A Multi-Scale Graph Learning Framework with Temporal Consistency Constraints for Financial Fraud Detection in Transaction Networks under Non-Stationary Conditions

Yiming Lei; Qiannan Shen; Junhao Song

cs.LGMar 15, 2026

A Multi-Scale Graph Learning Framework with Temporal Consistency Constraints for Financial Fraud Detection in Transaction Networks under Non-Stationary Conditions

Authors: Yiming Lei, Qiannan Shen, Junhao Song

Organizations: Georgia Institute of Technology, Atlanta, GA, USA · Boston University, Boston, MA, USA · Imperial College London, London, UK

Abstract

Financial fraud detection in transaction networks involves modeling sparse anomalies, dynamic patterns, and severe class imbalance in the presence of temporal drift in the data. In real-world transaction systems, a suspicious transaction is rarely isolated: rather, legitimate and suspicious transactions are often connected through accounts, intermediaries or through temporal transaction sequences. Attribute-based or randomly partitioned learning pipelines are therefore insufficient to detect relationally structured fraud. STC-MixHop, a graph-based framework combining spatial multi-resolution propagation with lightweight temporal consistency modeling for anomaly and fraud detection in dynamic transaction networks. It integrates three components: a MixHop-inspired multi-scale neighborhood diffusion encoder a multi-scale neighborhood diffusion MixHop-based encoder for learning structural patterns; a spatial-temporal attention module coupling current and preceding graph snapshots to stabilize representations; and a temporally informed self-supervised pretraining strategy exploiting unlabeled transaction interactions to improve representation quality. We evaluate the framework primarily on the PaySim dataset under strict chronological splits, supplementing the analysis with Porto Seguro and FEMA data to probe cross-domain component behavior. Results show that STC-MixHop is competitive among graph methods and achieves strong screening-oriented recall under highly imbalanced conditions. The experiments also reveal an important boundary condition: when node attributes are highly informative, tabular baselines remain difficult to outperform. Graph structure contributes most clearly where hidden relational dependencies are operationally important. These findings support a stability-focused view of graph learning for financial fraud detection.

Figures & tables

Symbol	Description
$G_{t}=(V_{t},E_{t},X_{t})$	Snapshot transactional network at window $t$
$V_{t},E_{t}$	Account nodes and directed transfers within window $t$
$X_{t}$	Node attribute matrix within window $t$
$A_{t},\hat{A}_{t}$	Adjacency matrix and normalized adjacency form
$A_{t}^{(k)}$	$k$ -hop propagation operator within window $t$
$K$	Maximum hop distance for multi-resolution diffusion

Table 1: Summary of key symbols used throughout this manuscript.

Figure 1: Complete architectural diagram of the STC-MixHop framework. The architecture comprises a multi-hop spatial diffusion encoder (MixHop) for capturing extended-range topological context, a temporal attention fusion module for synthesizing information across snapshots, and a two-stage training protocol involving self-supervised contrastive pretraining followed by supervised fine-tuning.

Figure 2: Complete performance comparison using the PaySim corpus. The bar charts illustrate the performance of STC-MixHop (red) against tabular baselines and other GNN variants across ROC-AUC, PR-AUC, $F_{\beta}$ , and Recall. While tabular methods excel in several ranking metrics, STC-MixHop maintains strong recall characteristics that are valuable for high-recall fraud screening.

Method	ROC-AUC	PR-AUC	$F_{\beta}$	Precision	Recall	Accuracy	Threshold
LogReg	0.956	0.753	0.770	0.469	0.469	0.983	0.51
RF	0.892	0.760	0.865	0.573	0.573	0.985	0.54
MLP	0.981	0.854	0.869	0.578	0.578	0.986	0.52
GCN	0.688	0.056	0.069	0.056	0.982	0.982	1.00
GraphSAGE	0.609	0.045	0.055	0.045	0.973	0.981	1.00
GAT	0.853	0.112	0.137	0.112	0.977	0.984	0.99

Table 2: Complete performance comparison using the PaySim corpus. Thresholds are determined from the validation partition via probability-quantile enumeration and rounded for presentation.

Figure 3: Component ablation study on the PaySim corpus. The results highlight the critical role of multi-resolution spatial diffusion (same-step structure) in maintaining ROC-AUC, while also showing the condition-dependent impact of contrastive learning and temporal attention on the model’s overall discriminative power.

Variant	ROC-AUC	PR-AUC	$F_{\beta}$	Precision	Recall	Accuracy
Full STC-MixHop	0.717	0.061	0.075	0.061	0.987	0.985
w/o same-step structure	0.648	0.052	0.066	0.052	0.981	0.982
w/o time-decay weighting	0.725	0.064	0.072	0.064	0.978	0.984
w/o temporal attention	0.688	0.060	0.069	0.060	0.973	0.983
w/o contrastive learning	0.742	0.069	0.084	0.069	0.982	0.984

Table 3: Component ablation results for STC-MixHop on the PaySim corpus.

Figure 4: STC-MixHop sensitivity to MixHop diffusion depth $K$ on the PaySim corpus. Increasing $K$ generally improves ROC-AUC and Precision, while Recall peaks at $K=2$ , suggesting that moderate topological propagation provides the best balance for identifying elevated-risk nodes.

Figure 5: STC-MixHop sensitivity to temporal attention dimensionality $d_{k}$ on the PaySim corpus. The performance metrics exhibit sensitivity to the attention size, with an optimal balance for ROC-AUC and Precision found around $d_{k}=64$ , while Recall reaches its maximum at $d_{k}=96$ .

Figure 6: Overall performance comparison on the Porto Seguro dataset across ROC-AUC, PR-AUC, $F_{\beta}$ , and Recall. Graph-based models do not consistently dominate tabular baselines, indicating that strong relational inductive bias is not guaranteed in real-world insurance data.

Method	ROC-AUC	PR-AUC	$F_{\beta}$	F1	Precision	Recall	Accuracy
Logistic Regression	0.614	0.056	0.074	0.081	0.070	0.096	0.920
Random Forest	0.580	0.055	0.071	0.100	0.059	0.322	0.788
MLP	0.559	0.048	0.052	0.067	0.045	0.130	0.867
GCN	0.560	0.044	0.058	0.071	0.051	0.116	0.889
GraphSAGE	0.602	0.057	0.080	0.068	0.091	0.055	0.946
GAT	0.547	0.043	0.025	0.023	0.027	0.021	0.937

Table 4: Overall performance comparison on the Porto Seguro auto insurance fraud dataset. All methods are evaluated under the same data split and threshold selection protocol. Besides ROC-AUC, we emphasize PR-AUC and threshold-dependent metrics to reflect operational performance under extreme class imbalance.

Figure 7: Sensitivity analysis with respect to MixHop depth $K$ on the Porto Seguro dataset. Moderate multi-hop aggregation achieves the best trade-off, while deeper diffusion introduces noise propagation and performance degradation.

Figure 8: Sensitivity analysis with respect to attention dimension $d_{k}$ on the Porto Seguro dataset. Performance peaks at intermediate dimensions, suggesting diminishing returns from increasing attention capacity under sparse and noisy relational signals.

Figure 9: Visualization of component ablation results on the Porto Seguro dataset. Removing same-step structural diffusion leads to the most consistent degradation in threshold-dependent metrics, while temporal and contrastive components mainly affect precision–recall trade-offs.

Variant	ROC-AUC	PR-AUC	$F_{\beta}$	F1	Precision	Recall
Full (STC-MixHop)	0.609	0.058	0.075	0.078	0.074	0.082
w/o same-step structure	0.603	0.056	0.076	0.062	0.089	0.048
w/o time-decay weighting	0.609	0.057	0.069	0.100	0.057	0.438
w/o temporal attention	0.608	0.056	0.089	0.072	0.105	0.055
w/o contrastive learning	0.610	0.056	0.059	0.057	0.060	0.055

Table 5: Ablation study of STC-MixHop components on the Porto Seguro dataset. Each variant removes one component while keeping all other settings unchanged. Results highlight the relative importance of structural diffusion, temporal modeling, and contrastive regularization.

Figure 10: Overall performance comparison on the FEMA NFIP dataset across ROC-AUC, PR-AUC, $F_{\beta}$ , and Recall. The performance gap among methods is modest, highlighting that strong relational inductive bias is not guaranteed across domains and that metric choice (especially PR-AUC and thresholded measures) remains crucial.

Method	ROC-AUC	PR-AUC	$F_{\beta}$	F1	Precision	Recall	Accuracy
Logistic Regression	0.4998	0.4872	0.5467	0.6553	0.4923	0.9797	0.4933
Random Forest	0.4987	0.4891	0.5445	0.6434	0.4939	0.9227	0.4970
MLP	0.4945	0.4822	0.5469	0.6545	0.4929	0.9736	0.4945
GCN	0.5106	0.4927	0.5465	0.6556	0.4920	0.9822	0.4925
GraphSAGE	0.5004	0.4934	0.5478	0.6582	0.4927	0.9914	0.4938
GAT	0.4996	0.4903	0.5472	0.6565	0.4925	0.9842	0.4935

Table 6: Overall performance comparison on the FEMA NFIP dataset. All methods are evaluated under the same data split and threshold selection protocol. We report ROC-AUC together with PR-AUC and threshold-dependent metrics to reflect operational behavior under high class imbalance.

Figure 11: Sensitivity analysis with respect to MixHop depth $K$ on the FEMA NFIP dataset. Performance varies mildly across $K$ , indicating that deeper diffusion provides limited marginal benefit under this domain and that moderate multi-hop aggregation is sufficient.

Figure 12: Sensitivity analysis with respect to attention dimension $d_{k}$ on the FEMA NFIP dataset. Results are relatively stable across a wide range of $d_{k}$ , suggesting diminishing returns from increasing attention capacity in this setting.

Figure 13: Component ablation results on the FEMA NFIP dataset. Removing individual temporal/contrastive components yields only minor changes, supporting the view that these modules mainly act as regularizers under this domain. Interestingly, excluding same-step structural modeling can slightly improve recall, suggesting potential noise from immediate neighborhood signals in this dataset.

Variant	ROC-AUC	PR-AUC	$F_{\beta}$	F1	Precision	Recall
Full (STC-MixHop)	0.4989	0.4879	0.5467	0.6543	0.4927	0.9736
w/o same-step structure	0.5036	0.4907	0.5477	0.6582	0.4926	0.9919
w/o time-decay weighting	0.5008	0.4886	0.5472	0.6564	0.4926	0.9832
w/o temporal attention	0.5033	0.4911	0.5475	0.6575	0.4925	0.9888
w/o contrastive learning	0.4972	0.4876	0.5464	0.6563	0.4915	0.9873

Table 7: Ablation study of STC-MixHop components on the FEMA NFIP dataset. Each variant removes one component while keeping all other settings unchanged. Differences are relatively small across variants, suggesting that on this dataset temporal/contrastive components behave primarily as regularizers and that certain same-step structural signals may introduce noise depending on the domain.

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