Heterogeneous Graph Structure Optimization with Dual-View Contrastive Learning for Fraud Detection

Abstract

Fraud detection on multi-relational graphs is challenging because real-world fraud-related data often contains heterogeneous relations, noisy structures, and imbalanced labels. Existing GNN-based methods usually rely on predefined graph structures, but real-world financial graphs often contain noisy, redundant, or missing relations, which undermine neighborhood aggregation and message passing. In addition, single-view learning is insufficient to capture both local structural patterns and high-order semantic dependencies, limiting performance in complex fraud scenarios. To address this issue, we propose HGSO-DVCL, a heterogeneous graph structure optimization framework with dual-view contrastive learning. The framework performs type-aware structure optimization for each relation subgraph and integrates optimized graphs with the original structure through channel attention. A dual-view encoder then learns complementary representations from the network schema view and the meta-path view, while contrastive learning promotes consistency and complementarity between the two perspectives. An end-to-end objective jointly optimizes fraud classification, structure regularization, and contrastive alignment. Experiments on public multi-relational fraud detection benchmarks show that HGSO-DVCL achieves strong and competitive performance, while ablation and sensitivity studies support the effectiveness and stability of the proposed framework under the evaluated benchmark settings.

1. Introduction

Financial fraud poses a significant and growing threat to the global economy, causing substantial losses for financial institutions and consumers alike [1]. With the rapid expansion of digital payment systems and online financial services, the volume and complexity of financial transactions have increased dramatically, creating intricate interaction networks among diverse entity types such as accounts, bank cards, merchants, and devices. These complex relational structures provide rich contextual information for fraud analysis, motivating the adoption of graph-based analytical approaches that can explicitly model the relational dependencies inherent in financial transaction data [2].

Graph neural networks (GNNs) have emerged as a powerful paradigm for fraud detection by leveraging the topological structure of transaction networks to propagate and aggregate information across connected entities [3]. Compared with traditional methods that treat each transaction as an independent sample, GNN-based approaches can capture multi-hop interactions, shared device usage patterns, and fund flow trajectories within a unified heterogeneous graph framework. Several recent studies have demonstrated the effectiveness of graph-based methods in identifying anomalous transaction patterns and detecting group-level fraud activities.

Despite these advances, existing GNN-based fraud detection methods face three fundamental challenges. (a) The real-world financial transaction graphs inevitably contain structural defects, including noisy edges, redundant connections, and missing key relationships, arising from data collection errors, entity resolution inaccuracies, and business rule biases. These structural imperfections directly interfere with the neighborhood aggregation mechanism in GNNs, introducing misleading or irrelevant information during message passing and degrading model robustness [4]. Most current approaches implicitly assume that the predefined graph structure is reliable and optimal, an assumption that rarely holds in practical financial scenarios. (b) Fraud detection faces the compounded challenges of extreme class imbalance and label scarcity. Fraudulent transactions typically constitute a very small fraction of total activity, and obtaining reliable fraud labels requires expensive manual investigation. Relying solely on supervised signals makes models prone to majority-class bias. Single-view graph modeling further limits detection capability, as it cannot simultaneously capture both local relational interaction patterns and high-order semantic associations across different relation combinations. Complex fraud strategies such as relation camouflage and coordinated gang activities demand multi-perspective analysis that single-view approaches fail to provide [5]. (c) The separation between graph structure construction and representation learning in existing pipelines prevents these two processes from mutually benefiting each other. Graph structure quality directly determines the effectiveness of downstream representation learning, while task-driven feedback from node classification can guide structure refinement [6]. Without joint optimization, suboptimal graph structures propagate errors into learned representations, ultimately limiting fraud detection accuracy.

To address these challenges, we propose a Heterogeneous Graph Structure Optimization framework with Dual-View Contrastive Learning (HGSO-DVCL) for fraud detection. The HGSO-DVCL first refines relation-specific heterogeneous graph structures by integrating optimized subgraph topology with the original graph, and then learns node representations from both the network schema view and the meta-path view. Cross-view contrastive learning is further introduced to align the two perspectives and encourage them to provide consistent yet complementary signals within an end-to-end prediction-oriented framework. The novelty of HGSO-DVCL lies in coupling relation-specific structure refinement with dual-view heterogeneous representation learning in a single fraud-oriented optimization framework. Unlike methods that directly encode the given graph, HGSO-DVCL first constructs relation-aware feature similarity and feature propagation graphs to correct unreliable topology. Unlike standard heterogeneous graph encoders, it then aligns a network schema view and a meta-path view through meta-path-guided contrastive constraints. Therefore, the main methodological contribution is the task-driven integration of heterogeneous graph structure optimization and dual-view contrastive learning for fraud detection.

In this work, we mainly address three core problems: (1) how to refine unreliable heterogeneous graph structures that contain noisy, redundant, or missing relations without discarding the original relational evidence; (2) how to learn node representations that jointly capture local relational interactions and high-order semantic dependencies in complex fraud scenarios; and (3) how to unify graph structure optimization and downstream fraud classification within a single collaborative learning framework. The main contributions of this paper are summarized as follows:

• We propose a type-aware heterogeneous graph structure optimization mechanism that constructs feature similarity graphs and feature propagation graphs for each relation type, and fuses them with the original adjacency through channel attention, effectively reducing structural noise and recovering potentially missing connections.
• We design a dual-view contrastive learning framework that combines a network schema view encoder with a meta-path view encoder, enhanced by meta-path-guided cross-view consistency constraints, to learn robust and discriminative node representations.
• We formulate an end-to-end joint optimization objective that unifies supervised classification, graph structure regularization, and contrastive alignment, enabling the graph optimization and representation learning modules to collaboratively improve fraud detection performance.
• We conduct experiments on two public multi-relational fraud detection benchmarks, showing that HGSO-DVCL achieves strong and competitive performance across multiple evaluation metrics, with ablation and sensitivity analyses supporting the contribution of its main components.

The remainder of this paper is organized as follows. Section 2 reviews related work on fraud detection methods. Section 3 introduces the necessary preliminaries and problem formulation. Section 4 presents the proposed HGSO-DVCL framework in detail. Section 5 reports the experimental evaluation. Section 6 concludes this paper and discusses future research directions.

2. Related Work

Fraud detection is not only a technical prediction task, but also a problem related to misconduct, information quality, institutional monitoring, and regulatory enforcement. Prior studies in economics and finance emphasize that detected fraud or misconduct represents only a subset of underlying misconduct, and that detection outcomes are affected by incentives, reporting mechanisms, enforcement resources, and regulatory design [7,8]. Predictive models are therefore more appropriately understood as decision-support tools for prioritizing suspicious cases rather than as direct measurements of the true prevalence of misconduct. In practical financial settings, false positives may increase investigation costs and reputational risks, while false negatives may allow harmful behavior to remain undetected. These concerns also highlight the importance of connecting fraud detection methods with concrete institutional environments, review budgets, and regulatory objectives [9,10].

2.1. Machine Learning-Based Fraud Detection

Machine learning-based financial fraud detection uses data-driven algorithms to learn patterns from historical transaction data and identify anomalous or fraudulent behaviors. Talukder et al. [11] proposed a comparative learning approach based on decision trees, random forests, and K-nearest neighbors, addressing the balance between computational efficiency and detection accuracy on large-scale fraud datasets. Khalid et al. [12] constructed an ensemble learning framework integrating support vector machines, random forests, and boosting algorithms, effectively alleviating model parameter tuning complexity and high false positive rates. Bala et al. [13] introduced an optimized XGBoost-based detection model to balance computational cost, precision, and recall in real-time fraud detection. Chen et al. [14] designed a LightGBM-based online transaction fraud detection system that addresses high-dimensional sparsity in large-scale online payment data through feature engineering optimization, achieving 99.5% detection accuracy. Wijaya et al. [15] systematically compared XGBoost with various data balancing techniques, finding that XGBoost combined with random oversampling achieves an F1 score of 92.43%, effectively mitigating model bias under class imbalance. Xia et al. [16] proposed a selective ensemble model that dynamically selects base learners to enhance detection robustness on highly imbalanced digital financial datasets. Lim et al. [17] introduced the TP-ERT method, which applies tree-structured Parzen estimators for hyperparameter optimization of extremely randomized trees, capturing complex transaction patterns through higher-randomness splitting. Tayebi et al. Tayebi and El Kafhali [18] proposed an XGBoost-based approach with Bayesian optimization for automatic hyperparameter search, combined with SMOTE, random undersampling, and cross-validation to suppress overfitting under extreme class imbalance.

While machine learning models offer greater adaptability than rule-based systems by learning fraud features in a data-driven manner, they fundamentally treat transactions as independent events, ignoring relational dependencies and sequential patterns. This limitation prevents them from capturing cross-transaction, cross-entity higher-order collaborative fraud patterns.

2.2. Deep Learning-Based Fraud Detection

Compared with traditional machine learning methods that rely on manual feature engineering, deep learning models can automatically extract hierarchical representations through nonlinear architectures. This enables stronger modeling of complex patterns and supports end-to-end adaptive learning. Elkenawy et al. [19] compared recurrent neural network architectures including RNN, LSTM, and GRU for credit card fraud detection, capturing temporal dependency features in transaction data to reduce false positives and improve overall detection accuracy. Yu et al. [20] constructed a Transformer-based fraud detection model that leverages self-attention mechanisms to address the inability of RNN-based models to effectively capture long-range contextual dependencies. Mienye et al. [21] proposed a hybrid deep learning framework combining generative adversarial networks (GANs) with recurrent neural networks, generating realistic fraudulent samples through GANs to address class imbalance and enhance detection capability. Du et al. [22] constructed a hybrid framework integrating autoencoders with conditional generative adversarial networks to address the co-optimization of feature learning and minority sample generation under extreme imbalance. Koo et al. [23] proposed an unsupervised anomaly detection method based on deep autoencoders, addressing the balance between fraud pattern discovery and low false positive rates under label-scarce scenarios. Delise et al. [24] introduced deep semi-supervised anomaly detection (Deep SAD), addressing model training challenges when only a small number of labeled anomalous samples are available.

Despite the potential of deep learning methods for improving fraud detection accuracy, several limitations persist. Most models fail to incorporate broad contextual information such as temporal patterns and entity relationships. Fixed models are susceptible to concept drift, making it difficult to maintain performance over time. Furthermore, most models adopt fixed fraud classification thresholds that may not be optimal across different scenarios.

2.3. Graph-Based Fraud Detection

Graph-based financial fraud detection [3] abstracts transaction entities and their relationships into nodes and edges, leveraging graph neural networks to mine anomalous association patterns and group fraud behaviors in transaction networks. Financial transactions inherently form relational networks, and graph models can explicitly capture topological dependencies, multi-hop interactions, and hidden association features that traditional tabular or sequential methods struggle to express. Duan et al. [25] proposed CaT-GNN, a causal temporal graph neural network that identifies causal nodes and implements causal interventions through a causal invariance learning mechanism, addressing the insufficient robustness, poor generalization, and limited interpretability caused by traditional GNNs ignoring local structural causal effects. Wang et al. [26] proposed a label information-enhanced fraud detection method that introduces label propagation and topological denoising mechanisms to address insufficient fraud node identification accuracy in low-homophily graph networks. Wan et al. [27] constructed the MDGC-LSTM model, which integrates dynamic graph convolutional networks with long short-term memory networks in a symmetric spatiotemporal architecture, achieving comprehensive modeling of complex spatiotemporal dependencies for dynamic fraud prediction. Wang et al. [28] proposed CoSemiGNN, a dynamic graph neural network that captures temporal dynamics using self-attention RNNs and integrates semi-supervised co-occurrence relationships, addressing the challenges of label scarcity and dynamic data distribution in blockchain environments. Pan et al. [29] proposed an unsupervised heterophily-guided graph fraud detection approach that employs label-agnostic heterophily learning mechanisms to address the dependency on labeled data in graph anomaly detection under annotation-scarce scenarios. Zou et al. [30] proposed a subgraph pattern-enhanced graph neural network that explicitly encodes high-order subgraph structural information, addressing the difficulty of capturing complex multi-hop association patterns in transaction networks. Wu et al. [31] proposed SplitGNN, a spectral graph neural network that separates heterogeneous signals through spectral decomposition, addressing the neighbor aggregation noise caused by network heterophily in fraud detection.

Although graph-based methods have significantly advanced fraud detection, most existing approaches implicitly assume that the predefined graph structure is reliable and optimal, conducting representation learning directly on the original graph. This assumption is difficult to satisfy in real financial scenarios where graphs inevitably contain noise and structural defects. Moreover, single-view graph modeling cannot simultaneously capture multi-level semantic information under different relation combinations, limiting adaptability to complex fraud patterns. Our proposed method addresses these gaps by jointly optimizing graph structure and learning dual-view representations within a unified framework.

3. Preliminaries

3.1. Financial Fraud Pattern

As a motivating setting, financial transaction fraud encompasses a broad range of illicit activities, including credit card fraud, identity theft, money laundering, account takeover, and coordinated group fraud schemes [32]. As digital payment ecosystems expand, fraudsters continuously develop increasingly sophisticated strategies, often forming organized networks that exploit the complex interactions among multiple entities. The relational nature of financial transactions, where accounts, bank cards, merchants, and devices interact through diverse channels, creates intricate networks with inherent heterogeneity.

In practice, constructing a graph from financial transaction data involves mapping different entity types as nodes and their interactions as edges. For example, two transactions may be connected through a shared user account, a common merchant, or the same device identifier. These diverse relationship types encode rich semantic information that can reveal hidden fraud patterns. However, the graph construction process is susceptible to multiple sources of imperfection. Data collection mechanisms may miss certain interactions, entity resolution algorithms may incorrectly merge or split entities, and predefined business rules may introduce systematic biases in which edges are included [33]. As a result, the constructed graph typically contains noisy edges that connect unrelated entities, redundant connections that provide no additional discriminative information, and missing relationships that would otherwise reveal important fraud signals. These structural defects directly compromise the quality of neighborhood aggregation in graph neural networks, where message passing may propagate irrelevant or misleading information across the network.

3.2. Heterogeneous Information Networks

In transaction-level financial settings, fraud detection may involve multiple entity and interaction types, such as users, transactions, merchants, devices, and accounts. Since fraudulent behavior often emerges from shared attributes, repeated interactions, and hidden group-level collaboration rather than isolated transactions, HINs provide a unified graph structure for modeling multi-entity and multi-relation financial systems. As shown in Figure 1, HINs support the proposed framework by capturing both direct transaction dependencies and richer cross-type semantic associations for structure optimization and dual-view representation learning.

A heterogeneous information network (HIN) [34] is defined as a graph $\mathcal{G}=(\mathcal{V},\mathcal{E},\varphi ,\psi )$, where $\mathcal{V}$ denotes the set of nodes, $\mathcal{E}$ denotes the set of edges, $\varphi :\mathcal{V}\to \mathcal{A}$ is a node type mapping function, and $\psi :\mathcal{E}\to \mathcal{R}$ is an edge type mapping function. Here $\mathcal{A}$ and $\mathcal{R}$ represent the sets of node types and edge types, respectively. A heterogeneous graph satisfies $\left|\mathcal{A}\right|+\left|\mathcal{R}\right|>2$, indicating the presence of multiple node types or edge types.

The semantic structure of a heterogeneous information network is characterized by two key concepts: network schema and meta-paths. The network schema $\mathcal{S}=(\mathcal{A},\mathcal{R})$ serves as an abstract, type-level representation of the HIN, where nodes represent entity types and edges represent the allowed relationship types between them. The network schema defines the local connectivity patterns and captures direct interactions among different entity types. For instance, in a financial transaction HIN, the network schema specifies that users conduct transactions and that transactions are associated with merchants. A meta-path is defined as a path on the type-level graph in the form $A_1\stackrel{R_1}{\to }{A}_2\stackrel{R_2}{\to }\dots \stackrel{R_l}{\to }{A}_{l+1}$ (abbreviated as $A_1{A}_2\dots A_{l+1}$), which describes the composite relation $R=R_1\circ R_2\circ \dots \circ R_l$ between node types $A_1$ and $A_{l+1}$, where ∘ denotes the composition operator. For example, in a financial transaction graph with users (U), transactions (T), and merchants (M), the meta-path $T\to M\to T$ (abbreviated $TMT$) captures the semantic relation that two transactions occur at the same merchant, while $U\to T\to U$ (abbreviated $UTU$) indicates that two users are connected through a common transaction, such as a fund transfer. Since meta-paths compose multiple relations, they encode complex high-order semantic information that complements the local direct connectivity captured by the network schema.

These two perspectives are complementary for fraud detection. The network schema captures local type-constrained interactions and immediate transaction behaviors, while meta-paths reveal high-order semantic dependencies such as relation camouflage, collusive groups, and cross-entity risk propagation. This motivates the dual-view design: the schema view models local heterogeneous interactions, whereas the meta-path view captures broader semantic associations, jointly providing a more comprehensive fraud representation.

3.3. Problem Formulation

In real-world construction, financial transaction graphs are vulnerable to missing data, entity resolution errors, and business-rule biases, resulting in noisy edges, redundant connections, and missing critical relations [35], as illustrated in Figure 2. These structural defects interfere with GNN neighborhood aggregation by introducing irrelevant or misleading messages, thereby reducing model robustness. Meanwhile, severe class imbalance, limited labels, and evolving fraud patterns make purely supervised models prone to majority-class bias. Single-view modeling also struggles to capture multi-level semantics from different relation combinations, limiting its adaptability to relation camouflage and collusive fraud. To address these challenges, this paper integrates heterogeneous GNNs, graph structure optimization, and cross-view contrastive learning for fraud detection.

Specifically, the research task addressed in this paper is formulated as a node classification problem on a heterogeneous fraud graph. Let $\mathcal{G}=(\mathcal{V},\mathcal{E},\mathcal{A},\mathcal{R},X)$ denote the heterogeneous transaction graph, where $\mathcal{V}$ is the node set, $\mathcal{E}$ is the edge set, $\mathcal{A}$ and $\mathcal{R}$ represent the node type set and edge type set respectively, and X is the node feature matrix. Given a set of meta-paths $\mathcal{P}=\{P_1,P_2,\dots ,P_m\}$ and a set of labeled nodes ${\mathcal{V}}_L=\left\{(v_i,y_i)\right\}$ where $y_i\in \{0,1\}$ denotes the class label of node $v_i$ (fraud or legitimate), the objective is twofold.

First, unlike methods that operate directly on the original graph, the proposed approach learns an optimized graph structure ${\mathcal{G}}^{\ast }$ that is more suitable for downstream fraud detection. Second, on the optimized graph, node representations are learned from both the network schema view and the meta-path view, and their robustness and discriminability are enhanced through multi-view collaborative mechanisms. The final fused node representations are used for classification prediction. The overall optimization objective can be expressed as:

$$\mathcal{L}={\mathcal{L}}_{\mathrm{cls}}+\alpha {\mathcal{L}}_{\mathrm{reg}}+\beta {\mathcal{L}}_{\mathrm{con}}$$

(1)

where ${\mathcal{L}}_{\mathrm{cls}}$ denotes the supervised classification loss, ${\mathcal{L}}_{\mathrm{reg}}$ represents the graph structure optimization regularization term, ${\mathcal{L}}_{\mathrm{con}}$ denotes the multi-view contrastive constraint, and $\alpha$, $\beta$ are the balancing coefficients. By minimizing this joint objective, the model jointly refines the graph structure and learns discriminative node representations. This formulation provides a unified task objective for HGSO-DVCL by combining structure refinement with complementary semantic information from different views. It also motivates the graph optimization and dual-view representation learning modules introduced in the following section. For clarity and reproducibility, the main notations used in the proposed framework are summarized in Appendix A.

4. Methodology

4.1. Overview

The proposed HGSO-DVCL framework consists of three tightly coupled modules, as illustrated in Figure 3. Given a heterogeneous graph, the framework first applies type-aware structure optimization to each relation subgraph. It constructs feature similarity graphs and feature propagation graphs, and then fuses them with the original adjacency through channel attention to obtain an enhanced topology. Based on the optimized graph, the network schema view encoder and the meta-path view encoder learn complementary representations for local relational interactions and high-order semantic associations, respectively. Cross-view contrastive learning enforces alignment between these two perspectives by leveraging meta-path connectivity to construct positive sample pairs. Finally, the dual-view embeddings are concatenated and fed into a supervised classifier. The total loss integrates classification, structure regularization, and contrastive objectives for end-to-end joint training.

4.2. Heterogeneous Graph Structure Optimization

Different types of nodes and relations in a heterogeneous graph exhibit distinct characteristics in terms of semantic strength, noise level, and statistical distribution. The original graph structure is often affected by business rules and data quality issues, leading to redundant edges, missing key relationships, and inconsistent cross-type connections [36]. These problems cause error accumulation and semantic aliasing during message passing. The goal of heterogeneous graph optimization is to perform type-aware reweighting, denoising, and completion of the graph structure, making the propagation process more aligned with relational semantics and reducing the risk of erroneous information propagation.

The optimized graph is expected to be more effective than the original topology when the observed graph is only partially reliable, namely when it still contains useful relational evidence but is affected by noisy, redundant, or missing links. In this setting, the feature similarity graph provides an attribute-consistent cue for discovering potential neighbors, while the feature propagation graph constrains this cue through the observed relation topology. These two graphs therefore offer complementary evidence: the former is content-driven, whereas the latter is topology-aware. Channel attention is adopted because the reliability of different structural cues may vary across relation types and datasets, and fixed fusion weights may not be suitable for all relations. To avoid over-smoothing and noisy pseudo-link propagation, HGSO-DVCL further applies sparsity thresholds to remove weak similarity links, performs propagation through the observed topology rather than a fully connected similarity graph, retains the original adjacency in the final fusion stage, and penalizes overly dense optimized adjacency matrices through L1 regularization. These designs make the learned topology a conservative refinement of the original graph rather than an unconstrained graph reconstruction.

Feature Similarity Graph. In heterogeneous fraud graphs, the original relation structure may contain noisy, redundant, or rule-biased edges that hinder fraud discrimination. To provide a content-driven cue for graph refinement, we construct a feature similarity graph for each relation type, which estimates attribute-based connectivity under relation r and serves as a candidate structure for later fusion with the original topology and the feature propagation graph. Since heterogeneous node types often have inconsistent feature dimensions, all node features are first projected into a unified common space to enable relation-aware similarity computation across heterogeneous entities. Its common-space representation ${\mathbf{h}}_v$ is obtained through a type-specific mapping layer:

$${\mathbf{h}}_v=\sigma ({\mathbf{W}}_t{\mathbf{x}}_v+{\mathbf{b}}_t)$$

(2)

where $\sigma (·)$ denotes a nonlinear activation function, and ${\mathbf{W}}_t$ and ${\mathbf{b}}_t$ are the projection matrix and bias term associated with node type t, respectively. Let $d_t$ denote the input feature dimension of node type t, and let d denote the hidden dimension shared by all node types. Then $W_t\in {\mathbb{R}}^{d\times d_t},b_t\in {\mathbb{R}}^d$, and $h_v\in {\mathbb{R}}^d$. The relation-specific parameter $M_r\in {\mathbb{R}}^d$ reweights hidden dimensions when computing weighted cosine similarity. This projection maps heterogeneous raw attributes into a type-normalized latent space, making different node types comparable for relation-specific similarity modeling. In HGSO-DVCL, it provides a unified feature basis for graph structure optimization and semantically aligned inputs for downstream dual-view representation learning. In the common feature space, for a given relation type r, the feature similarity graph ${\mathbf{S}}^r$ is constructed to measure attribute-level affinity between nodes. Specifically, the edge weight between nodes $v_i$ and $v_j$ is defined as:

$${\mathbf{S}}_{ij}^r=\left\{\begin{array}{cc}{\mathrm{sim}}_{{\mathbf{M}}^r}({\mathbf{h}}_i,{\mathbf{h}}_j),\hfill & \mathrm{if}{\mathrm{sim}}_{{\mathbf{M}}^r}({\mathbf{h}}_i,{\mathbf{h}}_j)\ge ϵ\hfill \\ 0,\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(3)

where ${\mathbf{h}}_i$ and ${\mathbf{h}}_j$ are the projected representations of nodes $v_i$ and $v_j$, respectively, and ${\mathbf{S}}_{ij}^r$ denotes their similarity-based edge weight under relation r. The threshold $ϵ$ controls graph sparsity; a larger $ϵ$ preserves only stronger similarities and thus yields a sparser graph. This thresholding operation retains only strong relation-aware associations, suppressing weak or potentially noisy connections before message passing. The similarity function ${\mathrm{sim}}_{{\mathbf{M}}^r}(·,·)$ is defined as a relation-aware weighted cosine similarity:

$${\mathrm{sim}}_{{\mathbf{M}}^r}({\mathbf{h}}_i,{\mathbf{h}}_j)={\displaystyle \frac{{({\mathbf{h}}_i\odot {\mathbf{M}}^r)}^{\top }({\mathbf{h}}_j\odot {\mathbf{M}}^r)}{\parallel {\mathbf{h}}_i\odot {\mathbf{M}}^r\parallel ·\parallel {\mathbf{h}}_j\odot {\mathbf{M}}^r\parallel }}$$

(4)

where ⊙ denotes the Hadamard (element-wise) product, and ${\mathbf{M}}^r$ is a learnable relation-specific parameter that weights the importance of each feature dimension for relation r. The numerator captures alignment between reweighted node features, while the denominator normalizes their magnitudes for comparable similarity scoring. This design enables relation-specific emphasis on fraud-relevant feature dimensions beyond raw attribute overlap.

By projecting heterogeneous features into a unified space, computing relation-aware similarities, and filtering weak connections, the feature similarity graph provides an attribute-consistent candidate topology. It complements the original graph by suppressing unreliable associations and revealing informative neighbors, providing a cleaner basis for feature propagation, graph fusion, and dual-view representation learning.

Feature Propagation Graph. While the feature similarity graph offers an attribute-driven candidate structure, it does not fully capture the observed transaction topology. In practice, suspicious nodes may lack strong direct feature similarity but still share related risk patterns through structurally similar neighborhoods. To capture such latent dependencies, we construct a feature propagation graph for each relation type, which propagates feature similarity over the original heterogeneous topology to recover potentially missing fraud-relevant connections while preserving structural constraints. This module bridges attribute-level similarity and topology-aware refinement, complementing the feature similarity graph in graph fusion.

For a given relation type r, let the head node set and tail node set be denoted by ${\mathcal{V}}_h$ and ${\mathcal{V}}_t$, respectively, and let the original topology under relation r be represented by the adjacency matrix ${\mathbf{A}}^r$. Here, ${\mathbf{A}}^r$ encodes the observed cross-type connections from head nodes to tail nodes in the financial transaction graph. For any two head nodes $v_i,v_j\in {\mathcal{V}}_h$, the head-node feature similarity graph ${\widehat{\mathbf{S}}}_h^r$ is defined as:

$${\widehat{\mathbf{S}}}_{h,ij}^r=\left\{\begin{array}{cc}{\mathrm{sim}}_{{\widehat{\mathbf{M}}}_h^r}({\mathbf{h}}_i,{\mathbf{h}}_j),\hfill & \mathrm{if}{\mathrm{sim}}_{{\widehat{\mathbf{M}}}_h^r}({\mathbf{h}}_i,{\mathbf{h}}_j)\ge {ϵ}_h\hfill \\ 0,\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(5)

where ${\widehat{\mathbf{S}}}_{h,ij}^r$ denotes the similarity weight between head nodes $v_i$ and $v_j$ under relation r, ${\mathbf{h}}_i$ and ${\mathbf{h}}_j$ are their projected node representations in the common feature space, ${ϵ}_h$ is the sparsity threshold for the head-side similarity graph, and ${\mathrm{sim}}_{{\widehat{\mathbf{M}}}_h^r}(·,·)$ is a weighted cosine similarity parameterized by the learnable relation-specific matrix ${\widehat{\mathbf{M}}}_h^r$. This construction identifies semantically or behaviorally similar head nodes while filtering weak and noisy associations. Feature similarity is then propagated through the original topology to obtain the head-node feature propagation graph:

$${\mathbf{F}}_h^r={\widehat{\mathbf{S}}}_h^r{\mathbf{A}}^r$$

(6)

where ${\mathbf{F}}_h^r$ denotes the propagated structural signal from the head side under relation r. This operation lets feature-similar head nodes reinforce their connections to tail nodes through ${\mathbf{A}}^r$. Thus, the model can infer topology-aware candidate links that are not directly observed but jointly supported by feature similarity and the existing relation structure. Similarly, a tail-node feature similarity graph ${\widehat{\mathbf{S}}}_t^r$ is constructed on the tail node set ${\mathcal{V}}_t$ using the corresponding learnable parameter matrix ${\widehat{\mathbf{M}}}_t^r$, and the tail-side feature propagation graph is obtained as:

$${\mathbf{F}}_t^r={\left({\mathbf{A}}^r\right)}^{\top }{\widehat{\mathbf{S}}}_t^r$$

(7)

where ${\mathbf{F}}_t^r$ denotes the propagated structural signal from the tail side under relation r. By propagating tail-node similarity through ${\left({\mathbf{A}}^r\right)}^{\top }$, the model captures additional structural evidence for hidden head-side associations. This is useful when fraud signals emerge indirectly through shared merchants, devices, accounts, or other intermediate entities rather than direct pairwise similarity.

Together, ${\mathbf{F}}_h^r$ and ${\mathbf{F}}_t^r$ extend the original topology with feature-guided neighborhood evidence from both sides of relation r. Compared with the feature similarity graph alone, the feature propagation graph better preserves observed interaction patterns, helping recover missing fraud-relevant links and suppress structurally isolated noise. These propagated graphs are then fused with the original adjacency and feature similarity graph to form a more reliable topology for the downstream schema view and meta-path view encoders.

Optimized Graph Construction. After obtaining the feature similarity graph ${\mathbf{S}}^r$ and the two feature propagation graphs ${\mathbf{F}}_h^r$ and ${\mathbf{F}}_t^r$ for relation type r, the next step is to integrate these complementary structural cues into a unified optimized topology for financial fraud detection. The three candidate graphs reflect different but related views of relation refinement: ${\mathbf{S}}^r$ emphasizes attribute-level consistency, while ${\mathbf{F}}_h^r$ and ${\mathbf{F}}_t^r$ capture topology-aware structural expansion from the head and tail sides, respectively. Since candidate structures vary in reliability across relations and datasets, we use channel attention to adaptively weight their contributions rather than assigning fixed weights. This enables the model to preserve graph patterns most informative for fraud detection.

Specifically, the three candidate feature graphs are stacked along the channel dimension to form a tensor ${\mathcal{T}}^r$, and the fused feature optimization graph is computed as:

$${\tilde{\mathbf{A}}}^r={\mathrm{ChannelAttn}}_{{\mathbf{W}}_c}\left({\mathcal{T}}^r\right)$$

(8)

where ${\mathcal{T}}^r$ denotes the stacked tensor composed of ${\mathbf{S}}^r$, ${\mathbf{F}}_h^r$, and ${\mathbf{F}}_t^r$, ${\tilde{\mathbf{A}}}^r$ is the fused feature-driven graph under relation r, and ${\mathrm{ChannelAttn}}_{{\mathbf{W}}_c}(·)$ represents a parameterized channel attention layer with learnable weight ${\mathbf{W}}_c$. This layer applies channel-wise transformation and softmax normalization to assign adaptive weights to candidate graphs, allowing the fusion process to emphasize graph evidence most useful for fraud-relevant connectivity under each relation. The fused graph ${\tilde{\mathbf{A}}}^r$ is still derived mainly from feature-guided structural cues. Although these cues help reveal missing or denoised connections, the original adjacency matrix ${\mathbf{A}}^r$ still contains observed transaction relationships that should not be discarded entirely. To retain this observed structural prior while correcting its defects, we further combine the fused feature graph with the original relation graph to generate the final optimized adjacency:

$${\mathbf{A}}^{r\ast }={\mathrm{ChannelAttn}}_{{\mathbf{W}}_f}\left([{\tilde{\mathbf{A}}}^r;{\mathbf{A}}^r]\right)$$

(9)

where $[{\tilde{\mathbf{A}}}^r;{\mathbf{A}}^r]$ denotes the concatenation of the fused feature graph and the original adjacency along the channel dimension, ${\mathbf{A}}^{r\ast }$ is the final optimized adjacency matrix for relation r, and ${\mathrm{ChannelAttn}}_{{\mathbf{W}}_f}(·)$ is another channel attention layer parameterized by ${\mathbf{W}}_f$. This second fusion stage balances feature-derived structure and observed topology to reconstruct a more reliable relation graph, preserving trustworthy links while suppressing noisy edges and recovering missing fraud-relevant associations. After performing this adaptive fusion for all relation types, the optimized heterogeneous graph structure is obtained as:

$${\mathcal{G}}^{\ast }=(\mathcal{V},{\left\{{\mathbf{A}}^{r\ast }\right\}}_{r\in \mathcal{R}}).$$

Here, $\mathcal{V}$ is the node set and ${\left\{{\mathbf{A}}^{r\ast }\right\}}_{r\in \mathcal{R}}$ is the collection of optimized adjacency matrices over all relation types. The resulting graph ${\mathcal{G}}^{\ast }$ serves as the refined structural foundation of the HGSO-DVCL framework. This completes the graph structure optimization module by transforming imperfect financial transaction relations into a topology better aligned with feature evidence and observed interactions. The optimized graph then provides a cleaner and more fraud-discriminative foundation for downstream schema view and meta-path view representation learning.

4.3. Dual-View Contrastive Learning

To enhance the synergy and complementarity between different structural perspectives, the proposed framework encodes nodes from both the network schema view and the meta-path view, leveraging the node embeddings obtained under these two views for contrastive learning. Cross-view consistency constraints promote the fusion and complementarity of different structural semantics [37].

Network Schema View Encoder. After the graph structure optimization module produces the refined graph ${\mathcal{G}}^{\ast }$, the network schema view encoder learns node representations from direct type-constrained interactions in the optimized heterogeneous fraud graph. This view captures local relation-specific patterns. In transaction-level financial settings, such patterns may correspond to suspicious transaction links, abnormal account–merchant associations, or device-sharing behaviors. In HGSO-DVCL, it serves as the local structural representation branch and complements the higher-order semantic modeling of the meta-path view encoder in dual-view learning.

For a target node v, let ${\mathcal{N}}_t\left(v\right)$ denote the set of its neighbors of type t in the optimized graph ${\mathcal{G}}^{\ast }$, and let ${\mathbf{h}}_u$ denote the projected common-space feature of neighbor node u obtained from the graph structure optimization module. Since neighbors and neighbor types contribute differently to fraud discrimination, hierarchical attention is used for weighted aggregation at both node and type levels. At the node level, for neighbors of type t, the type-specific representation of node v is computed as:

$${\mathbf{z}}_v^t=\sigma \left(\sum _{u\in {\mathcal{N}}_t\left(v\right)}{\alpha }_{vu}^t·{\mathbf{h}}_u\right)$$

(10)

where ${\mathbf{z}}_v^t$ denotes the aggregated representation of node v from its type-t neighbors, $\sigma (·)$ is a nonlinear activation function, ${\mathbf{h}}_u$ is the projected feature of neighbor node u, and ${\alpha }_{vu}^t$ is the attention coefficient measuring the importance of neighbor u to node v under neighbor type t. This aggregation allows the model to emphasize more informative neighbors while suppressing less relevant ones, which is particularly helpful in financial fraud detection where even within the same relation type, some neighbors may carry stronger risk evidence than others. The node-level attention coefficient is defined as:

$${\alpha }_{vu}^t={\displaystyle \frac{exp\left({\mathbf{a}}_t^{\top }[{\mathbf{h}}_v\parallel {\mathbf{h}}_u]\right)}{{\sum }_{u^{\prime }\in {\mathcal{N}}_t\left(v\right)}exp\left({\mathbf{a}}_t^{\top }[{\mathbf{h}}_v\parallel {\mathbf{h}}_{u^{\prime }}]\right)}}$$

(11)

where ${\mathbf{h}}_v$ and ${\mathbf{h}}_u$ are the projected features of the target node v and its neighbor u, respectively, ${\mathbf{a}}_t$ is the learnable node-level attention vector associated with neighbor type t, and ‖ denotes vector concatenation. Softmax normalizes the attention scores over all type-t neighbors of node v. This makes neighbor contributions adaptive to both the target node and relation-specific context, allowing the encoder to focus on relevant local interaction signals. To reduce computation and maintain representation diversity, we adopt neighbor sampling: if $|{\mathcal{N}}_t\left(v\right)|$ exceeds a threshold, a fixed number of neighbors are randomly sampled; otherwise, repeated sampling is used. The resulting type-specific representations are then fused by type-level attention. The importance weight of type t is computed as:

$${\beta }_t={\displaystyle \frac{exp\left({\mathbf{q}}^{\top }tanh({\mathbf{W}}_s{\mathbf{z}}_v^t+{\mathbf{b}}_s)\right)}{{\sum }_{t^{\prime }\in \mathcal{A}}exp\left({\mathbf{q}}^{\top }tanh({\mathbf{W}}_s{\mathbf{z}}_v^{t^{\prime }}+{\mathbf{b}}_s)\right)}}$$

(12)

where ${\beta }_t$ denotes the importance of neighbor type t to the representation of node v, $\mathcal{A}$ is the set of node types, and $\mathbf{q}$, ${\mathbf{W}}_s$, and ${\mathbf{b}}_s$ are learnable parameters. This type-level fusion helps the model identify which neighbor categories are more informative for fraud detection, as signals from devices, merchants, linked accounts, or transaction counterparts may contribute differently across financial scenarios. The final network schema view representation of node v is then obtained as

$${\mathbf{e}}_v^{\left(s\right)}=\sum _{t\in \mathcal{A}}{\beta }_t·{\mathbf{z}}_v^t$$

(13)

where ${\mathbf{e}}_v^{\left(s\right)}$ denotes the schema view embedding of node v. By hierarchically aggregating optimized local interactions across neighbor instances and types, the network schema view encoder captures direct heterogeneous relational patterns and produces locally discriminative node embeddings. These embeddings form one branch of the dual-view representation for cross-view contrastive learning and final fraud classification.

Meta-Path View Encoder. While the network schema view encoder captures direct type-constrained interactions, it is limited to local relational patterns. Fraudulent behaviors often emerge through high-order semantic associations, such as shared merchants, devices, or multi-step relation chains. Therefore, the meta-path view encoder learns representations under different meta-paths on the optimized graph ${\mathcal{G}}^{\ast }$, providing a high-order semantic branch that complements the local structural representation and supports more comprehensive fraud pattern modeling.

For a target node v, given a set of m meta-paths $\mathcal{P}=\{P_1,P_2,\dots ,P_m\}$, let ${\mathcal{N}}_{P_k}\left(v\right)$ denote the set of meta-path-constrained neighbors of v under meta-path $P_k$. These neighbors are not defined by a single direct relation, but by composite relation sequences that encode higher-order semantic connectivity in the heterogeneous financial graph. A meta-path-specific graph encoder is then used to aggregate the semantic information associated with $P_k$:

$${\mathbf{z}}_v^{P_k}=\sum _{u\in {\mathcal{N}}_{P_k}\left(v\right)}{\displaystyle \frac{1}{\sqrt{d_v·d_u}}}{\mathbf{h}}_u$$

(14)

where ${\mathbf{z}}_v^{P_k}$ denotes the representation of node v under meta-path $P_k$, ${\mathbf{h}}_u$ is the projected feature of meta-path neighbor node u, and $d_v$ and $d_u$ are the degrees of nodes v and u, respectively, within the meta-path-induced graph. The normalization term ${\left(d_v{d}_u\right)}^{-1/2}$ reduces the influence of high-degree nodes and stabilizes aggregation across different meta-path structures. In this way, the encoder captures semantic dependencies from composite relational patterns beyond direct neighbors. This is important for fraud detection because coordinated fraud, relation camouflage, and cross-entity risk propagation are often better revealed through multi-hop semantic connections. Based on the m predefined meta-paths, the encoder produces m meta-path-specific representations $\{{\mathbf{z}}_v^{P_1},{\mathbf{z}}_v^{P_2},\dots ,{\mathbf{z}}_v^{P_m}\}$. Since different meta-paths may contribute unequally to fraud identification, a semantic-level attention mechanism is introduced to adaptively fuse them into the final meta-path view representation:

$${\mathbf{e}}_v^{\left(p\right)}={\displaystyle \sum _{k=1}^m}{\gamma }_k·{\mathbf{z}}_v^{P_k}$$

(15)

where ${\mathbf{e}}_v^{\left(p\right)}$ denotes the final meta-path view embedding of node v, and ${\gamma }_k$ is the attention weight that measures the importance of meta-path $P_k$ in the fusion process. This aggregation allows the model to emphasize semantic channels that are more informative for downstream fraud detection, rather than treating all meta-paths equally. The semantic attention weight ${\gamma }_k$ is computed as:

$${\gamma }_k={\displaystyle \frac{exp\left(\frac{1}{|{\mathcal{V}}_{\mathrm{target}}|}{\sum }_{v\in {\mathcal{V}}_{\mathrm{target}}}{\mathbf{p}}^{\top }tanh({\mathbf{W}}_p{\mathbf{z}}_v^{P_k}+{\mathbf{b}}_p)\right)}{{\sum }_{k^{\prime }=1}^{m}exp\left(\frac{1}{|{\mathcal{V}}_{\mathrm{target}}|}{\sum }_{v\in {\mathcal{V}}_{\mathrm{target}}}{\mathbf{p}}^{\top }tanh({\mathbf{W}}_p{\mathbf{z}}_v^{P_{k^{\prime }}}+{\mathbf{b}}_p)\right)}}$$

(16)

where ${\mathcal{V}}_{\mathrm{target}}$ denotes the target node set, and $\mathbf{p}$, ${\mathbf{W}}_p$, and ${\mathbf{b}}_p$ are learnable parameters. The exponential term measures the overall usefulness of meta-path $P_k$ over target nodes, and softmax converts these scores into relative importance weights. This enables the model to prioritize meta-paths that better capture fraud-relevant semantic associations, such as shared behavioral contexts or hidden collaborative structures.

By aggregating and adaptively weighting multiple meta-path-induced neighborhoods, the meta-path view encoder captures high-order semantic dependencies in heterogeneous financial networks, complementing the schema view encoder with broader semantic evidence beyond direct interactions. The resulting meta-path view embedding ${\mathbf{e}}_v^{\left(p\right)}$, together with the schema view embedding ${\mathbf{e}}_v^{\left(s\right)}$, forms the dual-view representation used in the subsequent cross-view contrastive learning module and the final fraud classification objective.

4.4. Joint Collaborative Optimization

After obtaining the optimized heterogeneous graph ${\mathcal{G}}^{\ast }$, the network schema view encoder and meta-path view encoder generate the local structural representation ${\mathbf{e}}_v^{\left(s\right)}$ and high-order semantic representation ${\mathbf{e}}_v^{\left(p\right)}$, respectively. Since these two views provide complementary fraud-relevant information, we adopt an end-to-end joint optimization strategy that integrates supervised classification, structure regularization, and cross-view contrastive learning [38]. This allows graph refinement to receive task-driven feedback while encouraging the dual-view encoders to learn discriminative and semantically consistent representations.

Supervised Classification Loss. The schema view representation ${\mathbf{e}}_v^{\left(s\right)}$ and the meta-path view representation ${\mathbf{e}}_v^{\left(p\right)}$ are first concatenated and then fed into a single-layer perceptron classifier to predict the fraud probability of node v:

$${\widehat{y}}_v=\mathrm{sigmoid}\left({\mathbf{W}}_o[{\mathbf{e}}_v^{\left(s\right)}\parallel {\mathbf{e}}_v^{\left(p\right)}]+{\mathbf{b}}_o\right)$$

(17)

where $[{\mathbf{e}}_v^{\left(s\right)}\parallel {\mathbf{e}}_v^{\left(p\right)}]$ denotes the concatenation of the two view-specific representations, ${\mathbf{W}}_o$ and ${\mathbf{b}}_o$ are learnable classifier parameters, and ${\widehat{y}}_v\in (0,1)$ denotes the predicted probability that node v is fraudulent. This prediction layer directly converts the complementary dual-view embeddings into a task-oriented fraud score, thereby linking representation learning to the final classification objective in financial fraud detection. The supervised classification loss is defined as the binary cross-entropy between the predicted fraud probability and the ground-truth label:

$${\mathcal{L}}_{\mathrm{cls}}=-\sum _{v\in {\mathcal{V}}_L}\left[y_{v}log{\widehat{y}}_v+(1-y_v)log(1-{\widehat{y}}_v)\right]$$

(18)

where ${\mathcal{V}}_L$ is the set of labeled nodes and $y_v\in \{0,1\}$ is the ground-truth label of node v. This loss drives the model to learn node representations that are directly useful for distinguishing fraudulent and legitimate entities in the heterogeneous financial graph.

Structure Regularization. Although graph structure optimization improves the heterogeneous transaction graph, unconstrained structure learning may overfit by producing overly dense or flexible patterns. To control complexity and encourage sparse, interpretable refinement, we impose an $L_1$ regularization term on the optimized adjacency matrices:

$${\mathcal{L}}_{\mathrm{reg}}=\sum _{r\in \mathcal{R}}{\parallel {\mathbf{A}}^{r\ast }\parallel }_1$$

(19)

where ${\mathbf{A}}^{r\ast }$ is the optimized adjacency matrix for relation type r, $\mathcal{R}$ is the set of relation types, and ${\parallel ·\parallel }_1$ denotes the element-wise $L_1$ norm. This regularization reduces unnecessary structural complexity, helping preserve informative fraud-relevant connections while preventing graph optimization from merely increasing structural capacity.

Cross-View Contrastive Loss. The two encoders capture different semantics of the optimized transaction graph: the schema view focuses on direct heterogeneous interactions, while the meta-path view models high-order semantic associations. Cross-view contrastive learning is introduced to make these views complementary yet semantically consistent for fraud detection. Specifically, the view-specific representations ${\mathbf{e}}_v^{\left(s\right)}$ and ${\mathbf{e}}_v^{\left(p\right)}$ are first projected by an MLP with a hidden layer into a contrastive space, yielding ${\tilde{\mathbf{e}}}_v^{\left(s\right)}$ and ${\tilde{\mathbf{e}}}_v^{\left(p\right)}$, respectively. This projection makes embeddings more suitable for contrastive alignment without constraining the classifier input space. Positive samples are selected by meta-path connectivity, encouraging semantically related nodes to be closer across views. The meta-path connection strength between nodes $v_i$ and $v_j$ is defined as:

$$c(v_i,v_j)={\displaystyle \sum _{k=1}^m}⊮[v_j\in {\mathcal{N}}_{P_k}\left(v_i\right)]$$

(20)

where $⊮[·]$ is the indicator function, ${\mathcal{N}}_{P_k}\left(v_i\right)$ denotes the neighbor set of node $v_i$ under meta-path $P_k$, and m is the number of predefined meta-paths. The value $c(v_i,v_j)$ counts how many meta-paths connect $v_i$ and $v_j$, and thus reflects the strength of their high-order semantic association. Candidate nodes are ranked according to $c(v_i,v_j)$, the top-K nodes form the positive sample set ${\mathcal{P}}_i^{+}$, and the remaining nodes form the negative sample set ${\mathcal{P}}_i^{-}$. For each anchor node $v_i$, we compute $c(v_i,v_j)$ between $v_i$ and candidate nodes of the target type. The top-K nodes with the largest meta-path connection strength are treated as positive samples, while the remaining nodes serve as negative candidates for training. This construction makes contrastive pairs depend on heterogeneous semantic connectivity rather than random augmentation, ensuring that positive pairs are selected based on fraud-relevant semantic evidence in the transaction graph. Using the network schema view representation as the anchor and the meta-path view representation as the contrast, the contrastive loss for node $v_i$ is defined as:

$${\ell }_i^{\left(s\right)}=-log{\displaystyle \frac{{\sum }_{j\in {\mathcal{P}}_i^{+}}exp\left(\mathrm{sim}({\tilde{\mathbf{e}}}_i^{\left(s\right)},{\tilde{\mathbf{e}}}_j^{\left(p\right)})/\tau \right)}{{\sum }_{j\in {\mathcal{P}}_i^{+}\cup {\mathcal{P}}_i^{-}}exp\left(\mathrm{sim}({\tilde{\mathbf{e}}}_i^{\left(s\right)},{\tilde{\mathbf{e}}}_j^{\left(p\right)})/\tau \right)}}$$

(21)

where $\mathrm{sim}(·,·)$ denotes cosine similarity and $\tau$ is the temperature coefficient controlling the concentration of similarity scores. This objective encourages the schema view embedding of node $v_i$ to be close to semantically related meta-path view embeddings while remaining separated from unrelated ones. A symmetric loss ${\ell }_i^{\left(p\right)}$ is computed by swapping the anchor and contrast views, so that both encoders are jointly aligned instead of constraining only one direction. The overall cross-view contrastive learning objective is:

$${\mathcal{L}}_{\mathrm{con}}={\displaystyle \frac{1}{2\left|\mathcal{V}\right|}}\sum _{v_i\in \mathcal{V}}\left({\ell }_i^{\left(s\right)}+{\ell }_i^{\left(p\right)}\right)$$

(22)

where $\left|\mathcal{V}\right|$ is the number of nodes in the graph. This loss enhances cross-view consistency and complementarity, making node representations more robust to structural noise and more sensitive to complex fraud patterns involving both local and high-order semantic evidence.

Total Objective. The final training objective combines the three loss terms as:

$$\mathcal{L}={\mathcal{L}}_{\mathrm{cls}}+\alpha {\mathcal{L}}_{\mathrm{reg}}+\beta {\mathcal{L}}_{\mathrm{con}}$$

(23)

where $\alpha$ and $\beta$ balance structure regularization and cross-view contrastive learning against the supervised classification objective. Minimizing this unified loss allows graph optimization, dual-view representation learning, and fraud classification to reinforce each other during training.

Overall, the joint collaborative optimization module coordinates HGSO-DVCL by linking structure refinement with fraud-oriented representation learning. As shown in Algorithm 1, the optimized graph improves dual-view embeddings, while supervised and contrastive objectives guide the graph and encoders toward robust and discriminative fraud modeling. Thus, the framework is trained under a unified task-aligned objective to produce structurally denoised, semantically complementary, and fraud-discriminative node representations.

Algorithm 1: Training Procedure of HGSO-DVCL

5. Experiments and Results

5.1. Datasets

Due to privacy protection, regulatory compliance, and commercial sensitivity of real financial transaction data, publicly available transaction-level heterogeneous risk control datasets remain relatively scarce. Following widely adopted practice in graph-based fraud detection, we use YelpChi [39] and Amazon [40] as two public multi-relational fraud detection benchmarks. Although they are not pure transaction-level financial datasets, they have been extensively adopted in recent graph fraud detection studies. These datasets contain multi-relation graph structures, noisy connections, severe class imbalance, and fraud node labels, which are consistent with the key modeling challenges addressed in this paper. Therefore, they provide reproducible and commonly accepted benchmarks for validating the proposed graph learning mechanisms.

The YelpChi dataset contains hotel and restaurant reviews from Yelp with three edge types: R-U-R (reviews by the same user), R-S-R (reviews of the same product with the same star rating), and R-T-R (reviews of the same product in the same month). The Amazon dataset contains product reviews for musical instruments with three relation types: U-P-U (users reviewing at least one common product), U-S-U (users with at least one identical star rating within a week), and U-V-U (users with top-5% mutual review TF-IDF similarity). The detailed statistics are presented in

Table 1. Statistical information of the datasets.

Dataset	Nodes	Edge Type	Edge Count	Imbalance
YelpChi	45,954	R-U-R	49,315	6:1
		R-S-R	3,402,743
		R-T-R	573,516
Amazon	11,944	U-S-U	3,566,479	10.5:1
		U-V-U	1,036,737
		U-P-U	175,608

. In the empirical benchmarks used in this paper, this general HIN is instantiated as multi-relational fraud graphs, where different edge types encode different review-based relational semantics rather than full transaction-level economic entities. Across these two benchmark datasets, heterogeneity is mainly reflected in multiple relation types constructed from review co-occurrence patterns. Therefore, in our experiments, the schema view and meta-path view encoders are used to model relation-specific semantics and relation-combination semantic patterns in multi-relational fraud graphs.

5.2. Experimental Setup

We follow the commonly used static benchmark setting for YelpChi and Amazon. The labeled nodes are divided into training, validation, and test sets using a stratified random split of 7:2:1. Hyperparameters are selected only on the validation set, and the test set is used only for final reporting. All reported results are averaged over 7 runs with different random seeds, and the mean and standard deviation are reported. Since the main purpose of this paper is to evaluate graph representation learning mechanisms under standard public benchmark protocols, we follow prior graph fraud detection studies and report F1-macro, AUC, and G-Mean. The specific setup details of the experiment are as follows:

(1) Target. To comprehensively evaluate the proposed HGSO-DVCL framework for financial fraud detection, our experiments are designed to answer the following research questions:

• RQ1: Can HGSO-DVCL achieve competitive fraud detection performance compared with representative baseline methods on public benchmark datasets?
• RQ2: Are the graph structure optimization module, the dual-view contrastive learning module, and the joint collaborative optimization strategy all effective in improving model performance?
• RQ3: How stable is HGSO-DVCL under different hyperparameter settings and meta-path configurations in terms of detection performance?

(2) Baselines. Since the main purpose of this paper is to evaluate graph representation learning mechanisms under standard public benchmark protocols, we follow prior graph fraud detection studies and report F1-macro, AUC, and G-Mean. To thoroughly evaluate the proposed method, representative baseline models spanning different technical approaches are selected:

• General GNN methods: The GAT and GraphSAGE serve as standard message-passing baselines to examine the applicability boundaries of attention-based and sampling-based aggregation mechanisms for fraud detection.
• Heterogeneous graph methods: The HAN [41] and DiffMG [42] evaluate the contributions of semantic-channel attention fusion and structural relation combination search for complex relational pattern modeling.
• Fraud-specific methods: The PC-GNN [43], CARE-GNN [44], and H2-FDetector [45] specifically target class imbalance, camouflage neighbor contamination, and the co-existence of homophilic and heterophilic neighborhoods.
• Graph anomaly detection methods: The GDN [46] and BWGNN [47] represent deviation learning and spectral filtering paradigms for enhancing sensitivity and robustness to anomalous behavior patterns.

(3) Environment. All experiments are conducted on a system equipped with an Intel Core i7-13600KF CPU, 64 GB RAM, and an NVIDIA RTX 3090 GPU, running Ubuntu 24.04 LTS. The implementation uses Python 3.9.12, PyTorch 1.13.1, and PyTorch Geometric 2.3.1. The Adam optimizer is used for all experiments. For the YelpChi dataset, the similarity threshold $ϵ$ is set to 0.7, the positive sample count K to 15, the temperature coefficient $\tau$ to 0.65, with ReLU activation, a learning rate of 0.001, a dropout rate of 0.2, a hidden dimension of 128, and 2 graph convolution layers. For the Amazon dataset, $ϵ=0.5$, $K=7$, $\tau =0.80$, with ReLU activation, a learning rate of 0.001, a dropout rate of 0.4, a hidden dimension of 128, and 3 graph convolution layers. The experimental environment configuration is summarized in

Table 2. Experimental environment configuration.

Item	Details
Operating System	Ubuntu 24.04 LTS
CPU	Intel Core i7-13600KF
RAM	64 GB
GPU	NVIDIA RTX 3090
Programming Language	Python 3.9.12
Deep Learning Framework	PyTorch 1.13.1
Graph Learning Library	PyTorch Geometric 2.3.1

. The thresholds and hyperparameters are selected on the validation set and then fixed for the test set. The similarity threshold $ϵ$ controls the sparsity of the optimized graph, K controls the number of semantic positives in contrastive learning, and $\tau$ controls the sharpness of contrastive similarity scores.

5.3. RQ1: Comparison Study

To answer RQ1, we compare HGSO-DVCL with representative baseline methods on the YelpChi and Amazon datasets. The baselines cover general GNN models, heterogeneous graph learning methods, fraud-specific detection models, and graph anomaly detection approaches. The comparison is conducted using three evaluation metrics, namely F1-macro, AUC, and G-Mean.

As shown in

Table 3. Performance comparison of different methods on the YelpChi and Amazon datasets (%). Bold values indicate the best results. Results are reported as mean ± standard deviation.

Method	YelpChi			Amazon
	F1-Macro	AUC	G-Mean	F1-Macro	AUC	G-Mean
GAT	49.03 ± 2.21	57.08 ± 0.31	16.82 ± 7.74	64.52 ± 3.94	80.96 ± 1.83	66.61 ± 13.58
GraphSAGE	54.51 ± 0.26	44.21 ± 1.58	42.04 ± 0.37	75.76 ± 0.45	64.30 ± 0.81	59.61 ± 3.52
HAN	55.63 ± 1.04	74.19 ± 0.10	64.29 ± 1.05	69.95 ± 1.23	84.22 ± 0.67	66.41 ± 1.12
DiffMG	73.18 ± 1.36	88.11 ± 1.50	78.57 ± 1.55	88.36 ± 0.51	92.90 ± 0.44	88.50 ± 0.60
PC-GNN	62.96 ± 2.03	79.84 ± 0.14	71.68 ± 1.22	89.67 ± 0.72	95.85 ± 0.14	90.36 ± 0.42
CARE-GNN	63.09 ± 0.90	76.65 ± 2.86	67.68 ± 3.45	86.76 ± 1.79	90.74 ± 1.63	70.52 ± 0.20
H2-FDetector	74.52 ± 2.37	89.36 ± 1.21	79.04 ± 2.61	87.05 ± 0.98	95.97 ± 0.71	91.63 ± 0.49
GDN	75.99 ± 0.62	90.24 ± 0.73	80.85 ± 0.09	90.71 ± 0.44	97.08 ± 0.14	90.78 ± 0.12
BWGNN	77.05 ± 0.90	90.51 ± 0.43	76.94 ± 1.10	91.84 ± 0.81	97.42 ± 0.42	90.07 ± 0.35
HGSO-DVCL	80.62 ± 0.88	92.96 ± 0.52	79.41 ± 0.46	91.12 ± 0.67	98.01 ± 0.24	92.44 ± 0.39

, HGSO-DVCL achieves competitive performance on both datasets. On YelpChi, it obtains the best F1-macro of 80.62% and the best AUC of 92.96%, while achieving a G-Mean of 79.41%. On Amazon, it achieves the best AUC of 98.01% and the best G-Mean of 92.44%, with an F1-macro of 91.12%. Compared with the strongest baseline BWGNN, HGSO-DVCL improves F1-macro by 3.57% and AUC by 2.45% on YelpChi. On Amazon, it improves AUC by 0.59% and G-Mean by 2.37%, while remaining competitive in F1-macro. These results show that HGSO-DVCL performs favorably against representative methods on the evaluated benchmark datasets and achieves strong overall benchmark performance.

In summary, the comparison results provide a positive answer to RQ1, showing that HGSO-DVCL is competitive with representative baselines under the adopted public benchmark setting.

5.4. RQ2: Ablation Study

To answer RQ2, we conduct ablation experiments to evaluate the contribution of each core component in HGSO-DVCL, including the graph structure optimization module, the cross-view contrastive learning module, and the joint collaborative optimization strategy. Specifically, we compare the full model with three degraded variants: ➊ w/o StructOpt, which removes the graph structure optimization module; ➋ w/o CL, which removes the cross-view contrastive learning module; and ➌ w/o Joint, which removes the joint collaborative optimization strategy. The results are reported in Figure 4.

As shown in Figure 4, the full model achieves the best overall results across the evaluated metrics. Among the ablated variants, removing the graph structure optimization module leads to the largest performance drop on both datasets. On YelpChi, F1-macro, AUC, and G-Mean decrease to 77.3%, 90.8%, and 75.9%, respectively. On Amazon, the corresponding metrics decrease to 89.7%, 97.2%, and 90.7%. In comparison, removing the contrastive learning module yields 78.5%, 91.6%, and 77.1% on YelpChi, and 90.1%, 97.5%, and 91.2% on Amazon. Removing the joint collaborative optimization strategy gives 79.0%, 91.5%, and 77.5% on YelpChi, and 90.4%, 97.4%, and 91.6% on Amazon.

To more carefully isolate the contribution of each component, we further conduct a fine-grained ablation study. In addition to the original degraded variants, we evaluate the following model variants: ➊ w/o StructOpt removes the entire heterogeneous graph structure optimization module and directly performs dual-view representation learning on the original graph; ➋ w/o ChannelAttn replaces channel attention fusion with average fusion; ➌ Schema view only removes the meta-path view encoder; ➍ Meta-path view only removes the network schema view encoder; ➎ w/o CL removes the cross-view contrastive loss while keeping the dual-view encoders and the supervised classification objective; ➏ w/o Meta-path Attn replaces meta-path-level attention with uniform averaging; ➐ w/o Joint disables the joint collaborative optimization strategy by training the graph optimization and representation learning components in a separated manner, rather than updating them under a unified end-to-end objective.

These variants allow us to separately examine the effects of graph structure optimization, adaptive channel fusion, dual-view representation learning, contrastive alignment, meta-path attention, and joint collaborative optimization. As shown in Figure 5, the full HGSO-DVCL model achieves the best overall performance on both datasets. Removing the graph structure optimization module causes the largest performance degradation. On YelpChi, the F1-macro, AUC, and G-Mean decrease from 80.6%, 93.0%, and 79.4% to 77.3%, 90.8%, and 75.9%, respectively. On Amazon, the corresponding scores decrease from 91.1%, 98.0%, and 92.4% to 89.7%, 97.2%, and 90.7%. This confirms that structure refinement is the most influential component.

Overall, all three ablated variants perform worse than the full model on both datasets, which provides a positive answer to RQ2 and shows that each component contributes positively to the final fraud detection performance.

5.5. RQ3: Sensitivity Analysis Study

To answer RQ3, we analyze four key hyperparameters in HGSO-DVCL: the joint weight $\alpha$, the temperature coefficient $\tau$, the optimization threshold $ϵ$, and the positive sample count K. Each hyperparameter is varied within a predefined range while the others are fixed, and F1-macro, AUC, and G-Mean are reported on both datasets.

The joint-weight and temperature-coefficient sensitivity experiment examines the impact of $\alpha$ and $\tau$ on model performance, which is shown in Figure 6. On YelpChi, the best overall performance is achieved at $\alpha =0.3$, while on Amazon the best results are obtained at $\alpha =0.4$. For the temperature coefficient $\tau$, the best overall performance appears at $\tau =0.65$ on YelpChi and $\tau =0.8$ on Amazon. Across both datasets, the three evaluation metrics vary within a relatively narrow range as $\alpha$ and $\tau$ change, indicating that the model maintains stable performance under different settings of these two parameters.

The optimization-threshold and positive-sample-count sensitivity experiment evaluates the effect of $ϵ$ and K on fraud detection performance, which is shown in Figure 7. For the optimization threshold $ϵ$, the best overall results are achieved at $ϵ=0.7$ on YelpChi and $ϵ=0.5$ on Amazon. For the positive sample count K, the best overall performance is obtained at $K=15$ on YelpChi and $K=7$ on Amazon. In both datasets, performance first improves and then declines slightly as $ϵ$ and K increase, showing that excessively small or large values are less effective than moderate settings.

To further examine whether HGSO-DVCL relies excessively on a specific meta-path, we conduct a meta-path leave-one-out sensitivity analysis. For each dataset, we remove one meta-path at a time and compare the performance with that obtained using the full meta-path set. The reported values denote the performance change relative to the full setting, where negative values indicate performance degradation. As shown in Figure 8, removing any single meta-path leads to performance degradation, indicating that different meta-paths provide complementary semantic information. On YelpChi, removing R-S-R causes the largest decrease, with F1-macro, AUC, and G-Mean dropping by 1.8, 1.2, and 2.0 percentage points, respectively. Removing R-U-R and R-T-R also reduces performance, but the degradation is relatively smaller. On Amazon, removing U-S-U leads to the largest decrease, with drops of 1.2, 0.8, and 1.2 percentage points on the three metrics, respectively. Overall, the full meta-path setting consistently achieves the best performance, while the performance does not collapse after removing one meta-path. This suggests that HGSO-DVCL benefits from multiple semantic relations and has moderate robustness to meta-path selection.

Overall, all hyperparameters influence model performance to varying degrees, and the current parameter settings achieve competitive results across both datasets, validating the reasonableness of the parameter selection.

5.6. Discussion

The experimental results collectively show that HGSO-DVCL achieves strong and consistent fraud detection performance across the two benchmark datasets. The comparison study indicates that the proposed framework is particularly competitive in terms of AUC and balanced detection performance, suggesting that it is effective not only at separating fraudulent and legitimate nodes globally, but also at maintaining a better trade-off between fraud identification and normal-sample recognition under class-imbalanced conditions. This is consistent with the design objective of HGSO-DVCL, which does not rely solely on local neighborhood aggregation, but instead combines graph refinement and dual-view semantic modeling to improve the quality of learned node representations. For reference, runtime and memory information for HGSO-DVCL is provided in Appendix B.

The ablation study clarifies the contribution of each component. Removing the graph structure optimization module causes the largest performance drop, showing the importance of refining unreliable topology for fraud detection. Replacing channel attention with average fusion also reduces performance, indicating that adaptive fusion is more effective than treating structural channels equally. The two single-view variants underperform the full model, confirming the complementarity between the network schema and meta-path views. Removing contrastive learning weakens the model, suggesting that cross-view alignment helps maintain semantic consistency. The degradation caused by removing meta-path attention shows that different meta-paths contribute unequally and should be adaptively weighted. Finally, the performance drop of w/o Joint indicates that end-to-end coordination among graph refinement, dual-view representation learning, and classification brings additional benefits.

The results also reveal meaningful dataset-dependent patterns. On YelpChi, the gains of HGSO-DVCL over strong baselines are more pronounced, especially on F1-macro and AUC. This suggests that the proposed framework is particularly effective when the graph contains stronger structural noise or more complex heterogeneous associations, where relation-specific graph refinement and dual-view modeling can provide clearer advantages. On Amazon, the improvements are smaller in magnitude but remain consistent on key metrics, especially AUC and G-Mean. This indicates that when the underlying graph is relatively easier to model or existing baselines already perform strongly, the proposed framework still offers a more balanced and reliable decision boundary. Taken together, these observations suggest that the benefit of HGSO-DVCL is not tied to a single metric or a single dataset, but comes from its ability to improve both graph quality and representation quality in a coordinated manner.

The sensitivity analysis provides additional support for the proposed design. Across the hyperparameter experiments, HGSO-DVCL shows relatively stable trends, and the best results are generally obtained with moderate parameter values rather than extreme settings. This is consistent with the design intuition that structural regularization, contrastive temperature, graph optimization threshold, and positive sample count should balance useful signal preservation with noise control. The meta-path leave-one-out analysis further shows that removing any single meta-path leads to performance degradation, indicating that different meta-paths provide complementary semantic information. In particular, the larger drops caused by removing R-S-R on YelpChi and U-S-U on Amazon suggest that some semantic relations are more informative than others, while the absence of performance collapse shows that the model does not rely exclusively on one specific meta-path. Overall, these observations suggest that the proposed framework is not overly sensitive to narrow hyperparameter choices or a single meta-path configuration, and that its performance improvements mainly come from the combined design of structure optimization, dual-view representation learning, and adaptive semantic fusion.

Several limitations. First, the experiments are conducted on public multi-relational fraud benchmarks rather than proprietary transaction-level financial data. Although YelpChi and Amazon share several modeling challenges with financial fraud scenarios, such as structural noise, class imbalance, and heterogeneous relations, they cannot fully represent real financial systems involving accounts, cards, merchants, devices, and institution-specific risk-control processes. Therefore, the current results should be interpreted as evidence for the proposed graph learning mechanisms under reproducible benchmark settings, rather than as direct proof of deployment readiness in real-world financial transaction networks. Second, the current framework operates on static graph snapshots and does not explicitly model the temporal evolution of fraud behaviors, which may limit its applicability under concept drift and evolving fraud strategies. Third, the scalability of HGSO-DVCL on very large heterogeneous transaction graphs with millions of nodes and edges remains to be further investigated, especially because relation-specific structure optimization and contrastive positive-pair construction may introduce additional computational cost. Fourth, although attention weights provide some clues about relation and meta-path importance, the framework does not yet offer fine-grained explanations for individual fraud predictions, which is important for high-stakes financial decision-making. Finally, under highly imbalanced fraud settings, contrastive learning may still suffer from noisy positive pairs if semantic proximity does not always imply similar risk patterns. Future work will therefore focus on temporal-aware graph structure optimization, efficient large-scale training strategies, more reliable contrastive sample construction, interpretable fraud evidence extraction, and validation on real-world financial fraud datasets.

6. Conclusions

This paper proposed HGSO-DVCL, a heterogeneous graph structure optimization framework with dual-view contrastive learning for fraud detection. The framework addresses three key challenges in graph-based fraud detection, namely unreliable heterogeneous graph structures, insufficient single-view representation learning, and the disconnection between graph refinement and downstream classification. Specifically, it combines type-aware graph structure optimization, dual-view representation learning from the network schema and meta-path perspectives, and an end-to-end joint optimization objective within a unified framework. Experimental results on the YelpChi and Amazon datasets support the effectiveness and component-wise validity of HGSO-DVCL under public multi-relational fraud detection benchmark settings.

Overall, the results suggest that jointly improving graph structure quality and multi-view representation quality is a promising direction for heterogeneous graph-based fraud detection. Since the current experiments do not include transaction-level financial networks or temporal holdout evaluation, the findings should not be interpreted as direct evidence of deployment readiness in real-world financial systems. Future work will focus on temporal fraud dynamics, large-scale training efficiency, cost-sensitive evaluation, and validation on real-world financial transaction datasets.