Strategy-Architecture Synergy: A Multi-View Graph Contrastive Paradigm for Consistent Representations

1 Introduction

Advancements in multimedia technologies have enabled diverse data collection ways, capturing rich and multi-faceted information. For instance, in multimedia analysis, complementary information can be captured via images, audio, and textual descriptions of the same content. Such data deriving from different sources can be modeled as multi-view data [Wan et al., 2024b; Xu et al., 2025a; Zhuang et al., 2024]. Numerous traditional multi-view learning methods have been proposed, aiming to integrate these complementary views into cohesive representations [Zhang et al., 2025; Fu et al., 2023]. However, they struggle to model the complex intrinsic relationships among samples, particularly when such relationships extend beyond the feature space. In real-world scenarios, samples often exhibit interdependencies and intricate semantic relationships, making graph data a universal way to model these complex connections [Wu et al., 2023b; Tu et al., 2025]. By structuring multi-view data into graphs, latent relationships can be effectively captured and utilized.

∗Corresponding Author.

Graph Contrastive Learning (GCL), as an unsupervised paradigm for graph-structured data analysis, leverages unlabeled samples to provide rich information [Li et al., 2023; Zhuang et al., 2025]. Notably, multi-view graph data, with its inherent multiple views as augmentations, is naturally well-suited for GCL. However, the development of GCL for multi-view data is still in its early stages [Liu et al., 2023a; Wang et al., 2023]. Contrastive learning follows the "augmentation-contrast" paradigm, where augmentations and contrastive strategies are interdependent. Typically, augmentations are handcrafted to align with the contrastive objective. For instance, the contrastive objective in GRACE [Zhu et al., 2020] aims to maximize the mutual information between identical nodes across two augmented views. To achieve this, it employs perturbation strategies like edge dropout and feature masking to generate two lightly corrupted views for contrastive learning. Similarly, the contrastive objective in DGI [Velickovic et al., 2019] is to maximize the mutual information between patch-summary pairs, using stochastic corruption techniques, such as feature shuffling, to introduce negative samples.

However, directly applying the GCL paradigm to multiview graphs is suboptimal, as traditional GCL methods fail to account for the intricate heterogeneity inherent in multiview scenarios. Specifically, in contrastive learning, multiple views are typically generated through manually defined perturbations, often utilizing simple, controllable transformations where the relationships between views are explicit and relatively straightforward to model. In contrast, the views inherent to multi-view data exhibit complex consistency and complementarity relationships that are difficult to capture [Sun et al., 2024; Wang et al., 2021]. These relationships encompass view-shared, view-specific task-relevant, and viewspecific task-irrelevant information, which defy traditional quantification and modeling paradigms. Directly treating these multiple views as augmentations neglects potential distributional discrepancies and alignment issues, which may result in the shared GNN encoder failing to learn the desired representations across heterogeneous views. Thus, preprocessing strategies tailored for multi-view data are essential to make the discrepancies and interdependencies between views more manageable. Moreover, the contrastive objective and model architecture in GCL also lack consideration of the complexities of multi-view data and graph-specific properties, resulting in incomplete or potentially erroneous information interactions.

Based on the above analysis, we aim to design a novel contrastive learning paradigm tailored for multi-view graph data. Two key challenges remain for contrastive learning in the multi-view context: (1) Strategically, how to design a preprocessing strategy that better aligns multiple views with GCL and a contrastive strategy that captures richer information? (2) Structurally, how to design a model architecture that is well-suited for multi-view graphs?

To tackle these challenges, we propose a novel multiview learning framework, termed Consistency-Aware Multiview graph contrastivE Learning (CAMEL), which integrates meticulously designed strategies and architecture specifically tailored for multi-view graph data. Through rigorous mathematical analysis, we first reveal that the edge-dropping preprocessing promotes the consistency of multi-view representations. Moreover, we quantify the relationship between the impact of edge-dropping operations and the reweighting factor. To better learn consistency information and adapt to the heterogeneity across various views, we develop a learnable model architecture that enables each view to autonomously assimilate information and select the most suitable structure. Naturally, an adaptive edge-dropping preprocessing strategy is designed, where edge-dropping operations are steered by adaptive topology to ensure compatibility across different views. Finally, we introduce a neighborhood consistency multi-view contrastive strategy that redefines the construction of positive and negative pairs by considering graph properties. Specifically, the first-order neighbors of the anchor node, both within the same view and across views, are expanded as positive samples, facilitating the flow of consistency information. The flowchart of CAMEL is shown in Figure 1. Our contributions are summarized as

• We conduct a theoretical analysis that confirms edge dropping preprocessing promotes consistency learning and quantifies the factors influencing consistency.
• We propose a novel contrastive paradigm focused on multi-view graph data, termed CAMEL, which integrates a learnable model architecture with an adaptive edge-dropping preprocessing strategy and a neighborhood consistency multi-view contrastive objective.
• Extensive experiments on three types of datasets demonstrate the superiority of the proposed framework compared to state-of-the-art multi-view GNNs.

2 RelatedWork

2.1 Graph Contrastive Learning

Graph Contrastive Learning (GCL) has emerged as a pivotal research direction in graph data learning, focusing on maximizing mutual information between positive pairs while minimizing it for negative pairs. The core research focus of GCL lies in designing graph augmentation strategies, with edge deletion and attribute masking as the most prevalent techniques [Zhu et al., 2020; Liu et al., 2024b; Bu et al., 2024]. Besides, some methods employ contrastive losses commonly used in computer vision, such as InfoNCE and Triplet loss [Wu et al., 2022; Koromilas et al., 2024], to extract the shared core information across different augmented views, following the InfoMax principle. Despite the significant advancements in GCL, the standard paradigm still faces some limitations, particularly with regard to graph augmentations and contrastive objectives. Thus, other novel graph enhancement paradigms have also been proposed to expand the range of augmentation techniques. For instance, [Shen et al., 2023] adopts a multi-head graph attention mechanism to learn graph augmentations. Other notable approaches include motif centrality-based adaptive augmentations [Li et al., 2023] and similarity-preserving adversarial augmentations [In et al., 2023]. Nonetheless, the utilization of GCL for multi-view data is notably limited, primarily due to a critical shortage of augmentation and contrastive strategies that are tailored specifically for such datasets.

2.2 Multi-view Learning

Multi-view learning aims to integrate and encode information frommultiple sources to derive a low-dimensional representation that captures both the consistency and complementarity across different views. Graph-based multi-view learning [Wan et al., 2024a; Lu et al., 2024; Wu et al., 2024], with its superior capability to model complex relationships, has become a widely adopted learning paradigm. For instance, [Liang et al., 2022] defines a min-max formulation for robust learning that addresses issues of local optima. [Huang et al., 2023] enhances the graph-based multi-view model by utilizing an attention allocation approach and a sample-weighting strategy. Recent methodologies have also introduced contrastive techniques into multi-view learning to harness and contrast the unique features from each view. For instance, [Shen et al., 2023] introduces a contrastive multi-view kernel that implicitly embeds the views into a joint semantic space, while [Su et al., 2024] builds on this to address the issue of false negatives. Despite the notable strides of these GCLincorporated approaches in capturing graph-specific characteristics, their reliance on empirically derived heuristics and lack of theoretical rigor may limit generalization across diverse tasks and datasets.

3 ProposedMethod

3.1 Preliminaries and Notations

Let G = {G v }Vv=1 denote a multi-view graph, where V is the number of views and G v is the v-th view data. The feature matrix X ∈ Rn×m contains the node information, with each node having an m-dimensional feature vector. For the v-th view G v = (V, E v ), where V is the node set with |V| = n and E v ⊆ V × V is the edge set. The adjacency matrix of v-th view is defined as Av ∈ {0, 1}n×n with the degree matrix Dv , where dvi = ∑j Avij and Avij = 1 iff (vi, vj) ∈ E v .

GCL aims to maximize the agreement of representations across views, which naturally fits the processing of multiview data. Unlike conventional CL, Graph contrastive multiview learning treats multi-view data as a natural augmentation of samples. Specifically, pair construction is generated by categorizing the instances from identical samples as positive pairs and the others as negative [Liu et al., 2023b]. Typically, each view graph is first encoded by a shared GNN encoder to obtain normalized data representations, denoted as Zv = fΘ(Av ,X). Following InfoNCE [Oord et al., 2018], the loss for the i-th data sample between the v-th and v′ -th view can be defined as

where θ is a similarity measure defined over node representations and τ is a temperature parameter. The encoder fΘ can be substituted into any GNN model. Typically, the i-th node representation in the v-th view can be generalized using a basic form of message passing in single-layer GNN encoders:

where γ v ij is the weight for message passing trough the edge (vi, vj), termed reweighting factor, and is exemplified in vanilla GCN as γ v i,j = 1 √didj .

3.2 Consistency Analyses on Preprocessing

Based on the previous analysis, directly treating the views inherent in multi-view data as augmentations is unreasonable. Here, inspired by [Xu et al., 2025b], a theoretical analysis is conducted to explore the impact of view preprocessing on the consistency information within multi-view graphs. Initially, the Disruptive Index in each view can be evaluated by tracking the propagation of information through non-consensual edges, as defined by the following:

Definition 1 (Disruptive Index). Given a multi-view graph G v = (V, E v ), the Disruptive Index (DI) quantifies the extent to which each view hinders consistent decision-making across views, defined as

where Ni denotes the neighbor set of node i, N non i ⊆ Ni is the subset of neighbors connected by edges that hinder consensus learning, i.e., non-consensual edges. Conversely, the consensual edge set are defined as the edges in Ni \ N non i , which positively contribute to multi-view learning.

After DI is defined for each view based on the ratio of nonconsensual information, the effective preprocessing strategy seeks a smaller DI. Here, we focus on commonly used edge perturbation techniques, analyzing their impact on enhancing representation consistency across views and mitigating the negative influence of non-consensual edges. Specifically, we examine the effect of dropping or adding an arbitrary edge (a, b) ∈ E v on DI. Let ˜Iv denote the DI of the modified view with the corresponding reweighting factor ˜ γ v ij , the change of DI can be further represented as

Assume s = ∑i∈V ∑j∈Ni γ v ij and ˜ s = ∑i∈V ∑j∈Ni ˜ γ v ij , we deduce the following quantification operator ω as

which satisfies ω ∝ ∆, effectively reflecting the change in non-consensual information within the view. To further explore the changes of DI, we precisely quantify ω:

Lemma 1. Assuming each node vi in the view receives nonconsensual information at a ratio m relative to total information, it can be derived that:

The full derivation of Eq. (5) and Lemma 1 can be found in Appendix B. Overall, combining (5) and (6), the following theorem can be deduced:

Theorem 1. When any edge (a, b) ∈ E v is dropped or added from a graph G v , it results in:

For edge-dropping, the following holds:

For edge-adding, the following holds:

Assuming that the DI for the views in multi-view data is below 0.5, i.e., m < 0.5, which is typical in most cases, we observe the following effects of edge perturbation: For edgedropping, If the dropped edge is non-consensual, ∆ < 0, indicating an improvement in consistency with a greater consistency gain; If the dropped edge is consensual, ∆ > 0, resulting in disruption in consistency, but with less significant damage. Edge dropping results in a larger consistency gain than loss, while the trend is reversed for the edge adding operation. Thus, Theorem 1 confirms that edge dropping promotes consistency learning more effectively than edge adding.

3.3 Adaptive Edge-dropping GNNArchitecture

Following the theoretical analysis indicating that edgedropping promotes multi-view consistency learning, thus we adopt edge-dropping as a preprocessing step for each view. As per Theorem 1, the change in DI satisfies ∆ ∝ γ v ij , motivating the use of γ v ij to control edge-dropping. Previous GCL models employing GNN encoders indiscriminately smooth all node representations within a neighborhood, often struggling to accommodate the heterogeneity of multiview data. Therefore, we propose a more general and flexible model architecture suitable for multi-view contexts, adopting an adaptive reweighting factor γ v ij = ηv ij /√didj, where ηv ij ranges between 0 and 1. It enables nodes to selectively assimilate information during message passing across diverse views. Specifically, we employ a gating mechanism to learn ηv ij :

where σ(·) is the activation function, W ∈ R2F ′ is a trainable weight matrix with the hidden uints F ′ . Combining reweighting factors with Theorem 1, the probability of an edge (vi, vj ) being dropped is guided by the reweighting factor as follows:

where α is a hyper-parameter used to control the drop probability, and pτ is a cutoff probability that does not exceed 1. Based on the edge-dropping probability pvij , a masking variable svij can be sampled, whose value is drawn from a Bernoulli distribution: svij ∼ B(pvij ). The reweighting factor can be computed as γ v ij = (1-svij )·γ v ij if svij = 1 and γ v ij = 0 otherwise, with the probability of svij = 1 determined by pvij .

For each v-th view, a single-layer learnable GNN encoder fΘ(·) learns the embedding of each node by aggregating the embeddings of its neighbors with adaptive structure summarized as:

where (1 - β) is added for the trade-off between self feature and message from neighbors. The advantages of the proposed adaptive edge-dropping architecture method can be summarized as follows: (1) The edge-dropping preprocessing promotes multi-view consistency, ensuring that the discrepancies between views are controllable, in accordance with the theoretical analysis. (2) Unlike fixed structures, the shared learnable model architecture enables each view to autonomously adapt and discover an optimal structure tailored to its specific needs, without relying on prior knowledge. (3) The edge-dropping operation is highly related to the dynamically learned topology, enabling compatibility with each individual view.

3.4 Neighborhood ConsistencyMulti-View Contrastive Objective

Multi-view data modeled as graphs inherently exhibit graph properties like homogeneity, where connected nodes often share the same label. However, the pairing strategy in Eq. (1), which designates instances from the same sample as positive pairs while treating all others as negatives, risks separating nodes linked by consensual edges. To address this issue, we propose a neighborhood consistency contrastive objective tailored for multi-view graph data, redefining the construction of positive and negative pairs. Specifically, we expand positive samples by incorporating the first-order neighbors of anchors within the same view and across different views. The loss of the i-th data sample between the v-th and v′ -th view as defined in Eq. (1) can also be represented as:

In the proposed contrastive objective, the positive pairs and the negative pairs are reconstructed based on the first-order neighborhood:

where N v i , N v′ i are the neighbor sets of node i in view v and v′ . Specifically, with zv i as the anchor, positive pairs are not only derived from the instance zv′ i in a different view v′ but also incorporate neighbors from both the same and across views, i.e., {zv j |j ∈ N v i } and {zv′ j |j ∈ N v′ i } respectively. Naturally, all non-neighbors of sample i across view v and v′ serve as intra-view and inter-view negatives. Expanding positive samples through neighborhood structures harnesses the full topological information, especially the consensual edges, to capture the consistency and complementarity both within and across views.

Since any data view can be considered a semantic augmentation of another, we randomly choose one view as the pivot view, termed zp . The rationale behind constructing the loss in this manner is detailed in Appendix C. The overall loss is then implemented as the sum of the losses between the pivot view and the other views, as follows:

The algorithm procedure of CAMEL is given in Appendix A.

4 Experiments

4.1 Experimental Settings

Dataset. To assess the performance of CAMEL, we conduct experiments on three types of datasets, including four multi-relational datasets (ACM, DBLP, IMDB, YELP), two multi-attribute datasets (COIL20, NoisyMNIST), and two multi-modality datasets (Iaprtc12, NUS-Wide).

Compared Methods. We compare CAMEL with twentyone representative methods, categorized as follows: (1) Baseline methods: GCN [Kipf and Welling, 2017] and SGC [Wu et al., 2019]; (2) Heterogeneous methods: HAN [Wang et al., 2019], DMGI [Park et al., 2020], IGNN [Gu et al., 2020], MRGCN [Huang et al., 2020], SSDCM [Mitra et al., 2021], MHGCN [Yu et al., 2022], and AMOGCN [Chen et al., 2024]; (3) Multi-view classification methods: ERLMVSC [Huang et al., 2021], Dynamics [Han et al., 2022], PDMF [Xu et al., 2023], IMvGCN [Wu et al., 2023a], LGCN-FF [Chen et al., 2023a], and RCML [Xu et al., 2024]; (4) Multi-view clustering methods: OMSC [Chen et al., 2022], SDSNE [Liu et al., 2022], DSMVC [Tang and Liu, 2022], FSMSC [Chen et al., 2023b], RCAGL [Liu et al., 2024a], and SMVAGC [Wang et al., 2024].

Experimental Settings. The implementation details and parameter settings are introduced in Appendix D.

4.2 Node Classification Performance

In this section, we explore semi-supervised classification tasks, evaluating the efficacy of CAMEL in processing complex data across three types of multi-view graphs: (1) Multirelational Graphs. Classification results for four multirelational graphs, with a training ratio of 20%, are detailed in Table 1. From these results, we can see that CAMEL surpasses most methods designed for multi-relational data, affirming its effectiveness. Furthermore, CAMEL considerably outperforms baseline models like GCN and SGC, illustrating that static architectures are ill-equipped to manage the heterogeneity inherent in complex datasets. (2) Multi-attribute and multi-modality Graphs. We run six multi-view classification methods with a training rate of 10%, and the results are presented in Table 2. It can be observed that graph-based methods dominate the performance landscape, underscoring the pivotal role of leveraging relational information between multi-view samples for performance improvement. Among these, CAMEL achieves superior results through its adept adaptation to the heterogeneity of multi-view data, supported by the advanced contrastive strategy and model architecture.

4.3 Node Clustering Performance

In this section, we assessed node clustering performance on multi-attribute datasets COIL20 and NoisyMNIST, along with multi-modality datasets Iaprtc12 and NUS-wide. Table 2 indicates that CAMEL substantially exceeds the performance of state-of-the-art clustering methods on both ACC and NMI metrics, confirming the efficacy of the proposed contrastive paradigm in producing distinguishable representations. The superior clustering outcomes stem primarily from CAMEL enhancing connectivity density among node pairs distanced from estimated decision boundaries, facilitating the formation of compact, well-defined clusters.

4.4 Visualization

Beyond quantitative analysis, we also visualize the representations derived by the competitive baseline algorithm AMOGCN and the proposed method CAMEL in Figures 2 on the ACM and DBLP datasets using t-SNE [Van der Maaten L, 2008]. Contour lines within colored shaded areas indicate the density levels of different classes. Moreover, the histograms positioned at the top and right sides of each plot illustrate the distribution of t-SNE-transformed data along the X and Y axes, respectively. From the visualizations, it is observed that the embeddings generated by CAMEL show distinctly clearer class boundaries and tighter intra-class cohesion than those by AMOGCN. This distinction is observable in the density plots, where CAMEL's embeddings show reduced class overlap and more distinct peaks within each class's distribution. The histograms complement these findings by presenting a more noticeable separation along both axes. These results show that CAMEL excels in learning high-quality node representations, as evidenced by its ability to produce representations with well-defined and separate class clusters.

4.5 Hyperparameter Analysis

In this subsection, we conduct parameter sensitivity to explore the impact of α in Eq. (11) and β in Eq. (15) on model performance. Specifically, α modulates the adaptive edge-dropping probability, while β regulates the balance between self-features and neighbor messages in the learnable GNN encoder. Generally, α shows peak performance at midrange values across the datasets, indicating that moderate edge-dropping efficiently captures critical semantic information and promotes consistent learning in multi-view data. As α and β values vary, the performance exhibits stable fluctuations across most datasets, reflecting the CAMEL framework's insensitivity to parameter changes. Notably, both α and β yield suboptimal performance when set to zero, especially in the IMDB, highlighting the pivotal role of the adaptive edge-dropping architecture in optimizing model efficacy.

4.6 Ablation Study

To evaluate the importance of each component in CAMEL, we conducted ablation experiments by removing key elements: edge-dropping (denoted as E), the adaptive edgedropping architecture (denoted as AE), and the neighborhood consistency multi-view contrastive objective (denoted as N). Specifically, to evaluate the adaptive edge-dropping architecture, we replaced the encoder with a vanilla GCN. For the contrastive objective evaluation, we used the contrastive loss from the classic GCL method GRACE [Zhu et al., 2020]. The results of these experiments are shown in Figure 4. Notably, removing the adaptive edge-dropping architecture (w/o AE) leads to a sharp performance drop, highlighting the superiority of the learnable architecture in adapting to heterogeneous views. Subsequently, the absence of either the edge-dropping preprocessing or the contrastive objective results in a certain decrease in performance. Overall, CAMEL consistently outperforms each variant, validating its ability to effectively leverage consistency and complementarity across views.

5 Conclusion

In this paper, we reveal that multi-view graph contrastive learning requires preprocessing, with the edge-dropping strategy promoting consistency supported by mathematical derivation. Inspired by these findings, we introduce a multiview contrastive paradigm called CAMEL, which synergistically enhances both strategy and architecture to learn consistent representations. On the strategic side, the proposed adaptive edge-dropping preprocessing strategy, guided by dynamic topology, along with the neighborhood consistency contrastive objective, effectively extracts consistency information from multi-view data. On the architectural side, the learnable GNN encoder boosts the adaptability to diverse views. Extensive experiments on various datasets validate the superiority of CAMEL.

Acknowledgments

This work was partially supported by the National Key Research and Development Program of China (2023YFE0111100) and the National Natural Science Foundation of China under Grant Nos. 62202104 and U2441239.