Enhancing Multi-view Graph Neural Network with Cross-view Confluent Message Passing

Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-08 17:00:20

Abstract: With the growing diversity of data sources, multi-view learning methods have attracted considerable attention.
Among these, by modeling the multi-view data as multi-view graphs, multi-view Graph Neural Networks (GNNs) have shown encouraging performance on various multi-view learning tasks.
The message passing is the critical mechanism empowering GNNs with superior capacity to process complex graph data.
However, most multi-view GNNs are designed on the well-established overall framework, overlooking the intrinsic challenges of the message passing on multi-view scenarios.
To clarify this, we first revisit the message passing mechanism from a graph smoothing perspective, revealing the key to designing a multi-view message passing.
Following the analysis, in this paper, we propose an enhanced GNN framework termed Confluent Graph Neural Networks (CGNN), with Cross-view Confulent Message Passing (CCMP) tailored for multi-view learning. 
Inspired by the optimization of an improved multi-view graph smoothing problem, CCMP contains three sub-modules that enable the interaction between graph structures and consistent representations, which makes it aware of consistency and complementarity information across views.
Extensive experiments on four types of data including multi-modality data demonstrate that our proposed model exhibits superior effectiveness and robustness.

Main paper: 
 introduction: 
 Multimedia technology has constantly developed, allowing data to be collected in a variety of ways. For instance, text, images and social relationships are used to describe personal information of the same group of users. This type of data including multiple sources can be referred to as multi-view data that provides diverse perspectives of an entity and retains richer information than single-view data [5, 27] . For comprehensively utilizing features from multiple Post-fusion approaches separately implement message passing on each graph followed by merging the obtained results. Bottom: Our CGNN achieves interactions between graph structures and consistent representations.views to learn intrinsic representations, many traditional multiview algorithms have been proposed in a variety of situations, including data mining [20, 39] and natural language processing [4, 23] . These methods have achieved excellent performance in various downstream tasks. However, the inherent or implicit connections between entities exist in real scenarios, and graphs are a data form capable of modeling such complex relationships. Benefiting from the powerful expressive capability of graphs, numerous traditional multi-view methods have been extended to graph learning and have achieved fulfillment [35, 44] . They attain a consistent graph structure via projecting graphs learned by multiple views onto a shared subspace or adopting the weighted fusion manner. Although these approaches successfully integrate the knowledge implied in graphs, they are limited in ego information and fail to benefit from the message passing.The knowledge-fitting capability of neural networks enables complicated patterns and semantics in data to be captured. Graph Neural Networks (GNNs) [22] , as powerful deep learning-based methods for propagating signals along graph-structured data, expand the convolution to non-Euclidean space and have become one of the hottest topics in numerous domains, including fraud detection [38, 49] , computer vision [26, 53] and other areas [9, 33] . To leverage GNNs to mine more complex contacts and principles among multiple views, multi-view GNNs have emerged. For example, Li et al. [25] firstly combined the multi-view learning and GNNs to adaptively excavate relationships among views. Wu et al. [46] proposed an interpretable network to explore the multi-view data from the feature and topology spaces. Gong et al. [14] leveraged the self-paced way to add improved pseudo labels from other views to the target view to further optimize the model. Nonetheless, they learn the fixed graph based on the 𝑘-nearest neighbor algorithm or the distance between node pairs to perform the message passing, which treats vital and noisy edges as equal. As one of the critical steps of GNNs, the message passing mechanism performed on graph structures learns rich contextual semantics using relationships between nodes. Thus, most studies have been devoted to enhancing the graph structure by adjusting edges for discriminative node representations [24, 40] . GAT [37] , as a classic method for graph enhancement, utilizes learned representations to assign different weights to node pairs, thereby filtering out abnormal connections. Following this line of thought, diverse variants [19, 47] are proposed to process complex multi-view graphs. Among these, pre-fusion and post-fusion mechanisms are two main pipelines for learning a consistent representation. The first one consolidates multi-view graphs first to capture an overall graph, and then it is used to accomplish the message passing for the consistent representation, as illustrated in Figure 1 -Top. The second one realizes the message passing separately on each graph, and then integrates gained representations into consistent results, as shown in Figure 1 -Middle. These approaches built upon well-established networks have exhibited superb performance by modeling multi-view data as multi-view graphs. However, they overlook interactions between graph structures and consistent representation, in which the latter can direct the augmentation and incorporation of the former for more discriminative representations.To address the above challenges, we propose an effective multiview GNN framework, named Confluent Graph Neural Networks (CGNN), with Cross-view Confulent Message Passing (CCMP). Concretely, we first reveal the key to devising a multi-view message passing by revisiting the message passing mechanism from a graph smoothing perspective. To enhance information aggregation from complex messages across various views, we introduce an explicit optimization objective that considers the interaction between multiview graph structures and consistent representations. The layers in CCMP are transparently derived through alternating optimization of the objective, which includes three sub-modules dynamically supervising from each other: S-Block exploring graph structures, 𝜇-Block learning view-level coefficients, and Z-Block excavating consistent representations, as displayed in Figure 1 -Bottom. These three sub-modules facilitate cross-view message flow at the node level. Specifically, each edge senses consistent information encoded in the learned representation and the importance of different views. Subsequently, the message passing is applied in the optimized graphs with consistent and complementary awareness to learn the final representation. The flowchart of CGNN is shown in Figure 2 . Our contributions are summarized as  
related work 2.1 multi-view leaning: 
 For capturing the consistency and complementarity hidden in multiview features to gain intrinsic semantics, many traditional algorithms have been proposed. For example, Xu et al. [50] leveraged relationships among views to recover the missing instances from a shared subspace. Cai et al. [3] designed a scaled simplex representation to achieve non-negative coefficients, and adopted the tensorized manner to explore the common and complementary information across views. Actually, connections between entities exist in real scenarios, and graphs, as a data form capable of describing such interactions, can aid in modeling complex data. Due to the powerful expressive capability of graphs, graph learning and multi-view methods are combined to learn informative representations. For instance, Fang et al. [12] combined the adaptively integrated bipartite graphs with the learning of clustering structure to efficient clustering. Zhou et al. [56] constructed a graph filter based on multiple graph learning to explore the information from all views. These approaches can integrate the knowledge implied in graphs into objectives or constraints, thereby exploring the consistency and complementarity in multi-view graphs. In order to apply the advantages of neural networks to explore deep semantics among views, deep-based multi-view networks have been researched. Liu ey al. [28] introduced autoencoders to view-specific features and used contrastive learning to extract the common information among views. Jin et al. [21] constructed the sample-level alignment to mine the intra-view relationships and capture the inter-view semantics by prototype-to-prototype correspondence.To handle a large amount of graph-structured data present in the real world, GNNs-based paradigms have been extensively studied to perform the message passing along the graph structure for discriminative representations. However, noise and interference inherent in graphs could significantly impact the expressive power of GNNs, which is detrimental to downstream tasks. In light of this, many previous results have been devoted to improving graph structures and achieving notable accomplishments [11, 51] . These methods of modeling graph structures can be divided into three pipelines. The first is similarity-based approaches that utilize inner products or Gaussian kernel functions to compute the similarity between node representations, thereby assigning weights to edges. For example, Zhu et al. [58] computed the weight edges by fusing the topological and semantic knowledge from graphs to render the learned representations robust. The second approaches involve using neural networks to learn edge weights. For instance, Zhao et al. [55] designed neural edge predictors to enhance the intra-class links and separate the inter-class connections. The third modeling algorithms construct a learnable parameter matrix that is continually optimized during network optimization processes. For example, Ying et al. [52] utilized a mutual information-based loss to identify the important subgraphs. These models utilize optimized graph structures to aggregate neighbors for obtaining reliable representations. However, they lack interactions between graph structures and consistent representation. 
proposed method: 
 Notations. The major notations used throughout the paper are described below. Consider a multi-view graph G = {G 𝑣 } 𝑉 𝑣=1 , where 𝑉 is the number of views and G 𝑣 is the 𝑣-th view data. For the 𝑣-th view G 𝑣 , we have the adjacency matrix A 𝑣 ∈ {0, 1} 𝑛×𝑛 . The graph Laplacian matrix is defined asL 𝑣 = D 𝑣 -A 𝑣 , where D 𝑣 𝑖𝑖 = 𝑗 A 𝑣 𝑖 𝑗and A 𝑣 𝑖 𝑗 = 1 denotes the existence of edge 𝑒 𝑖 𝑗 ∈ E linking node 𝑣 𝑖 and 𝑣 𝑗 in the 𝑣-th view. X ∈ R 𝑛×𝑚 is the feature matrix containing the node information, where each node is associated with an 𝑚dimensional feature vector.Insights into Message Passing: We first review the key component of GNNs, that is, the message passing mechanism. Take the classical GCN as an example, the message passing process can be typically formed as a matrix-form graph convolution:EQUATIONwhere Â = D-1 2 Ã D-1 2 , Ã = A + I, and D is the degree matrix of Ã. Some previous work has revealed that Eq. ( 1) equals to iteratively solve the following graph smoothing regularization:EQUATIONwhere the normalized Laplacian L = I -Â is adopted. Actually, Problem (2) can be rewritten in a node-form:EQUATIONwhere z𝑖 = z 𝑖 / √ 𝑑 𝑖 and 𝑑 𝑖 = D𝑖𝑖 . It imposes a graph smoothing regularization that makes the representations of any two connected nodes more similar in the learned low-dimensional space. This node-form graph smoothing regularization essentially explains the message passing operation. More specifically, for the 𝑖-th node, the message passing is performed byEQUATIONwhich collects the message from neighbors of the node 𝑖 to update its representation. Problem (3) provides an insightful understanding of the message passing mechanism, and we further analyze it in the multi-view scenario.Towards Multi-view Message Passing: Although the multi-view graph typically contains diverse types of relations, it potentially possesses cross-view consistent and complementary information, as these relations share the same node set. Therefore, multi-view GNNs aim to integrate information from these complex relations to learn a consistent representation. For example, from the perspective of graph smoothing, a typical multi-view GNN corresponds to the following graph smoothing problem:EQUATIONHowever, the interaction between consistent representation and relations is not well-considered, such that the consistency and complementarity encoded in representation Z are learned on fixed graph structures. In other words, the edges are not aware of crossview consistency. To tackle this, we design a better multi-view graph smoothing:EQUATIONwhere 𝜔 𝑣 𝑖 𝑗 is an edge-level coefficient calculated on z 𝑖 and z 𝑗 , which measures the importance of edge 𝑒 𝑖 𝑗 to the consistent representation Z. Although this formulation weights each edge for every view to make the edges aware of the consistent and complementary information, this approach inherently overlooks the heterogeneity EQUATIONwhere 𝜇 𝑣 is the view-level coefficient which measures the importance of different views, and it is also supposed to be associated with the consistent representation Z.Then we determine how these coefficients interact with Z. Motivated by the Iterative Reweighted Least Square (IRLS) method [16] , we propose to define 𝜔 𝑣 𝑖 𝑗 as𝜔 𝑣 𝑖 𝑗 = 1/∥z 𝑖 -z𝑗 ∥ 𝛾 2 .In this manner, each edge in every view is reweighted by the consistent representation, which is denoted asEQUATION)As a result, the geometric structure in the consistent embedding space of Z influences the weighting of edges in each view, and these reweighted edges, in turn, encode structural information into the Z obtained in the next iteration. For 𝜇 𝑣 , we directly set it as a variable, leading to an auto-weighted optimization problem: minEQUATIONwhere 𝝁 = [𝜇 1 , . . . , 𝜇 𝑉 ], and ∥𝝁 ∥ 2 2 is a regularization term to avoid trivial solutions and promote a balanced representation across views. 𝜆 1 and 𝜆 2 are two trade-off parameters. 𝜇 𝑣 ≥ 0 denotes the weight assigned to the 𝑣-th view, ensuring that the sum of weights equals 1 to constrain the search space.Upon establishing the graph smoothing problem, an additional fitting term is required to constrain the similarity between node representations and original features, fully leveraging the feature information. In conclusion, we present a novel graph-smoothingbased framework that integrates node feature learning and graph structure learning in a unified approach: minEQUATIONwhereS 𝑣 𝑖 𝑗 = A 𝑣 𝑖 𝑗 /∥z 𝑖 -z𝑗 ∥ 𝛾 2 .Jointly optimizing Z, S, and 𝝁 in Problem (10) where𝑡 𝑣 = 1 2 𝑖,𝑗 S 𝑣 𝑖 𝑗 ∥z 𝑖 -z𝑗 ∥ 2 2 . When 𝜆 2 𝜆 1= 0, the coefficients will be focused on a particular view and it degenerates into the single-view scenario. When 𝜆 2 𝜆 1 = +∞, it is equivalent to the average fusion strategy, i.e., 𝜇 𝑣 = 1 𝑉 . Otherwise, Problem (11) serves as the problem of minimizing a convex function 𝑓 (•) on the unit simplex△ = {𝝁 ∈ R 𝑉 : 𝑉 𝑣=1 𝜇 𝑣 = 1, 𝝁 ≥ 0}.The Entropic Mirror Descent Algorithm (EMDA) [2] can be used to update 𝝁. For 𝝁 (𝑙 ) in the 𝑙-th layer, start with 𝝁 1 ∈ { 1 𝑉 , ..., 1 𝑉 } and generate for 𝑘 = 1, ... until convergence and obtain the optimal solution as follows:EQUATIONwhere𝑓 ′ (𝝁) = (𝑓 ′ 1 (𝝁), ..., 𝑓 ′ 𝑉 (𝝁)) T ∈ 𝜕𝑓 (𝝁) and 𝑓 ′ 𝑣 (𝝁 𝑘 ) = 2𝜆 2 𝜆 1 𝜇 𝑘 𝑣 + 𝑡 𝑣 . The objective function 𝑓 (•) is a convex Lipschitz continuous function with Lipschitz constant 𝐿 𝑓 with respect to a fixed given norm ∥•∥ 1 , i.e., 𝐿 𝑓 = 2𝜆 2 𝜆 1 + ∥𝒕 ∥ 1 ≥ ∥𝑓 ′ (𝝁)∥ 1 , where 𝒕 = {𝑡 1 , ..., 𝑡 𝑉 }.Update Graph Structure Matrix S: Similar to IRLS, with fixed 𝝁 and Z, S 𝑣 can be updated by reweighting the adjacency matrix A 𝑣 :EQUATION)Through Eq. ( 13), each edge can dynamically adjust its weight according to the pair-wise representation distance by iteratively updating the matrix S 𝑣 . Update Node Representation Z: Finally, Z can be updated with fixed 𝝁 and S, the subproblem for Z becomes:EQUATIONWe calculate the derivative with respect to Z and set it to zero:EQUATIONwhere L𝑣 S = I -Ŝ𝑣 , Ŝ𝑣 = ( D𝑣 ) -1 2 S𝑣 ( D𝑣 ) -1 2 and S𝑣 = S 𝑣 + I. Since 𝜆 1 1+𝜆 1 < 1 for ∀𝜆 1 > 0, and matrix 𝑣 𝜇 𝑣 Ŝ𝑣 has absolute eigenvalues bounded by 1, thus all its positive powers have bounded operator norm. Then the inverse matrix can be decomposed efficiently with 𝑙 → ∞ using Taylor series, that is (𝑖 ) . So we consider solving Eq. ( 15) iteratively and the detailed derivations are in Appendix A. In conclusion, we derive a new message passing mechanism, named Crossview Confulent Message Passing (CCMP), summarized as follows:I -𝜆 1 1+𝜆 1 𝑣 𝜇 𝑣 Ŝ𝑣 -1 = lim 𝑙→∞ 𝑙 𝑖=0 𝑣 𝜆 1 1+𝜆 1 𝑖 𝜇 𝑣 [ Ŝ𝑣 ]EQUATIONwhere z(𝑙 )𝑖 is the representation of node 𝑖 from the 𝑙-th layer.The CCMP learns the dynamic graph structures S and the viewlevel coefficients 𝝁 by extracting information from both consistent representations and relations simultaneously. The graph structures S adjust the edge weights to evaluate their significance in capturing consistent representations through the connected node pairs' representations. The view-level coefficients 𝝁 associate each edge with various views in a cross-view manner. Therefore, during the message passing process, the overarching consistent representation information and the distinctive information across various views can flow between each edge. Moreover, the term 1 1+𝜆 1x 𝑖 in Eq. ( 16) can be regarded as a residual unit that helps the model mitigate over-smoothing issues. Discussion on Robustness: Due to the graphs' advantages to represent both entities and their relations, constructing graphs on real-world data (e.g. multi-modality data) can lead to better modeling of them. However, there is no such thing as a free lunch, the noisy edges come during the collection or construction process of graphs, which destroys the performance of GNNs. Many studies have pointed out that classical GNNs lack robustness, we then analyze that issue from the perspective of graph smoothing and demonstrate that our proposed method is more robust.The problem of classical GNN is based on ℓ 2 -norm-based graph smoothing (Eq. ( 3)), and our method (Eq. ( 9)) can be rewritten minEQUATIONwhere 𝑝 = 2 -𝛾, 1 < 𝑝 < 2. In problem (17) , we derive a ℓ based on the ℓ 2 -norm-based graph smoothing. In this way, the variation of node embeddings on edges (measured by the norm of graph gradient) can be used to detect the existence of outlier edges according to homophily assumption [1, 10] . When nodes 𝑖 and 𝑗 are connected but dissimilar, the resulting edge is likely an outlier edge. Consequently, a small weight would be assigned to this edge accordingly, meaning that A 𝑖 𝑗 /∥z 𝑖 -z𝑗 ∥ 2-𝑝 2 would have a small value. Thus the robustness of the model is greatly enhanced by reducing the impact of outlier edges.In this subsection, we design the architecture of CGNN using Crossview Confulent Message Passing. Given node features x 𝑖 ∈ R 𝑛×𝑚 of node 𝑖, the maximum layer number of 𝐿, and view-level coefficients update function U(•) given by Eq. ( 12), we perform the proposed architecture:EQUATIONwhere 𝑙 = 0, 1, ..., 𝐿 -1 and 𝑡 (𝑙 ) 𝑣 = 1 2 𝑖,𝑗 [S 𝑣 𝑖 𝑗 ] (𝑙 ) ∥z (𝑙 ) 𝑖 - z(𝑙 ) 𝑗 ∥ 2 2 , 𝒕 (𝑙 ) = {𝑡 (𝑙 ) 1 , ..., 
experiments: 
 In this section, we conduct experiments to evaluate CGNN by answering the following Research Questions (RQ):• RQ1: Does CGNN outperform competitors in semi-supervised classification when processing various graph data? • RQ2: How do reweighted edges boost the robustness? • RQ3: How does the view-level dynamic coefficients work? • RQ4: How does each component or hyperparameter affect the performance of CGNN? In the subsection, we focus on constructing semi-supervised classification experiments to validate whether the proposed CGNN can effectively process various types of graph data. • Our model CGNN outperforms other competitors and achieves the optimal performance on most datasets. • Especially on BlogCatalog, we improve the accuracy by 10.31% over the second-best method AMGCN.It is noted that compared with other models with graph enhancement GAT, ScGCN and DefGCN, CGNN obtains significant improvement. These results can be attributed to the effectiveness of CGNN with reweighted edges guided by the final representation.Multi-view Graphs. For the sake of displaying the advancement of our method in handling multi-view graphs, we conduct diverse experiments on three kinds of datasets with multiple views. Experimental setups and analyses on these datasets are as follows: 1) Multi-relational Graphs denote that there are multiple relationship types between nodes in the graph structure. We record Macro-F1 and Miscro-F1 of all models in Table 2 . Here, the training percentage varies in {20%, 40%, 60%}, and the validation and test ratios are fixed at 10% and the rest, respectively. From this 3 . It is obvious that the champion and runners-up are typically GNN-based methods, validating the role of message passing in performance improvement. Among them, CGNN is the best due to its advanced cross-view confluent message passing mechanism.To verify the robustness discussed in Section 3.2, we use the stateof-the-art adversarial attacks, Mettack [59] , to perturb the graph data with a 25% perturbation rate. Specific implementation details and robustness analysis on multi-view datasets are available in Appendix C. The adversary usually adds adversarial edges rather than deleting edges in structural attacks [59] . We design a visualization task using the edge-level coefficients 𝝎 in Eq. ( 18) to calculate the edge weights. For a fair comparison, we compute the weight for each edge in the last layer and normalize them. We visualize the weight density distribution of normal and adversarial edges with and without CCMP as well as from two datasets respectively in Figure 3 . From the figure, it is evident that the peak of the density for adversarial edges shifts towards lower weights, whereas the peak for normal edges remains relatively constant. Meanwhile, the classification accuracy reduction after the attack has been noticeably alleviated. Consistent with earlier discussion, the outlier edge is allocated a smaller weight, alleviating its impact and validating the robustness of the learned graph structure.In this subsection, we explore whether the proposed view-level coefficients generated by CGNN are reasonable. For datasets with more than two views, we assess the classification performance for each individual view and rank them in descending order, starting from the highest F1 score as the 1st F1, followed by the 2nd F1, and so on up to the 6th F1. The coefficient 𝜇 𝑣 of each view (denoted by color length) and its corresponding F1 rank are presented in Figure 4 . We can observe that obtaining better performance is basically associated with larger coefficient values. Beyond that, we calculated Pearson correlation coefficients (PCCs) between the F1 scores and dynamic graph structures in CCMP) and CGNN-𝝁 (without considering view-level coefficients in CCMP). Figure 5 presents the node classification performance across all datasets, which demonstrates:• For the single graph scenario, the adoption of CCMP leads to performance improvements on all datasets. It indicates that the learned graph structures via edge-level coefficients enable a more effective capture of structural information for each view. • For the multi-view graph scenario, CGNN outperforms each variant in terms of classification performance, validating that the proposed CCMP can efficiently and rationally leverage consistency and complementarity information across views.4.5.2 Parameter Sensitivity. In this subsection, we conduct the parameter sensitivity to analyze the impact of these parameters on the models. Due to page limitations, we present results on 2 multiattribute datasets, 2 multi-modality datasets, and 1 multi-relational dataset. Results for the remaining datasets can be found in Appendix C. This paper contains three main hyperparameters: 𝛼 = 1 (𝛼,𝜆 2 ) with the fixed 𝛾. It is obvious that the model's peak is achieved when 𝛼 = 0.2 for the multi-relational and multi-modality datasets, and the optimal value occurs when 𝛼 varies from 0.1 to 0.2 for the multi-attribute datasets. This indicates that the appropriate 𝛼 can promote the performance and validate the effectiveness of the graph smoothing term. For the parameter 𝜆 2 , the model performance varies as it is changed, implying the role of this term balancing multiple views. Figure 6 (f)-(j) presents the effect of 𝛾 on the performance. The model stays at a promising level with slight fluctuations as 𝛾 varies, which supports the validity of the dynamic graph structures driven by edge-level coefficients. 
conclusion: 
 In this paper, we revealed the key to designing multi-view message passing and connecting it with the graph smoothing problem of GNNs. Motivated by our findings, we introduced a novel optimization objective that fully utilized the interaction between graph structures and consistent representation. By iteratively optimizing the objective, we naturally derived a Cross-view Confluent Message Passing (CCMP), seamlessly integrating it into the Confluent Graph Neural Networks (CGNN). The dynamic weight facilitated the flow of consistency and complementarity information across views along edges during the aggregation process. Extensive experiments on node classification tasks on various datasets demonstrated the effectiveness of the proposed CGNN, and also exhibited the robustness on graphs with noisy edges. 
 
 Appendix:  


Decision: According to all the review comments, rebuttals, discussions and final ratings, the majority of the reviewers gave positive ratings to this paper and the concerns were well addressed. I am happy to recommend to accept this paper. Please carefully revise the final manuscript according to the comments and discussions.

Reviews: review: paper_summary: paper_summary: The paper proposes a novel multi-view Graph Neural Network (GNN) framework called Confluent Graph Neural Networks (CGNN) with Cross-view Confluent Message Passing (CCMP). The key contributions are: 
- 1) revealing the key to designing effective multi-view message passing from a graph smoothing perspective;
- 2) introducing an explicit optimization objective that considers the interaction between multi-view graph structures and consistent representations;
- 3) deriving the CCMP layers through alternating optimization of the proposed objective, which includes three sub-modules (S-Block, $\mu$-Block, and Z-Block) that enable interactions between graph structures and consistent representations. 
Extensive experiments demonstrate the superior effectiveness and robustness of the CGNN framework compared to existing multi-view GNN methods.
strength_weakness: strength_weakness: Strengths:

- The motivation is clear, and paper writing is excellent and easy to follow;
- The proposed method, Confluent Graph Neural Networks (CGNN) with Cross-view Confluent Message Passing (CCMP), can effectively integrate graph structures and consistent representations across multiple views;
- Additionally, the CCMP learns dynamic graph structures and view-level coefficients by simultaneously extracting information from consistent representations and relations, enabling consistency and complementarity information across views during the aggregation process;
- Robustness analysis and computation complexity are provided. Specifically, the experimental results demonstrate that the proposed method can effectively mitigate the impact of noisy edges by allocating smaller weights to outlier edges and verify the hypothesis on adversarial attack experiments;
limitations: limitations: Weakness:
- In the single-view graph experiments, more effective and novel GNN methods, such as GraphCon[1], GREAD[2], and ACM-GCN, should be considered for fair comparisons. This question must also be considered in the other two parts of the experiments.
- The computational complexity of CGNN may be overhead compared to other more straightforward graph neural network models, where incorporating multiple sub-modules and the interaction between graph structures and consistent representations in the proposed Cross-view Confluent Message Passing mechanism leads to increased training time and resource requirements. 
- The performance of CGNN on extremely large or high-dimensional datasets needs to be thoroughly evaluated, raising questions about its scalability to real-world applications with massive amounts of data.
- Some small grammar issues should be solved:
   - The second approaches -> approach
   - The third modeling algorithms construct -> The third modeling algorithm constructs
   - from two datasets respectively -> from two datasets, respectively,
paper_summary: paper_summary: In response to the insufficient consideration of the interaction between views in existing multi-view graphs, the paper proposes a multi-view GNN framework, which understands the mechanism of graph message propagation from the perspective of graph smoothing and considers the mutually reinforcing interaction between multi-view graph structures and consistent feature representations. Numerous experiments have verified its effectiveness and its robustness to noise immunity.
strength_weakness: strength_weakness: 1. From the perspective of novelty, considering message passing from the perspective of graph smoothing is interesting.

2. Open source code helps to enhance the understanding of the paper.

3. Thorough experiments and a clear algorithmic process.
limitations: limitations: 1. The lack of citation for previous work at line 300 seems to be a crucial omission.

2. Eq.(2) can also be referred to as Laplacian Eigenmaps (LE), or a key element of spectral clustering. Is this related to graph smoothing?

3. Eq.(9) seems to share some similarities with the ideas presented in the following paper. The authors need to provide further explanation.

    AAAI17: Multi-View Clustering and Semi-Supervised Classification with Adaptive Neighbours.

4. Combining the idea of iteratively solving variables from shallow methods with the automatic differentiation concept of deep methods is a good attempt. However, can the authors provide a deeper insight about GNN, perhaps purely from the perspective of shallow or deep methods?

5. Perhaps it would be better to add references to contrasting algorithms and datasets in Table.
paper_summary: paper_summary: The authors propose a novel GNN model that establishes a node-level message passing by introducing an enhanced multi-view graph smoothing problem. The motivation is to connect multi-view message passing with the graph smoothing problem of GNNs, aiming to address the shortcomings of traditional multi-view GNNs from an optimization perspective. Extensive experiments demonstrate the proposed model’s effectiveness and robustness.
strength_weakness: strength_weakness: 1.	The paper is structured clearly and the writing is coherent.
2.	The study presents a novel approach by extending classical message passing to multi-view scenarios, solving limitations of multi-view GNNs.
3.	The proposed CGNN improves performance and robustness from both node-level and view-level aspects.
4.	The experimental section is comprehensive, comparing the proposed method against many SOTA competitors across various datasets, including large-scale ones.
5.	The code has been made available for reproducibility and is well-organized according to the authors.
limitations: limitations: There are some questions for the authors:
1. I wonder if the proposed CCMP can be connected to other message-passing mechanisms.
3. Although the paper boosts the performance in various semi-supervised classification tasks, can it also achieve excellent results on other tasks, such as link prediction?
3. On some datasets, the improvement of CGNN compared with other models is not obvious (such as IMDB and Citeseer) and on the YELP dataset, the model obviously outperforms the suboptimal one. The reasons should be clarified.
paper_summary: paper_summary: The paper studies the inherent problem of multi-view message passing. The authors analyzed the graph smoothing problem of multi-view GNN cannot fully utilize the interaction between consistent representation and relations. The solution is to redesign the optimization problem that enable message passing at both the edge and view levels. By optimizing the proposed objective, the new message passing mechanism is obtained. Extensive experiments are employed to demonstrate the effectiveness of CGCN. Particularly, CGCN achieves robustness in scenarios with high attack rates while maintaining competitive performance on clean graphs of different data types.
strength_weakness: strength_weakness: S1. The paper is generally of high quality. 
S2. This paper naturally proposes a GNN architecture specifically designed for multi-graph data, inspired by the graph smoothing problem. 
S3. The concept of 'confluent message passing' seems reliable and novel, different from existing pre- or post- fusion-based frameworks.
S3. The robustness is validated through experiments against adversarial attack, which is persuasive.
limitations: limitations: L1. Some experimental details should be reported. For example, it seems that not all adopted datasets are graph-structured, the process of graph construction needs to be further explained.
L2. Some important results, such as the adversarial attack experiments on multi-view graphs, are placed in the Appendix rather than in the main paper. The authors are advised to reorganize the paper to show these results in the main body.
L3. This is just a suggestion. Datasets like Cora only contain single graphs. The authors could try constructing multiple graphs using some graph augmentation techniques. I am curious to see how the CGNN would perform.