continual Fiedler Vector Graph model (ConFVG), a fraud detection model designed for label-scarce and non-stationary environments. ConFVG (shown Figure 2) consists of two core modules. 1) To handle label scarcity, we develop Fiedler Vector- guided graph autoencoder that incorporates spectral information from the second smallest eigen- vector of the graph Laplacian (Fiedler, 1973). This vector captures global structural properties, such as community boundaries and connectivity bottlenecks, which are often associated with collusive fraud. By integrating these signals into the autoencoder, the model learns structure-awar node representations that highlight fraud-relevant patterns without requiring labeled data. 2) To adapt to evolving fraud behaviors, we introduce a Subgraph Attention Fusion (SAF) module that dynamically augments and reweights local subgraphs based on attention. This enables the model to prioritize emerging high-risk structures, such as unusually dense clusters or temporally synchronized activity. A Mean Teacher architecture is used to stabilize updates and prevent catastrophic forgetting during online training. Experiments on real-world datasets, including but not limited to insurance fraud, demonstrate that the ConFVG consistently outperforms state-of-thee-ar baselines in both lowel and distribution-shift scenarios, providing scalable and structure- aware solution for real-time fraud detection and beyond.
Our main contributions are follows:
We propose the Continual Fiedler Vector Graph model (ConFVG) for fraud detection under label- scarce and non-stationary conditions, integrating spectral self-supervision with adaptive online learning.
We develop a Fiedler Vector cettor-giided graph autoencoder that leverages global topological signals to learn structure-aware representations in the absence of labels.
We introduce a Subgraph Attention Fusion (SAF) module for unsupervised online learning, en- abling dynamic risk representation and continual adaptation to evolving fraud patterns.
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RELATED WORK
Fraud Detection, Fraud detection has become an active area of research across various domains, including credit card transactions, insurance claims, and online payments (Cheng et al., 2025). Early systems were largely rule-based or built upon conventional machine learning techniques (Chan et al., 2002; Srivastava al., 2008; Maes et al., 2002), which proved insufficient for capturing the complex and evolving nature of modern fraud patterns. More recently, deep learning approaches, particularly Graph Neural Networks (GNNs), Long Short-Term Memory (LSTM) networks, and Large Lan- guage Models (LLMs), have been widely adopted for fraud detection. Among them, GNNs have emerged as the most effective for modeling the relational structure inherent in fraud data. GNN- based fraud detection methods can be broadly categorized into three scenarios: fully supervised GNNs, semi-supervised GNNs, and online GNNs. Fully supervised models assume access to large- scale laheled datasets, allowing for comprehensive pretraining. For example, CARE-GNN (Dou et al., 2020) and PC-GNN (Liu et al., 2021) use label-aware node selection strategies to improve fraud detection performance. Semi-supervised GNNs operate under the more realistic assumption of label scarcity. They exploit graph structure through self-supervision and pseudo-labeling. For in- stance, SemiGNN (Wang et al., 2019) incorporates hierarchical attention, and GTAN (Xiang al., 2023) uses gated temporal attention to improve fraud representation learning. Online GNNs are designed for dynamic environments where fraud patterns evolve over time, requiring continual up- dates post-pretraining. POCL (Zhang et al., 2024), for example, adjusts parameters based on their contribution to previous tasks.
Although prior studies have explored either label-efficient pretraining or adaptive fraud detection in evolving environments, these directions have largely been treated in isolation. In real-world medical insurance streams, however, extreme label scarcity and shifting fraud patterns often occur simultaneously. What remains missing is a unified approach that can both generalize from limited supervision and adapt continuously to unseen behaviors. Our work addresses this gap by jointly tackling the structural complexity of fraud graphs and the temporal dynamics of fraud evolution, providing more realistic and robust solution for fraud detection under deployment constraints.
Online Learning. Online learning addresses the challenge of training models on continuously ar- riving data while mitigating catastrophic forgetting (Hoi et al., 2021). Existing approaches can be broadly classified into three categories: parameter regularization, data rehearsal, and dynamic archi- tecture. Parameter regularization methods constrain model updates to preserve previously learned knowledge. Techniques such as EWC (Li et al., 2020) and EVCL (Batra and Clark, 2024) ap- ply regularization penalties to sensitive parameters, balancing plasticity and stability across tasks. Data rehearsal strategies, including iCaRI. (Rebuffi et al., 2017) and GEM (Lopez-Paz and Ran- zato, 2017), maintain buffer of past samples or prototypes to reduce forgetting. Dynamic network approaches adapt the model structure itself to accommodate new knowledge. Notable examples in- clude DEN (Yoon et al., 2017) and BC-DEN (Yang et al., 2022), which expand network capacity based on task complexity. Several methods have applied these ideas to GNNs. For instance, Contin- ualGNN (Wang et al., 2020) and SGNN-GR (Wang et al., 2022b) combine parameter regularization with data replay for online fraud detection. However, most of these approaches assume access to ground-truth labels during online updates, which is rarely the case in real-world fraud detection scenarios. To address this, we adopt a Mean Teacher framework in combination with our SAF mod- ule, enabling unsupervised, structure- updates that integrate new information while preserving previously learned representations.
PROPOSED METHOD
3.1 PROBLEM DEFINITION
In online fraud detection scenario, we generate graph series G = (Go. 92,.2..... 9 gg) from raw dataset where each graph G; represents the graph composed of claims in time periods. In medical insurance claim graph G(X',,, E.Y), each node V; has its features represented by F, E R xd con- stituting the node feature matrix X 2axd E E Rax* denotes the edges between claim nodes, where claims have the same medical provider or beneficiary get connected. Node label y e R denotes the label of each node: fraud (1), not fraud (0), none (-1).
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Fiedler Vector-guided graph autoenceder
Node Features
80
Pretroin model
Graph Froud Degree
Cets
Decomposition
Projection
(e)
Pretrain Stoge
Initialize
Graph Structure
Fiedler
Auto Encoder
Subgroph Attention Fusion
Outputs
Teachar
Model
Lattn
Original Groph
EMA
Concate
Lain
Get Top
Student Enceder
classifier
Student
Component
(b) Online Stage
Complement Groph
Feature Embedding
Figure 2: The illustration of Continual Fiedler Vector Graph model (ConFVG). (a) Pretrain Stage employs Fiedler Vector-guided graph autoencoder to learn structure-ane awarr node representations. (b) Online learning stage utilizes Subgraph Attention Fusion (SAF) module construct neighborhood subgraphs and apply iitention-basee reweighting to emphasize high-risk structures.
To demonstrate the continual learning problem, we divide the whole dataset into the historical dataset Gr (9), 9/, 9h..- and the online dataset G. (5% g. -.....). In the pretrain stage, the model can only access the historical dataset Gi, to train the parameter Ohistory- While in the online learning stage, tasks come long sequence Go and the model can only access the current task G without access to the previous dataset. We update the parameters 0, of the model after the new incoming task 9¹ to adapt to the ever-changing environment.
However, in real-world scenarios, historical datasets are scarce, and labeled samples only occupy small portion (Lebichot al., 2016), the model accesses only unlabeled samples in the online learning phase. To simplify the problems above, we design new challenging scenario with partially labeled dataset in the pretrain stage and an unlabeled dataset in the online stage, as detailed in the experiment.
3.2 FIEDLER VECTOR-GUIDER GRAPH AUTOENCODER
In semi-supervised scenarios, the autoencoder is commonly used for providing additional informa- tion to the supervised learning process. Given the model encoder and decoder D, our goal is to regenerate node features X' from the feature embeddings E(G) to force the model encoder to learn the graph. For the purpose node classification, we use feature
the deeper feature representation mask (Li et al., 2023) to randomly mask part of the node features and reconstruct the masked features by comparing them to the real ones.
For the vanilla random masking method (Hou al., 2022), given graph G(X, E,Y) and mask ratio r, we obtain the masked node features Kmask by applying the mask matrix M E (0. 1 X. where Mif Bernoulli(1 r), (I,,....,n), E {1,2,... d). After obtaining the reconstruction features & = D(E(G(Xmask: E, we use mean squared error (MSE) loss Lmask to pull closer X' and X' as follows
Lmask
(1 M.y) (Ki &2,)), where I f(i M. = 0}.
7
However, the vanilla random mask is not solid and may mask some of the fruitless features or fail to mask important features (Liu al., 2024), which may cause information loss and semantic
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irrelevance. To address the limitations of the above masking techniques, incorporate the global structural information with node features to take into account the fraud importance to the masking strategies.
In the context of graph representation for fraud detection, fraudulent nodes often exhibit significant anomalous connectivity patterns (Pourhabibi et al., 2020), such isolated nodes abnormally dense local subgraphs. These structural deviations disrupt the global homophily of the graph, leading sharp increases in feature label discrepancies among node neighborhoods. From the perspective of spectral graph theory, such anomalous connectivity can be interpreted as 'non-smooth" signals: normal nodes tend maintain smooth representations within communities, while fraudulent nodes introduce strong 'nonnnnnooo non-smooth' values and high local gradients. This phenomenon is illustrated in Appendix A.1.
To capture these non-smooth nodes and find out the fraud features, given a graph E, )") we calculate its degree matrix D, adjacency matrix A, and laplacian matrix L D A with the edge set E. To better quantify the smoothness of the node, we denote each node i has its smoothness value yú, which constitutes the smoothness vector q E 12x1 We defined the global smoothness Graphsmooth follows
Graph smoph
Σ 9;)
(K,))E
To better optimize the smoothness of each node, we hypothesize that the connected nodes share similar smoothness values, while the disconnected nodes have dissimilar values. Therefore, we aim to minimize Graphymooth follows
min Σ (9 (9--9)) =p3=minn mmnn Lq min (NJ)E
(3)
where A; denotes the eigenvalue of L, and is the projection of eigenvector i. To ensure the Eq. is minimized and meaningful, we make 21 = 0, 22 1, 23 2, 0. So ""'qq=""" Xg where is the eigenvector U2 corresponding to A2 as the Fiedler vector uf indicating the fraudulent probability of each node.
In the medical insurance fraud scenario, graphs are not always connected and may even have mul- tiple connected components. Because of that, the Laplacian spectral decomposition in Eq. de- generates, and the Fiedler vector loses its ability to capture anomalies. To address this problem, add fully connected perturbation to the original matrix, weakly connecting the multiple connected components into single connected graph follows
A' A + (J-I),
where A' the perturbed adjacency matrix, e the perturbation parameter, is a matrix of all ones, and I is the identity matrix. The bound of perturbation is discussed in Appendix, A.2.
While the smoothness values of node solely represent the inner graph structure, we combine that with the semantic features of nodes to show the contribution of each feature. We normalize the node feature matrix and make linear projection with x to get the mask probability s, as follows
8, =
Ufa X Xnormit
j j= 1,2,..... d.
(5)
1=1
With the mask weight we can reformulate the mask matrix M in Eq. with sampling probability equal to s, incorporating the fraud importance to the masking strategies.
To summarize, the total loss in the pretrain stage Epertain is defined follows
Epeariin
Lets + Qmaskk Lmask:
(6)
where Oraskk is hyperparameter of reconstruction loss.

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In the online learning scenario where labels are inaccessible, utilize the mean-teacher structure (Tarvainen and Valpola, 2017) with Latn from Eq. 10 to update its parameter in data streams. We denote the teacher model Mr, and the student model Ms, with their parameter O, and 0.. Published as a conference paper at ICLR 2026
3.3 SUBGRAPH ATTENTION FUSION MODULE
3.3.1 SUBGRAPH COMPLEMENT STRATEGY
Traditional graph models, i.e., GraphSAGE and Ying, 2017), GAT(Veličkovié et al., 2017) use top-k neighbors to transfer information between convolutional layers as follows
hx + AGGREGATE; ((h Vu (())))
where h, (v) denotes the feature vector and neighbor nodes of node v, respectively, and & denotes the kthh layer of the model. These methods only focus on the subgraph that fully connected in the graph, which overlooks the correlation between each connected part. The performance of the model becomes highly dependent on the initial graph connection, resulting in weaker generalization capability. In addition, focusing solely on single connected graph may weaken the model ability to capture similar fraudulent patterns from the entire graph, especially when the environment is dynamic and fraudulent activities are ever-changing.
Therefore, we propose subgraph attention-fuse fuseed complement strategy to combine the original graph with its subgraph complement to capture evolving fraudulent behavior. Suppose ( V, is graph with m connected components, denoted as C1, C2..... Cm- Each connected component C; = (X, V:) consists of a node feature matrix set X; S X and node set V; S V. We can get the graph complement Geomp from the selected connected components follows
Gcomp (10, (10,1,..... M 1}. {(((1), <G)) i i,j E V, (i.5) (
where V U Cs <() is the index projection function, and & denotes the top-k largest compo- nents. The value of k is discussed in Appendix, A.3.Then we can obtain the original graph embed- dings Zorig E(G) and the complement graph embeddings Zeomp E(gcomp). So our attention- fused embedding is defined as follows
= a (W WWRReLU(WW (Zorigi Zeomp) + bb) + b2).
where W1 and W2 are parameter matrix for autention-fused, by and b2 are bias value, and o is the sigmoid active function. To force the model to adaptively capture the fraudulent pattern in the online learning stage, we use the attention loss Laun to control its weights on the complement graph as follows,
Laun ReLU
Σ a,
Σ as
(10)
( [V\VVl
iEV'Vo
ieVo
where G = (Ve, FEg) is the subgraph induced by the selected nodes Vi C V, V \ Vg is the set of unselected nodes, a R= the attention weight vector with a; for node
3.3.2 MEAN TEACHER STRUCTURE
respectively. The task sequence is denoted by task (fo. f1, .),...., where t, denotes the graph G.. When a new task to comes, the teacher model predicts the outputs, and the student model uses the outputs to update its parameters. We use the KL divergence to restrict the outputs of the teacher model and student model as follows
Leim (L((otmaax(z..) || Softmax(z:))
(11)
So the total loss in the online learning scenario Conline is
Lantine Lsim + O'attn Latt:
(12)
where asim is a hyperparameter. After jth task, the parameter of the student model gets updated by Contine. while the parameter of the teacher model gets updated using exponential moving average (EMA) as follows
0 (((-)2)) + (1 a) o(.)
(13)

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In summary, the pseudocode of the proposed Continual Fiedler Vector Graph Model is presented in Algorithm 1.
Algorithm Continual Fiedler Vector Graph Model
1: Input: Historical graph Gr. online graph dataset Go
2: Output: Model M& with parameter 0,,
3: Initialize: Model Mg, decoder D
4: Compute graph laplacian matrix L .get Vy from decomposition
5: Compute mask weight 8, = |=x=1 US Xnorm,kjl get mask matrix M
6: Compute Lmmask feels
7: Update 0₂ with ppeetrain Lus + O'musk Liank set 0s t- 0x
8: for each online graph Gj. 1.2.3.... do
9: Make top k component graph complement Goump
Fuse attention
o W2ReL.U((, (Zoiigi Zeomp] + bi) + b2)
11: Compute Lei, Latt
12:
Update 0g with Couline = Lsim + aatt
13: Update Or < al; + (1 a)0;
14:
end for
EXPERIMENTS
In scenarios with various proportions of scarce labels, conduct experiments the medical health insurance dataset and other real-world fraud datasets. We first introduce the datasets and experimen- tal settings, then validate the model's exceptional performance and generalization capability under real-world scenarios. Subsequently, we perform ablation studies to demonstrate the importance of each component. Finally, we analyze the role of the autoencoder and subgraph complement strategy through case studies.
4.1 DATASET AND EXPERIMENT SETUP
Dataset and metrics. To evaluate the performance of our model on real-world datasets, we utilized large-scale medical insurance dataset (Ma et al., 2023). This dataset comprises over 100,000 unique beneficiaries with a total of 517,737 distinct claims. All samples in the dataset are labeled and timestamped, facilitating temporal grouping and validation. In the experiments, year of the data and construct daily medical diagnosis graphs. The initial 15 days were designated as the historical dataset, while the remaining served the online learning dataset. To better simulate real-world scenarios, we randomly retain labels in the historical dataset with probabilities of 1% 10%, while removing all labels from the online learning dataset. To demonstrate the generalizability of our model across different scenarios, we conducted additional experiments using two widely used datasets: Amazon (McAuley and Leskovec, 2013) and YelpChi (Rayana and Akoglu, 2015). As the evaluation metric, we use the average accuracy, Fl score, and AUC to measure the model's performance in online learning scenarios.
select one
Baseline. We compare method with the state-of-the-art (SOTA) GNN models in fraud detec- tion, including well-cstablished baselines: CAREGNN(Dou et al., 2020), PCGNN (Liu et al., 10,1), SAD(Tian al., 2023), GTAN((iang et al., 2023), GAD (Chen et al., 2024), ContinuesGNNN (Wang et al., 2020), FGN(Wang et al., 2022a), POCL(ZZhng et al., 2024). CAREGNN and PCGNN are traditional offline models, while SAD, GTAN, and GAD are designed for the semi-supervised sce- nario. FGN and POCL are online models with parameter updates. In light of previous work not applicable the unsupervised learning scenario, subsequent online learning. To ensure the fairness of comparison, we make extra experiments on traditional online learning scenario where labels are abundant, denoted 100% * label rate.
utilize their pre-trained model complete the
4.2 EXPERIMENTAL RESULTS
We conduct extensive experiments compare model against SOTA baseline methods. As shown in Table I, our model demonstrates superior performance, achieving the highest AUC and Fl-score across real-world scenarios with different label ratios. With 10% label rate, fully supervised
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Table 1: Performance comparison of different models on medical insurance dataset at different label
rates. 100% label rate denotes the traditional online scenario.
1% label rate
10% label rute
100%
label rate
Model Type
Model
AUC
Fl Score
AUC
FI Score
AUC
Fl Score
CAREGNN
62.08 # 1.31 40.58 = 3.05 67.35 = 1.20 49.61 = 1.50 75. = 0.78 54.23 # 0.24
Traditional Offliee
PCGNN
63.75 # 1.72 50.16 = 2.14 69.38 = 0.55 54.25 = 0.91 78.11 # 0.33 60.10 # 0.55
SAD
72.58 # 1.29 55.40 = 1.95 76.12 1.23 62.30 = 2.24 78.56 + 0.21 62.04 # 0.41
Semi- Semi-Supervised Offline GTAN
72.43 # 1,30 57.33 = 1.71 75.60 1.12 61.38 = 2.57 76.54 # 0.53 61.29 + 0.67
GAD
73.29 1.11 56.81 * 2.19 76.54 0.83 61.73 1.88 77.56 + 0.18 62.35 + 0.28
ContinuesCINN 63, 14 # 1.07 49.22 # 2.83 69.52 + 1.97 53.26 + 1.36 78.60 # 0.10 57.32 a 0.22
Traditional Online
FGN
62.83 1.21 43.30 3.21 65.71 1.01 50.11 1.92 73.91 +: 0.25 56.42 + 0.51
POCL.
70.64 1.34 52.45 2.57 74.76 1.12 60.31 1.88 80.32 0.21 63.56 * 0.28
Proposed
Ours
76.13 1.05 62.24 2.26 80.48 0.86 64.48 1.24 80.61 0.08 63.24 0.16
Table 2: Performance comparison of models across different real-world datasets at 10% label rate.
Medical
Yelpchi
Amazon
Model Type
Model
AUC
Fl Score
AUC
Fl Score
AUC
Fl Score
CAREGNN
67.35 1.20 49.61 + 1.50 71.12 1.83 61.05 + 2.12 87.31 # 0.06 84.24 + 0.26
Traditional Oftine
PCGNN
69.38 + 0.55 54.25 = 0.91 73.45 # 1.17 61.21 # 1.60 88 # 0.12 86. 12 + 0.35
SAD
76.12 1.23 62.30 2.24 73.17 0.59 61.01 = 2.23 87.53 + 0.62 84.16 + 0.99
Semi-SSpeevised Oflline
GTAN
75.60 1.00 61.38 = 2.57 74.74 1.01 62.22 88.67 # 0.20 83 16 # 0.77
GAD
62.61 = 1.93 89.56 0.18 85.05 + 0.31 76,54 0.83 61.73 1.70 0.96
ContineeSGNN 69.52 # 1.97 53.26 1.36 71.62 1.68 60.95 = 2.05 81.28 0.14 73.52 0.35
Traditional Online
FGN
65.71 1.01 50.11 = 1.92 70.37 2.01 56.41 = 2.57 81.12 1.14 74.56 # 1.55
POCL
74.76 1.12 60.31 1.88 73.18 0.92 61.60 87.57 = 0.38 80.12 1.53
Proposed
Ours 80.48 0.86 64.48 1.24 76.85 0.12 64.53 = 1.92 91.07 = 0.04 87.32 = 0.52
model like CAREGNN requires full labels for pretraining and updating. which presents challenge. Although POCL is fully supervised model, it utilizes the contrastive learning method to enhance its discriminative capability between positive and negative samples, as seen in the pre-training stage, which performs stably when the source dataset is scarce. Semi-superviss better performance for their data augmentation mechanics. When the label rate drops to 1%, tradi- tional methods perform much worse with infeasible supervised information. And semi-supervised methods drop less. In contrast, our model shows excellent performance when the label rate drops from 10% to 1% with minimal degradation, which highlights the superiority of our approach.
models apparently present
Besides, we also make an experiment on traditional scenario denoted as 100% * label rate, where the pretrain and online datasets are fully labeled. We can see that the traditional offline model is the worst, while the semi-supervised model performs a little better at catching the inner pattern for fraud activities, which is a good backbone for the upcoming task. But they cannot update themselves to adapt to the dynamic environment. Traditional online models update themselves in the online learning stage and perform better. Interestingly, our model still presents its SOTA performance compared to the traditional online model (despite the minimal difference in F1 score). We think that in the historical dataset, our graph autoencoder has already learned nearly complete fraud patterns. Furthermore, the subgraph completion strategy in the online learning phase accurately captures and translates domain shifts in fraudulent behavior, which boosts our model performance in a traditional scenario.
To better visualize the performance of the methods above during the online learning stage, we em- ploy the monthly average accuracy to measure the performance. As shown in Figure 3, in the 10% labeled data scenario, our model and sumissupeeeied model achieve a relatively high initial aceu- racy. During the online learning process, our model stays solid in accuracy by adapting to fraudulent domain shifts. Other models have a certain degree of accuracy reduction, especially for traditional ones. With 1% labeled data, our model still demonstrates notably high initial accuracy and better adapts to the environment with higher accuracy, while other models exhibit larger fluctuations in accuracy. Most of the methods suffer from a continual decrease over time. To further validate our method on world scenarios, we conduct extensive experiments on Yelpchi and Amazon datasets. As shown in Table 2, model greatly outperforms other methods.
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ContinuesGNN PCGNN
FGN
GTAN
ContinuesGNN
FGN
GTAN
CAREGNN
GAD
PCGNN
CAREGNN
GAD
0.76
180
0.75
Accuracy 185)
0.74
0.68
0.73
0.67
0.66
(Monthss)
(Monthi) (b) Average monthly accuracy on 1% label rate
(a) Average monthly accuracy on 10% label rate
Figure 3: Performance comparison different fraud detection methods with different label rates on average monthly accuracy and average accuracy decline rate for online learning within year in the medical fraud dataset.
Table Ablation study on medical insurance fraud dataset with different component combinations.
Medical Dataset
Auteencoder
Graph Complement
Mcan-Teacher
AUC
F1-Score
Accuracy
67.21 2.41
39.13 5.62
63.43 2.12
X
67.43 + 2.12
40.52 = 4.03
63.21 2.01
X
X
68.35 + 2.06
46.41 + 3.47
64.55 # 2.31
76.13 0.88
61.56 + 1.10
74.29 1.05
78.21 + 1.23
63.11 1.52
74.12 1.11
72.08 1.78
6.114
66.56 1.75
X
77.35 = 1.54
64.25
73.81 = 1.92
80.48 0.86
64.48 1.24
76.45 0.62
4.3 ABLATION STUDY
4.3.1 COMPONENT ANALYSIS
To evaluate the role of each component in the medical insurance fraud model, we conduct series of ablation studies on the label rate 10% scenario.
As shown Table 3, we observe that the model performs weakly with only one component for poor pretrain model or online parameter update. Combining the graph autoencoder with the mean- teacher framework yields better results, yet the addition of the graph completion mechanism still necessary to enhance the learning of fraudulent representation. Without the graph autoencoder, the model has suboptimal performance due to the weak backbone. Finally, the integration all three components shows the best performance. This whole model not only strengthens the generalization of fraud patterns from the pretrain model but also leverages the advantages of the graph completion strategy during online learning, enabling effective dynamic adaptation evolving environments.
4.3.2 ANALYSIS ON DIFFERENT MASK STRATEGY
To prove our extraordinary performance of mask strategy, we compare our proposed Fiedler Vector- based feature masking approach with existing advanced methods, including random masking (Hou et al., 2022), edge-based masking (Tan et al., 2023), and subgraph masking (Jiao et al., 2024), as well VGAE (Kipf and Welling, 2016). As shown in Table the Fiedler vector-based graph autoencoder selectively reconstructs the core features to capture deeper fraudulent representation, outperforming the other baseline methods.
CONCLUSION AND FUTURE WORK
In this paper, we introduce ConFVG, which integrates a Fiedler Vector-guides graph encoder and Subgraph Attention Fusion module to address the challenges of pre-training label scareity and

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Table 4: Performance comparison of different mask strategies medical insurance fraud dataset with label ratio of 10%.
Mask Strategies
AUC
Fl-score
Accuracy
Random Mask(Hou et al., 2022)
74.14 0.68
59.23 1.28
68.46 = 1.50
Edge Mask(Tan et al., 2023)
73.25 # 1.23
58.36 2 2.13
67.15 # 1.31
Subgraph Mask(Jiao et al., 2024)
75.24 0.93
56.15 1.23
69.59 1.78
VGAE(Kipf and Welling, 2016)
77.87 = 1.86
63.24 1.02
74.25 = 0.24
Fiedler-vector Mask
80.48 # 0.86
64.48 + 1.24
76.45 # 0.62
unlabeled online learning in real-world scenarios. Our model leverages the graph encoder to learn robust representations of fraudulent patterns, while incorporating a subgraph complement strategy to enrich fraud representations during the online learning phase. We conduct extensive experiments on multiple real-world datasets under two supervupe settings. The results demonstrate that our model significantly outperforms existing methods in semi-supervised scenarios while remain- ing competitive in traditional settings. In the future, we aim to extend our approach to other graph anomaly detection tasks, such as network security intrusion detection and abnormal behavior iden- tification in social networks. also plan to explore the integration of multimodal graph data to further enhance feature extraction and graph representation learning capabilities.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Grant No. 62302170), Guangdong Basic and Applied Basic Research Foundation (Grant
No. 2024A1515010187) Guangdong Natural Science Funds for Distinguished Young Schol-
ars (Grant No. 2023B1515020097) the National Research Foundation, Singapore under its AI Singapore Programme (AISG Awards No. AISG3-GV-2023-01 1 and AISGA--CC-2025-018--- and the Lee Kong Chian Fellowships.
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A APPENDIX
A.1 STUDY ON FIEDLER VECTOR
To better explain the relationship between fraudulent nodes and Fiedler vector, we choose four slices medical insurance claim graph and visualize the distribution of the Fiedler value (smoothness value each node. The results are shown Figure 4.
Fiedler Value Visualization Day
Fraud rodea
Fiedler
Value Visualization of Day
Froud nodes
Fladler Value Visualization of Day 161
Fiedler Value Visualization 267
Figure 4: The visualization of Fiedler value in four medical insurance claim graphs. We use spring layout visualize the node distribution, where connected nodes are put closer while disconnected nodes are put further. The fraudulent nodes are circled in red.
From Figure we can easily conclude: 1) Connected nodes share similar Fiedler value (smoothness value) in analogous colors. 2) Fraudulent nodes always exhibit isolated nodes or dense local sub- graphs like little clusters in the center of the graph, which are identified by the Fiedler vector with higher Fiedler value. Additionally, we conduct a statistical analysis on the same dataset. The results shown Table also demonstrate the strong guidance of the Fiedler vector.
A.2 BOUND OF PERTURBATION
In our fraud detection framework, the difference between the original null space U and the perturbed
subspace U arises from added noise via the perturbation E c(nl - J). To assess whether the perturbed Fiedler vector v/g retains indicative significance for anomaly detection, we need to evaluate its closeness to the original null space U, measured by the projection error Epraj 1|06
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Table 5: Statisties of nodes in the medical insurance dataset across days. We ratio mean fraud node Fiedler value mean normal node Fiedler value to measure the detection ability.
Day
All Nodes
Fraud Nodes
Normal Nodes
Edges
Ratio (Fraud Normal)
1596
599
997
3616
1.864
50
1608
616
992
3996
2.017
100
1599
602
997
3664
1,857
150
1608
586
1022
4014
2.141
200
1555
577
978
3292
1.922
250
1467
602
865
3218
1.837
300
1440
573
867
2970
2.032
All
554407
211270
343137
1255698
1.924
Pr.olle. A smaller error Epraj indicates closer alignment with U, preserving the soft indicator function structure.
To measure the error, make orthogonal decomposition of the Fiedler vector t/ U' with respect to the subspace U as follows
1/2 = Purl + (I Po)c2
(14)
where Pu E the orthogonal projection of 2/2 onto the null space U, and (I- Pu)y E U the component of 0/ in the orthogonal complement of U. So the Epraj can be derived as follows
Eprof = 1|1// Po = II(I Po)ebl2,
(15)
Given that oy a unit vector, |/u/ l2 = 1, it follows that
[[] Po)eúll2 / PPooll
Epoo
(16)
We denote the angle (12, U) the angle between v/g and the subspace U, given by the angle the closest vector u U. So we can conclude that
cos U)
max UEU,
(0bg u)]-
(17)
Apparently, u is equal to the unit vector that
Pord |Pooddl
of the projection of v/ onto U, so we can conclude
Pung
cos (0(. (0/2
(18)
|Poc/
Using the trigonometric identity:
sin (vg U) V cos? 0(u,, U) = / P
(19)
Comparing the projection error and the angle:
sin 0(u6, U). Epro = 11- 1|
(20)
Table 6: Performance comparison of different on medical insurance fraud dataset on label ratio of 10% with time consumption (seconds).
ne
AUC
Fl-score
Accuracy
Time
0.01
79.32 + 1.06
63.23 + 1.73
75.22 1.50
309.22 + 2.41
0.05
80.48 + 0.86
64.48 + 1.24
76.45 + 0.62
328.14 2.85
0.1
80.51 0.76
64.42 1.10
76.22 0.45
384.50 # 2.73
0.2
80.05 # 0.94
64.10 1.02
74.25 + 1.23
470.62 # 3.59
0.3
78.08 + 1.27
62.70 1.56
73.45 + 1.60
612.05 + 5.17
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By the theorem(Davis and Kahan, 1970) in its single vector form, for any U", the projection enror is bounded by the maximum canonical angle between and U":
sin (v, , U) = (I - Pullul2 - sin @UU, U2)
(21)
Furthermore, the 2-norm of the sine of the angles satisfies:
sin OU, < sin (U, < |
(22)
Thus, for 1/2 E U we obtain:
|
10/ Puuzll2 = sin ((2, < sin ((U, S sin (UU, I 8
(23)
As |Bll l2- = en is the spectral norm of the perturbation and 5 min (4), {1 ~ \4t1 we can derive the upper bound of Eproj as follows,
Epros = 1l15 - Purglla - E
en
(24)
1
This bound, approximately 0.04 for medical insurance claim networks (n 2000, (L) se 0.5), ensures that t/2 remains close to U, retaining its ability to capture anomalies via projections like 1x"'g]-
10-5
To prove our assumption above, We test our model with different values. The results are shown in Table
Table 7: Performance of the model under different pertubation e values.
Perturbation
le-6
lc-5
5e-5
lc-4
le-3
1e-2
AUC
78.72 : 0.53
80.48 # 0.86
80.46 # 0.78
80.33 = 1.02
78.30 + 1.22
76.05 : 1.53
F1-score
64.02 # 1.29
64.48 # 1.24
64.52 # 1.33
63.67 = 1.67
63.08 + 1.93
61.22 + 1.86
From Table 7, we can see that when is very small (e 1e 6). the pertubation matrix is too weak to overcome the sparsity of the original graph, resulting in an insufficient correction effect on the Fiedler vector. When c in the range of le optimally strengthen the connectivity within communities without altering the macroscopic com- munity structure, thereby sharpening the boundaries between communities and better reflecting the true community structure. However, when becomes too large (e >> le 3), the global pertubation matrix overwhelms the original community structure, leading to decline in performance.
le 4, the subtle global connections
A.3 STUDY ON TOP K COMPONENT
We conduct a series of experiments to test the best value for the connected component. Concerning that the number nodes in each component may be different, we use the indicator n. node..t to measure our selection, where node denotes the number of nodes in our selected component, nodeau denotes the number of nodes in the whole graph. Our experiment result is as follows,
nodeall
As shown in Table 6, the value n. achieves a balance between accuracy and efficiency at 0.05. When ne is lower, the number of selected nodes is too small for the model to effectively utilize attention information during online learning. Conversely, when n. is higher, excessively noisy and potentially meaningless edges may be introduced, leading to performance degradation. So the value of k depends on n. to approximate.
B IMPLETION DETAILS
For hyperparameters, choose mask ratio = 0.2, Q'ask 10, Q'atn 0.1, pertubation = 1e-5. We use Adam as the optimizer with pretrain learning rate = 1e-3 and online learning rate encoder 3e-3. The implementation details are shown in Table 8.
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Table 8: Training and hyper-parameter settings of ConFVG. All experiments with single
NVIDIA 4090 GPU.
Setting
Medical Insurance
YelpChi
Amazon
Optimizer
Adam
Adam
Adam
Learning rate (pretrain)
le-3
le-3
le-3
Learning rate (online)
3e-3
3e-3
3e-3
Pre-training epochs
100
100
100
Number of pretrain tasks
14
Number of online tasks
351
351
351
Epochs per online task
10
10
10
Dropout
0.5
0.5
0.5
Feature mask ratio
0.2
0.2
0.2
Oraak
10
10
10
Oatn
0.1
0.1
Perturbation
le-5
le-5
Top-k components The
0.05
0.05
0.05
EMA decay a
0.99
0.99
0.99
Table 9: Comparison of scalability and complexity among different models. We compare the whole online learning time and trainable parameters with proposed models. CAREGNN, PCGNN, GTAN static models without online learning period.
Method
Online learning time (Minutes)
# Trainable Parameters
CAREGNN
2.2K
PCGNN
/
2.7K
GTAN
/
61K
ContinuesGNN
8.52
12K
POCL
1.35
7.6K
ConFVG (Ours)
5,46
11.8K
C COMPLEXITY AND SCALABILITY ANALYSIS
As shown in Table 9, we can see that our model has relatively large number of parameters due the autoencoder and mean-teacher architecture, yet demonstrates better speed compared to ContinuesGNN during the online learning phase.
D SENSITIVITY ANALYSIS
Table 10: Hyperparameter sensitivity analysis.
Volae
Mene
0.01
AlCC
0.
$0.00
5048 0:56
20.58.000
8002 1.37
76 2222
80 80.00000
75.35
102
70.30
Flosore
62.30 1.65
63.50
6412 1.20
64.8
1.24
63.75 1.44
6425
$4.8 1.34
64.1 2.5
63.35
1.22
62.38
61 18
Meni
1099
10m
16-9
16-1
AUL
17.36.1.5
1 16
9000 BAD
86124658
9146 20-7
8033
1222
1618 1.3 63
Fliscee
64
60.50
6000-1
1.34
63.07
We systematically evaluate the sensitivity of our model to key hyperparameters, with results pre- sented in Table 10. The model exhibits strong robustness across reasonably wide range of values. Performance consistently improves the mask loss weight Omukk increases from 1 to 10, peaking at Ormakk = 10 with the highest AUC of 80.48 + 0.86 and Fl-score of 64.48 1.24; further increas- ing Otmask beyond 10 leads to slight degradation and higher variance. The attention regularization coefficient Oamm achieves optimal results at 0.1, while values 2 0.5 excessively suppress meaning- ful Traud-noman interaction patterns, causing sharp performance drop. The EMA decay rate performs best around 0.99. Perturbation parameter e shows excellent stability in the [10 [10-3, 10 7,1044 range. Overall, the proposed approach maintains stable and superior performance across broad
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hyperparameter intervals, fully demonstrating its robustness and practicality for real-world fraud detection deployment.
E ROBUSTNESS ANALYSIS
In addition to the scenarios we mentioned earlier, fraudsters may deliberately connect with normal users to conceal malicious activities, which would lead to significant attribute discrepancies between connected nodes. To evaluate our model robustness against adversarial fraud, we performed a con- trolled test by connecting 1 1, 10%, 30%, 50% of fraud nodes to random normal nodes with camouflage edges connected in medical insurance dataset with 10% label rate.
Table 11: Robustness of ConFVG with or 3 camouflage edge connected.
Camouflage edge
Proportion of fraud nodes
AUC
Fl-score
0% (original graph)
80.48 = 0.86
64.48 1.24
1%
80.12 = 0.72
64.50 + 1.52
10%
79.39 = 1.10
64.12 1.48
30%
79.30 + 1.35
63.29 1.32
50%
78.70 = 1.44
62.57 + 0.71
0% (original graph)
80.48 = 0.86
64.48 + 1.24
1%
79.71 0.77
65.10 1.16
3
10%
78.84 1.02
6
30%
78.82 = 1.48
63.56 1.57
50%
77.63 = 1.65
63.14 1.48
As shown in Table 11, ConFVG demonstrates remarkable robustness against deliberate camouflage attacks. When fraudsters randomly connect to only 1 normal node, if 50% of fraud nodes perform such behavior, AUC drops merely from 80.48 to 78.70 (A = 1.78). When the attack in- tensity is increased to camouflage edges per fraud node, the performance decline is still gracefully controlled. These results indicate that the artificially injected camouflage edges, although intended help fraudsters blend into normal communities, may inevitably create locally abnormal dense subgraphs or spectral perturbations. The Fiedler vector is highly sensitive to such structural irreg- ularities and successfully captures them as useful guiding signals for community-awan learning, thereby suffering less from adversarial fraud.
F
LLM USAGE
We utilized large language models (LLMs) to assist in drafting and refining this manuscript. Specif- ically, LLMs helped optimize language expression, enhance readability. and ensure clarity across sections. They assisted with tasks such as sentence restructuring, grammar checking, and improving overall fluency the text.
It should be noted that LLMs were not involved in the conceptualization, research design, or ex- perimental planning. All research concepts, ideas, and analyses were independently developed and implemented by the authors. The contribution of LLMs was limited to enhancing the linguistic quality the manuscript and did not involve scientific content or data analysis.
The authors take full responsibility for the integrity of the manuscript's 's content, including any text generated or refined by LLMs. We have ensured that the content produced by LLMs adheres to ethical standards and is free from plagiarism academic misconduct.
17


Reviews:
[{"review_id": "hqpxKgepjg", "reviewer": "Reviewer_Kwxx", "summary": "The authors propose the Continual Fiedler Vector Graph model (ConFVG), a framework designed to address two challenges in healthcare insurance fraud detection: label scarcity and non-stationary environments (i.e., evolving fraud patterns). The model consists of two key components. First, to handle label scarcity, it employs a Fiedler Vector-guided graph autoencoder for pretraining. This uses the Fiedler vector, derived from the graph Laplacian, to identify global topological structures like community bottlenecks and guide the autoencoder's learning process without relying on labels. Second, to adapt to evolving graph streams in an unsupervised online setting, it introduces a Subgraph Attention Fusion (SAF) module. This module constructs and fuses neighborhood subgraphs with their complements, using attention to emphasize emerging high-risk structures. A Mean Teacher mechanism is used to stabilize these online updates and prevent catastrophic forgetting. Experiments on real-world medical fraud datasets demonstrate that the approach outperforms baselines in both low-label and distribution-shift scenarios.", "questions": "Please address the weaknesses mentioned above.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "There are a few things I like about the paper:\n1. The paper tackles a realistic real-world problem setup: pre-training with scarce labels and performing online learning.\n2. The use of the Fiedler vector to guide a graph autoencoder in self-supervised pretraining is interesting.\n3. The Subgraph Attention Fusion (SAF) module is an interesting mechanism for online adaptation. The idea is to complement the original graph with a complement graph to allow the model to capture evolving patterns that might not be visible from a single connected component's perspective.\n4. The experimental results on multiple datasets support the paper's claims.\n5. The authors performed an ablation study to show that the components described in the paper are relevant to the final prediction.", "weaknesses": "1. [Motivation]. The problem of label scarcity and non-stationary graph streams are actually not unique to health care insurance data. These two problems exist in most real-world fraud detection systems. I suggest the authors reframe the motivation to be more generic.\n2. [Scalability and Complexity] I suggest the author provide discussion on the scalability and complexity of the proposed models. Particularly since the model is more complex than the baselines.\n3. [Hyperparameter Sensitivity] The model introduces several new hyperparameters. Could the authors discuss more on sensitivity of the parameters vs results?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aQlzspuUTB", "reviewer": "Reviewer_Vz2D", "summary": "This paper introduces the Continual Fiedler Vector Graph (ConFVG) model, a novel framework for healthcare insurance fraud detection. The model is specifically designed to tackle two prevalent challenges in this domain: the scarcity of labeled data and the dynamic, evolving nature of fraudulent activities (non-stationary environments). The core of ConFVG consists of two main components. First, a Fiedler Vector-guided graph autoencoder is proposed for the pre-training stage. It leverages spectral graph properties—specifically the Fiedler vector derived from the graph Laplacian—to learn structural-aware node representations without relying heavily on labels. This helps in identifying anomalous graph structures often associated with collusive fraud. Second, for the online learning phase, the paper introduces a Subgraph Attention Fusion (SAF) module. This module, combined with a Mean Teacher mechanism, allows the model to adapt to new fraud patterns in data streams in an unsupervised manner, by focusing on emerging high-risk subgraphs and ensuring stable knowledge updates.", "questions": "- Regarding the Fiedler vector calculation: Given the scalability concerns with eigendecomposition, did you explore or can you comment on the feasibility of using approximation algorithms for the Fiedler vector on much larger graphs? How might this affect the quality of the learned representations?\n\n- In the online phase, the Subgraph Attention Fusion (SAF) module operates on a graph complement created from the \"top-k largest components.\" Could you elaborate on the intuition behind using the complement? Traditional attention mechanisms in GNNs focus on aggregating information from neighbors (existing connections). How does incorporating information from non-neighbors via the complement graph specifically help in adapting to new fraud patterns?\n\n- How was the hyperparameter 𝜖 for the graph perturbation (Eq. 4) selected? Could you share results from a sensitivity analysis showing how different values of 𝜖  impact the final performance?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper tackles a significant and practical problem in fraud detection: handling label scarcity and concept drift simultaneously. The proposed solution, combining spectral graph theory (Fiedler vector) for unsupervised representation learning with a continual learning framework (subgraph attention and mean teacher) for adaptation, is a novel and clever integration of ideas from different domains.\n\n- The experimental results are comprehensive and convincing. The authors demonstrate that ConFVG consistently outperforms a wide range of state-of-the-art baselines, including both offline and online models, across multiple datasets (Medical, YelpChi, Amazon) and under challenging low-label rate scenarios (1% and 10%). The performance improvement is substantial, which highlights the effectiveness of the proposed components.\n\n- The method is well-grounded in theory. The use of the Fiedler vector to capture global topological anomalies like community boundaries and bottlenecks is theoretically sound for identifying collusive fraud. The design of the Subgraph Attention Fusion module to handle evolving graph structures is intuitive and addresses a key limitation of traditional GNNs that focus only on existing connections.", "weaknesses": "- The core of the pre-training phase relies on calculating the Fiedler vector, which involves an eigendecomposition of the graph Laplacian matrix (𝐿). This operation can be computationally prohibitive for very large graphs, with a complexity that can approach 𝑂(𝑁3) where \n𝑁  is the number of nodes. While the paper demonstrates strong results on the given datasets, it does not address how this approach would scale to real-world graphs containing millions or billions of nodes.\n\n- The online learning phase introduces a Subgraph Attention Fusion (SAF) module that unconventionally operates on the complement of the graph's largest components. The paper lacks a clear and deep intuition for this design choice. While traditional GNNs learn by aggregating information from existing connections (neighbors), it is not immediately obvious how aggregating features from non-connected nodes helps the model adapt to new and emerging fraud patterns.\n\n- The method introduces a critical hyperparameter 𝜖  in Equation 4 to connect disparate graph components. The choice of this value is crucial, as too small a value may not enforce connectivity, while too large a value could introduce significant noise and distort the graph's original spectral properties, which are fundamental to the Fiedler vector's utility. The paper does not provide a sensitivity analysis for \n𝜖, making it difficult to assess the model's robustness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "W1S4lE3UoR", "reviewer": "Reviewer_GUk3", "summary": "The manuscript proposes ConFVG, a Fiedler vector–guided graph learning framework for medical fraud detection. By integrating spectral topology signals into pretraining and using attention-based online adaptation, it effectively handles label scarcity and evolving fraud patterns. Compared with POCL, ConFVG advances from contrastive learning to structure-aware self-supervision, achieving higher adaptability and stability in low-label settings.", "questions": "See above, thanks.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper addresses a realistic and practically important problem in medical insurance fraud detection. Its two-stage framework—pretraining followed by online learning—suggests strong potential for real-world application.\n\n- Compared with the latest and most relevant baseline POCL, ConFVG introduces the Fiedler vector to alleviate data sparsity and adds a subgraph attention–based online adaptation module, showing clear methodological innovation.\n\n- Experimental results demonstrate that ConFVG achieves the most stable and robust performance over continuous time periods, confirming its superior resilience for dynamic fraud detection tasks.", "weaknesses": "- The challenges outlined for medical insurance fraud detection appear too generalized and are not empirically verified, relying mostly on conceptual descriptions. While label sparsity is indeed a common issue across many domains, the claim of “adaptation deficiency” remains unclear and weakly justified. As a reviewer experienced in fraud detection research, I find these arguments repetitive and somewhat unoriginal, diminishing the paper’s novelty.\n\n- The motivation for the model design lacks clarity—particularly, it is not well explained why the Fiedler vector can alleviate data sparsity, even though experiments suggest it works.\n\n- The introduction of graph perturbation to ensure weak connectivity for computing the Fiedler vector seems somewhat ad hoc and theoretically awkward. While the paper provides an upper bound to justify this step, such a perturbation could distort graph structure, and this critical design choice deserves deeper discussion and validation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "s2M8kkgcIG", "reviewer": "Reviewer_Dr17", "summary": "This paper tackles an important fraud detection problem characterized by limited label availability during pretraining and dynamically evolving fraud patterns. To address these challenges, it introduces a two-stage framework: (1) an unsupervised pretraining module that incorporates spectral information into a masked graph autoencoder, enabling node representations to capture global topological irregularities indicative of potential collusive behavior; and (2) an online adaptation module that constructs complementary subgraphs, integrates their embeddings through an attention-based fusion mechanism, and stabilizes unsupervised updates using a mean-teacher consistency objective. Extensive experiments demonstrate the effectiveness of the proposed approach.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 1, "contribution": 3, "strengths": "1. The problem addressed in this paper is both novel and significant, with strong practical implications for real-world applications. \n2. Unlike conventional masked graph autoencoders that rely on random masking, this paper introduces a Fiedler vector-guided masking strategy, enabling the model to effectively capture global connectivity patterns. \n3. Comprehensive evaluations are conducted across multiple datasets and under various scenarios—including low-label settings and temporal distribution shifts—to thoroughly validate the proposed approach.", "weaknesses": "1. The design of the proposed method heavily relies on the core assumption that \"connected nodes share similar smoothness values.\" However, it does not provide relevant statistical evidence on the medical insurance dataset to validate this assumption. Furthermore, the paper lacks an evaluation of robustness against adversarial fraud. In realistic attack scenarios, fraudsters may deliberately connect with normal users to conceal malicious activities, which would lead to significant attribute discrepancies between connected nodes—directly contradicting the fundamental assumption of the method.\n2. The paper does not include a sensitivity analysis of its hyperparameters, such as the perturbation magnitude and the attention regularization coefficient.\n3. The paper requires strengthening in its mathematical notation, as there are multiple instances where symbols are ambiguous. For example, the symbol $X_{ij}$ denotes a node representation in Line 192, whereas $x_i$ refers to a smoothness value in Line 213.\n4. The paper lacks sufficient implementation details, such as the choice of optimizer and the learning rate schedule.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)