Dual-Optimized Adaptive Graph Reconstruction for Multi-View Graph Clustering

Authors: zichen  wen
tianyi  wu
yazhou  ren
yawen  ling
chenhang  cui
xiaorong  pu
lifang  he
Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-01 05:45:52

Abstract: Multi-view clustering is an important machine learning task for multi-media data, encompassing various domains such as images, videos, and texts. Moreover, with the growing abundance of graph data, the significance of multi-view graph clustering (MVGC) has become evident. Most existing methods focus on graph neural networks (GNNs) to extract information from both graph structure and feature data to learn distinguishable node representations. However, traditional GNNs are designed with the assumption of homophilous graphs, making them unsuitable for widely prevalent heterophilous graphs. Several techniques have been introduced to enhance GNNs for heterophilous graphs. While these methods partially mitigate the heterophilous graph issue, they often neglect the advantages of traditional GNNs, such as their simplicity, interpretability, and efficiency. In this paper, we propose a novel multi-view graph clustering method based on dual-optimized adaptive graph reconstruction, named DOAGC. It mainly aims to reconstruct the graph structure adapted to traditional GNNs to deal with heterophilous graph issues while maintaining the advantages of traditional GNNs. Specifically, we first develop an adaptive graph reconstruction mechanism that accounts for node correlation and original structural information. To further optimize the reconstruction graph, we design a dual optimization strategy and demonstrate the feasibility of our optimization strategy through mutual information theory. Numerous experiments demonstrate that DOAGC effectively mitigates the heterophilous graph problem.

Main paper: 
 introduction: 
 Clustering is a fundamental unsupervised learning task with broad applications across various fields [14, 18, 56] . Multi-view clustering (MVC) has obtained considerable interest owing to its capacity to harness information from multiple views [40, 50] , thereby enhancing clustering performance [41, 42, 59, 63, 67] . Over the past few years, many MVC methods have been proposed, which can be generally classified into three primary categories [60] : co-training approaches [6, 12, 24, 70, 72] , low-rank matrix factorization techniques [48, 65, 66, 68] , and subspace-based methods [7, 15, 19, 37, 45, 46, 51, 52, 61] . Nevertheless, they often fail to effectively utilize the common multi-view graph-structured data. With the development of graph neural networks (GNNs) [11, 13, 44] , researchers have been interested in utilizing GNNs to extract the abundant structural information embedded in graph data [47] . However, labeling graph data becomes increasingly challenging as the amount of graph data grows. Therefore, multi-view graph clustering (MVGC) has emerged as a popular and valuable research area. Many GNN-based approaches have been proposed and have effectively advanced the development of MVGC. For example, Fan et al. [9] develop a one2multi graph autoencoder clustering framework (O2MAC) to capture the shared feature representation. Hassani and Ahmadi [16] propose to learn node and graph level representations by contrasting structural views of graphs. However, traditional GNNs are typically designed for homophilous graphs, where edges connect nodes of the same class. As a result, existing GNN-based MVGC methods are less effective when applied to heterophilous graphs, where edges connect nodes of diverse classes. In reality, heterophilous graph data is prevalent. For instance, in the context of protein chemistry, interactions often occur between different types of amino acids [2, 73] . In financial transaction networks, fraudulent users frequently engage in transactions with non-fraudulent users [39] . Additionally, dating networks often exhibit a higher number of connections between individuals of opposite genders [39, 69] .To address this challenge, several techniques have been introduced to improve GNNs for heterophilous graphs. These novel GNN variants aim to overcome the limitations of traditional GNNs, which rely on neighborhood aggregation mechanisms. They can be roughly divided into two groups [69] : non-local neighbor extension methods [1, 29, 36, 73] and GNNs architecture refinement methods [5, 29, 62] . Most of these methods enable newly designed GNNs to partially address the issue of heterophilous graphs by aggregating feature information from higher-order neighbors [17] or adapting the internal GNN structure. However, these methods increase the computational complexity of the model and even may degrade the performance of homophilous graph data [39] after structural modification to accommodate heterophilous graph data. Meanwhile, Li et al. [26] also point out that traditional GNNs have advantages in terms of simplicity [55] , explainability [55] , and efficiency [64] that GNN variants cannot match.In addition, some studies have attempted to explore the reasons for the poor performance of traditional GNNs in dealing with heterophilous graphs and propose novel solutions from the point of the spectral domain [22] . For example, Bo et al. [2] design a mechanism that can integrate low-frequency signals, high-frequency signals, and raw features. Liu et al. [31] propose a novel graph representation learning method with edge heterophily discriminating (GREET) that learns representations by discriminating and leveraging homophilous edges and heterophilous edges. Luan et al. [32] propose adaptive channel mixing to exploit local and node-wise information from three channels: aggregation, diversification, and identity. Wen et al. [53] propose an adaptive hybrid graph filter related to homophily degree that adaptively captures low and highfrequency information. These spectral domain filtering methods aim to capture rich information in every frequency band of the graph to acquire distinguishable node representations. Inevitably, however, to capture information in various frequency bands, these methods usually design multiple filters or design filters with multiple channels. Undoubtedly, training multiple filters will increase the training cost as it multiplies the parameters. Several studies have pointed out that traditional GNNs based on the homophily assumption are actually low-pass filters spectrally [25, 34] . In other words, designing diverse filters to capture graph signals in multiple frequency bands is actually equivalent to modifying GNNs in the spatial domain, which would also suffer from the same drawbacks as the previously mentioned GNN variants. Considering that traditional GNNs mining graph structure information still has advantages in some aspects and there are drawbacks in transforming GNNs in spatial and spectral domains, we propose to reconstruct the original graph structure so that the reconstructed graphs can be adapted to the traditional GNNs, as a way to solve the problem of heterophilous graphs in MVGC.Our motivation is to reconstruct the graph that can be applied to message passing and neighborhood aggregation mechanisms of GNNs. To achieve this goal, we propose a dual-optimized adaptive graph reconstruction method. To be specific, we first construct the node correlation matrix. Although directly utilizing the node correlation matrix as a reconstruction graph can improve the homophily degree as shown in Table 3 of Appendix B, the node correlation matrix is only constructed based on the node feature information, which completely discards the original structural information of the graph, resulting in suboptimal performance. Taking into account both the degree of homophily and original structural information, we propose an adaptive mechanism for reconstructing the graph. Specifically, we utilize pseudo-labeling information to quantify the homophily degree of the original adjacency matrix. Based on this, the weight of the original adjacency matrix is assigned in the reconstruction graph to selectively preserve a certain amount of original structural information when the graph type is unknown.To further optimize the graph structure, we develop a dual optimization strategy for the autoencoder. The first optimization comes from the autoencoder's reconstruction loss function, which can compress and denoise the data while preserving valid information about the input data. Furthermore, a random mask is applied to the original node feature information leading to the creation of an additively noisy feature matrix. Next, GNNs' message passing and neighborhood aggregation mechanisms are utilized to recover the noisy feature, followed by the use of a noise recovery loss function to minimize any differences between the recovered feature information and the original feature information. However, trainable parameters are not set for the GNN applied to recover feature information. Instead, only its aggregation mechanism is utilized. The training objective has now shifted to the autoencoder, and the noise recovery loss function directly propagates the gradient back to the autoencoder, optimizing its training process.In summary, our main contributions are as follows:• To alleviate the poor performance of GCN on heterophilous graphs, we design an adaptive graph reconstruction mechanism, employing the pseudo-labeling information. • We devise a dual optimization strategy for reconstruction graphs, which makes reconstruction graphs more adaptable to neighborhood aggregation mechanisms.• We demonstrate the feasibility of using the processing of noisy node feature recovery to assist the GCN aggregation process based on mutual information. [57] . In addition to designing diverse graph encoders, contrastive learning methods are employed to extract information from graphs. Hassani and Ahmadi [16] introduce a self-supervised model to learn the node representations by contrasting structural views of graphs. Pan and Kang [35] employ contrastive learning to uncover the shared geometry and semantics in order to learn a consensus graph. Additionally, Lin and Kang utilize graph filtering techniques to smooth the features and learn a consensus graph for clustering [27] . Zhou and Du [71] enhance clustering by learning a consensus graph filter from multiple data views. Despite the attractive performance of these methods, they are often sensitive to the quality of graph structure. In other words, they generally do not perform well with heterophilous graphs. 
heterophilous graph representation learning: 
 Several efforts have been extended to address the issue of heterophilous graphs. Chien et al. [5] tackle heterophilous graph issues by employing GNNs that propagate using specially learnable weights. Chanpuriya and Musco [3] develop a feature extraction technique capable of adapting to graph structures exhibiting both homophily and heterophily. Li et al. propose an innovative graph restructuring approach that extends spectral clustering through alignment with node labels [26] . However, applying them to MVGC poses challenges as they heavily depend on true node label information. Additionally, there are unsupervised techniques aimed at addressing the heterophilous graph issue that do not depend on true labeling information, such as GREET [31] , which discriminates between homophilous and heterophilous edges using an edge discriminator, enabling separate processing of these edges. Xiao et al. propose a decoupled self-supervised learning framework to decouple various underlying semantics among different neighborhoods [58] . While these methods partially address the heterophilous graph challenge, they are difficult to generalize to MVGC since these methods are designed for node classification tasks. The lack of a feasible and effective solution to mitigate the negative impact of heterophilous information still persists for heterophilous graphs in multi-view graph clustering. 
methodology 3.1 preliminaries: 
 In the task of multi-view graph clustering, the objective is to group a set of 𝑛 nodes into 𝑘 clusters. To achieve this, we utilize the notation G = (V, E) to denote a graph. Here, V represents the nodes set, and the set of all nodes belonging to class 𝑖 is represented as V 𝑖 , with 𝑁 = |V |, and E ⊆ V × V represents the edge set with selfloops. The feature matrix for the nodes is denoted as X ∈ R 𝑁 ×𝑑 , and the symmetric adjacency matrix of the graph G is represented by A ∈ R 𝑁 ×𝑁 , with elements 𝑎 𝑖 𝑗 = 1 indicating the presence of an edge between node 𝑖 and node 𝑗, and 𝑎 𝑖 𝑗 = 0 otherwise. Additionally, we define the degree matrix of A asD 𝑣 𝑖𝑖 = 𝑗 𝑎 𝑣 𝑖 𝑗 , enabling the normalization of each view's A 𝑣 to A 𝑣 = (D 𝑣 ) -1 A 𝑣 .The normalized graph Laplacian matrix, denoted as L 𝑣 , is then calculated as I -A 𝑣 , with I representing the identity matrix.To ensure the adaptability of GCN's neighborhood aggregation mechanism, it is necessary for a majority of the neighboring nodes in the reconstruction graph to be of the same class as the central node. Nodes belonging to the same class tend to have similar node feature vectors. Therefore, we prioritize the feature information of the nodes and aim to construct the graph by mining the correlation between their features. In this way, the resulting graph aligns with our expectation of connecting nodes to neighboring nodes that share the same label.Firstly, we harness the remarkable capabilities of autoencoder to extract node feature information and refine the original features of the nodes within the graph:EQUATIONEQUATIONwhere Z 𝑣 ∈ R 𝑁 ×𝑑 𝑍 𝑣 , 𝑣 ∈ 𝑉 . W 𝜃 and W 𝜑 represent the learnable parameters of the encoder and decoder in the 𝑣-th view respectively, and 𝜎 (•) is the activation function.After this, we explore the correlation among nodes by computing the cosine similarity between nodes features and derive the correlation matrix S 𝑣 :EQUATIONwhere 𝑆𝑖𝑚(•) represents the cosine similarity function in vector space. Intuitively, if node 𝑖 and node 𝑗 belong to the same class, then S 𝑣 𝑖 𝑗 will have a larger value in the correlation matrix S 𝑣 , indicating that nodes 𝑖 and 𝑗 are similar and connected.Directly using S 𝑣 as a reconstruction graph improves the homophily degree of the graph to some extent. Nevertheless, only utilizing the node feature information and totally disregarding the original structural information of the graph may not be entirely beneficial to our graph reconstruction. Therefore, we propose a selective utilization of the original graph structure information to reconstruct graphs while maintaining a high degree of homophily. To accomplish this, we design an adaptive reconstruction graph mechanism. Specifically, we attempt to quantify the degree of homophily in the original graph structure and subsequently assign appropriate weights. However, in the unsupervised context, access to true labeling information is not available. For this reason, we choose to approximate the homophily degree of the original graph structure by using the pseudo-labeling information obtained from the final consensus embedding H of Eq. ( 12):GNN GNN GNN •••••• GNN •••••• •••••• View Fusion Mask Pseudo-Label Pseudo-LabelEQUATIONwhere 𝑤 𝑣 denotes the original graph weight obtained after homophily degree computation from the last iteration, ⊙ represents the Hadamard product, Ȳ ∈ {0, 1} 𝑛×𝑐 is the pseudo label obtained from the clustering of consensus embedding H. Finally, we obtain the reconstruction graph that incorporates the assessment of the homophily level and original structural data:EQUATION)As shown in Fig. 2 , 𝑤 𝑣 can converge from different initialization values to the same value that is close to the true homophily degree through the adaptive mechanism, which indicates that the adaptive mechanism is stable and meets our expectations.There is a significant disparity between solely reconstructing graphs based on extracting correlation information among nodes and our objective, which is to construct graphs optimized for GCN neighborhood aggregation mechanism. Therefore, we devise a dual optimization strategy to improve the reconstruction graph in Section 3.2.Specifically, we first design the reconstruction loss function of the autoencoder utilizing the cross-entropy loss:EQUATIONAs the first optimization of the reconstruction graph, the reconstruction loss of the autoencoder mainly ensures the validity of the information extracted from the node feature matrix, i.e., Z is able to reflect the essential attributes of the nodes, and the valid information of the node features will not be lost in the process of dimensionality reduction and denoising.Furthermore, we design the second optimization process. Specifically, we begin by adding a random mask as noise to the original matrix X of node features. Then, we utilize GCN's neighborhood aggregation mechanism to recover the feature information following the addition of noise, which can be represented fromX 𝐴𝐺𝐺 Â → X → X (Process 2), where X denotes the nodes features with random mask (noisy features), X means the nodes features recovered by the aggregation mechanism of GCN and 𝐴𝐺𝐺 Â denotes the aggregation operation of GCN using reconstruction graph. The noise recovery loss is defined as follows:EQUATIONwhere X𝑣 = 𝐺𝐶𝑁 ( Â𝑣 , X𝑣 ).In fact, the second optimization process attempts to optimize the reconstruction graph in the form of supervised learning. Due to the unknowability of labels in unsupervised tasks, we cannot directly utilize the true label information to supervise the reconstruction of graph, making the aggregated features h approximate the true label Y, i.e., X𝐴𝐺𝐺 Â → h → Y (Process 1). Intuitively, we believe that a graph suitable for predicting node features is also suitable for predicting node labels. Therefore, we introduce Process 2 to enhance Process 1. As shown below, we utilize mutual information theory to speculate on the validity and rationality of Process 2. Specific symbol explanations are shown in Table 1 of Appendix A. Lemma 3.1. [10] Let Xȳ i and Xy i be mutually redundant for 𝑥 𝑖 , i.e., the feature of node 𝑖 , where Xȳ i and Xy i denotes the nodes features with random masks belonging to different and the same class as node 𝑖 respectively. The recovered feature x𝑖 is aggregated from Xy i . If x𝑖 is sufficient for Xȳ i (𝐼 ( Xȳ i ; Xy i | x𝑖 ) = 0), the mutual information between 𝑥 𝑖 and x𝑖 have the following relationship:EQUATIONwhere 𝜃 denotes the learnable parameters of the autoencoder. The proof is given in Appendix A.The left side of Eq. ( 8) is the object we need to optimize, i.e., L 𝑁 𝑟𝑒𝑐 in Eq. (7) .Similarly, replacing the symbol of Process 2 in Eq. (8) with the corresponding symbol of Process 1, we have:EQUATIONHypothesis 1: The distribution of node features X can be seen as a joint distribution of fragmented information of node label y ( Ỹ) and random noise (𝑒).Based on Hypothesis 1, we have:EQUATIONEq. (10) implies that the process of aggregating node features in GCN, with the goal of maximizing the mutual information between 𝑦 𝑖 and ℎ 𝑖 (𝐼 𝜃 (𝑦 𝑖 ; ℎ 𝑖 )), can be viewed as a way of consolidating fragmented label information.Then, we obtain two formulas: 𝐼 𝜃 (𝑥 𝑖 ; x𝑖 ) = 𝐼 𝜃 (𝑥 𝑖 ; X) and 𝐼 𝜃 (𝑦 𝑖 ; ℎ 𝑖 ) = 𝐼 𝜃 (𝑦 𝑖 ; Ỹ) that correspond to Process 2 and Process 1, respectively. We can also observe similarity between the two processes: they are both the process of integrating fragmented information that belongs to the same category. These two processes share same graph structure, and the elements involved can all correspond oneto-one. So, if we can train Process 2 well and optimize the reconstruction graph i.e., minimizing L 𝑁 𝑟𝑒𝑐 , the Eq. ( 10), alternatively, the aggregation process of GCN, can also benefit from it.In a multi-view task, different views contain not exactly the same information, i.e., there is consistency and complementarity among the views [21, 54] . To fully utilize the complementary information among views, we attempt to get a consensus embedding containing rich information by fusing the node embedding h 𝑣 of each view [20] . However, to account for the varying information values of different views, it is essential to assign suitable weights to each view based on their quality evaluation. This weighting scheme ensures that different views make distinct contributions to the final consensus embedding. We first obtain the node embedding for each view:EQUATIONNaturally, it occurs to us to utilize the obtained consensus embedding H to in turn guide the embedding h 𝑣 of each view to assign weights to it. Specifically, if a view's embedding h 𝑣 is similar to the consensus embedding, then the information it carries must be important and we assign larger weight to it, and vice versa. We obtain the consensus embedding H as follows:EQUATIONwhere 𝛼 𝑣 denotes the weight of the node embedding for the 𝑣-th view and is calculated as follows:EQUATION)Here 𝑒𝑣𝑎 𝑣 is obtained from the evaluation function that computes the similarity between the consensus embedding H and each view embedding h 𝑣 , i.e., 𝑒𝑣𝑎 𝑣 = 𝑒𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛(h 𝑣 , H). The hyperparameter 𝜌 is used to adjust the degree of smoothing or sharpening of the view weights. For the final consensus embedding H, we apply the 𝑘-means algorithm to get the clustering results. different homophily degrees. ACM [9] is derived from the ACM database 1 and is composed of two graphs: the co-paper network and the co-subject network. DBLP [9] , sourced from the DBLP database 2 , consists of three graphs: co-author, co-conference, and co-term. Minesweeper is a synthetic graph emulating the eponymous game [39] . Wisconsin and Cornell [36] are webpage graphs from WebKB 3 and Chameleon is a subset of the Wikipedia network [43] . The detailed statistics of the datasets are presented in Table 1 and Appendix B. 
experiments 4.1 evaluation setup and metrics: 
 , G 2 G 1 , G 2 , G 3 G 1 , G 2 G 1 , G 2 G 1 , G 2 G 1 ,4.1.2 Evaluation Metrics. We utilize accuracy (ACC), normalized mutual information (NMI), adjusted rand index (ARI), and F1-score (F1) to evaluate the clustering performance of the proposed model.To validate the superiority of the proposed method, we utilize popular benchmarks for comparative experiments and analysis. VGAE [23] and AGE [8] represent 1 https://dl.acm.org/ 2 https://dblp.uni-trier.de/ 3 http://www.cs.cmu.edu/afs/cs.cmu.edu/project/theo-11/www/wwkb two distinct graph encoding techniques. DAEGC [49] is a goaldirected deep attentional embedded graph clustering framework. O2MAC [9] is an approach that acquires information from both node features and graph structures. MvAGC [4] and MCGC [35] represent two recent graph-based methods that utilize graph filtering to acquire a consensus graph. AGCN [38] is an attention-driven graph clustering network. DCRN [30] is a method that improves the performance of graph clustering by reducing the information correlation. DualGR [28] utilizes soft-labels and pseudo-labels to provide guidance in the process of refining and fusing graphs for clustering. respectively. Meanwhile, it surpasses others on most metrics in both DBLP and Minesweeper. Specifically, it increases ACC, ARI, and F1 on DBLP by 1.0%, 2.6%, and 1.1%, respectively, and ACC, F1 on Minesweeper by 8.8%, and 17.8%, respectively. Furthermore, unlike the poor performance of other baselines on heterophilous graph datasets, DOAGC achieves excellent performance on graphs with low homophily degree. The ACC of our model reaches 79.7% on Wisconsin, while the second-best DualGR [28] is only 56.4%, which appears similar on Cornell and Chameleon. Table 3 demonstrates the comparison results on six synthetic ACM datasets, and the results show that DOAGC also performs well on the same dataset with different homophily degrees. Comparing DOAGC with other baselines on diverse homophily degrees, our method effectively addresses the challenge faced by previous graph clustering approaches on heterophilous graphs. This enables traditional GNNs, relying on homophily assumptions, to fully leverage structural information mining on heterophilous graphs. 3 , the model's performance is impacted by the removal of either S 𝑣 or A 𝑣 . Removing S 𝑣 has a greater impact on the model's performance compared to removing A 𝑣 . S 𝑣 is constructed using node feature information based on the cosine similarity between each pair of nodes. Intuitively, due to the high probability that the nodes with similar feature information belong to the same class, the constructed S 𝑣 has a greater edge weight among similar nodes, i.e., a higher homophily degree. Removing S 𝑣 will greatly reduce the homophily degree of the reconstruction graph, leading to the inability of the GCN message passing mechanism to function, which in turn leads to a decrease in the model performance. A 𝑣 is the original adjacency matrix, and although the removal of A 𝑣 still allows the reconstruction graph to maintain a high homophily degree, the complete abandonment of the original structural information still has an impact on the model performance.We performed experiments on eight real-world datasets with varying degrees of homophily. Fig. 4 shows the detailed results of the experiments about convergence analysis, where the left subgraph refers to the ACM, DBLP, and IMDB with a high homophily degree; the right subgraph refers to the EAT, Texas, Chameleon, Wisconsin, and Cornell with a low homophily degree. As depicted in Fig. 4 , the three real-world datasets ACM, DBLP, and IMDB, start to converge before the 50th epoch. implies that the node can aggregate information from more distant nodes. 𝑤 represents the initial weight of adjacency matrix A 𝑣 in Eq. ( 5). A higher value of 𝑤 indicates that the reconstructed graph Â𝑣 contains more of the original structural information at the beginning of the iteration. As shown in subfigures (a) and (c) of Fig. 3 , we perform experiments on the Wisconsin and Cornell datasets using different combinations of 𝑜𝑟𝑑𝑒𝑟 and 𝑤 to examine the variations in ACC. As observed, fixed 𝑜𝑟𝑑𝑒𝑟 renders initial 𝑤 insignificant. DOAGC shows consistent and stable performance regardless of weights in the initial adjacency matrix A 𝑣 . Regarding 𝑜𝑟𝑑𝑒𝑟 , DOAGC achieves excellent performance at 𝑜𝑟𝑑𝑒𝑟 = 3. Further increasing 𝑜𝑟𝑑𝑒𝑟 does not improve the model's performance and may even result in a slight decline. This indicates that our method does not require high-order aggregation with increased complexity. Moreover, it suggests that the reconstructed graph Â𝑣 predominantly consists of neighboring nodes with the same classifications.For subfigures (b) and (d) in Fig. 3 related to NMI, the NMI on Wisconsin parallels the description of ACC on Wisconsin above. Cornell's NMI demonstrates slight sensitivity to its parameters, yielding higher values at 𝑜𝑟𝑑𝑒𝑟 ∈ {3, 5, 7}, and lower values when the 𝑜𝑟𝑑𝑒𝑟 is either too low or too high. When 𝑜𝑟𝑑𝑒𝑟 is low, nodes struggle to aggregate extensive neighbor information. Conversely, with a high 𝑜𝑟𝑑𝑒𝑟 , nodes tend to aggregate feature information from distant nodes. However, in our reconstruction graph Â𝑣 , distant high-order neighbor nodes are more likely to belong to different classes, resulting in the aggregation of conflicting information. This, in turn, contributes to a decrease in NMI. 
conclusion: 
 In this paper, we address the challenge of heterophilous graphs in MVGC and propose DOAGC, a dual-optimization adaptive graph reconstruction multi-view clustering method. DOAGC focuses on reconstructing graphs to facilitate the message passing and neighbor aggregation mechanisms of conventional GNNs. We extract node correlation from feature information and introduce an adaptive mechanism utilizing pseudo-labeling information derived from consensus embedding. Additionally, we propose a dual optimization strategy to enhance the compatibility of the reconstructed graph with traditional GNNs. The efficacy of the optimization strategy is validated through mutual information theory. Our proposed approach achieves outstanding results on eight real-world datasets and six synthetic datasets with varying homophily degrees, providing evidence that DOAGC effectively addresses the heterophilous graph problem encountered by MVGC, while simultaneously maintaining exceptional clustering performance on homophilous graphs. 
 
 Appendix:  


Decision: This paper studies heterophilous graph issue in multi-view graph clustering while striving to maintain the simplicity, interpretability, and efficiency of traditional GNNs. It introduces an adaptive graph reconstruction mechanism for node correlation, and provides a dual optimization scheme to update the reconstruction graph. After rebuttal and discussion, all reviewers recognize the contributions and give positive scores. So, acceptance is recommendated.

Reviews: review: paper_summary: paper_summary: In this paper, the authors propose a novel multiview graph clustering method based on dual-optimized adaptive graph reconstruction, named DOAGC. In this framework, an adaptive graph reconstruction mechanism that accounts for node correlation and original structural information is developed. To further optimize the reconstruction graph, a dual optimization strategy is devised, and theorectial analysis is provided to demonstrate the feasibility of our optimization strategy.
strength_weakness: strength_weakness: S1. Overall, the paper is easy to read.

S2. The idea of this paper is interesting, and theorectial analysis is provided to demonstrate the feasibility of our optimization strategy.

S3. Extensive experiments on several benchmarks are made to validate the effectiveness of the proposed method.
limitations: limitations: However, there are still some concerns about this paper,
1. The topic of this paper is meaningful. Concerned about this problem, DualGR[21] is recently proposed. What about the differences between DOAGC and DualGR. To some extend, there are some components similar with DualGR. Actually, the problems/motivations mentioned in this paper are not clear enough.

2. The paper is well-written, but the overall flowchart of DOAGC is a little unsmooth. Moreover, the pseudo code is missing.

3. Figure 1 is not clear to direactly show the idea of DOAGC, and more introductions should be made in the caption.

4. How does the process 1 reflect in Figure 1? The existence of process 1 is to demonstrate the rationality of Process 2?

5. What is the used evaluation function in this paper, i.e., 𝑒𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛($h^𝑣$,H).

6. As shown in Table 4, why only choose Wisconsin and Cornell to do such ablation studies? Additionally, the neccessity of L𝑁𝑟𝑒𝑐 seems not so important. The author are suggested to provide more anaysis about  L𝑁𝑟𝑒𝑐 in this paper.
paper_summary: paper_summary: The motivation of this article is to reconstruct graphs that can be effectively applied to the message passing and neighborhood aggregation mechanisms of GNNs, addressing the issue of GNNs being unsuitable for widely prevalent heterophilous graphs. An adaptive graph reconstruction mechanism is proposed to not only consider node feature information but also preserve the structural information of the original graph. A dual optimization strategy is proposed to compress and denoise data through the reconstruction loss of the autoencoder.
strength_weakness: strength_weakness: 1. The use of pseudo labels to calculate the homophily degree of the original adjacency matrix is reasonable and interesting.
2. The dual optimization strategy for reconstructing graphs is well-designed.
3. Experiments on both real-world and synthetic datasets demonstrate that the proposed method has significant advantages over baselines. The ablation experiment further proves the effectiveness of each component of this method.
limitations: limitations: 1. Fig. 2 requires more detailed explanations. Specifically, it should clarify how it demonstrates that "w^v can converge from different initialization values to the same value, which is close to the true homophily degree."
2. Some typos should be corrected, such as the inconsistent number of real-world datasets mentioned in the Introduction and Conclusion sections.
paper_summary: paper_summary: To alleviate the poor performance of GCN on heterophilous graphs, an adaptive graph reconstruction mechanism is proposed in this paper. A dual optimization strategy for reconstruction graphs is also designed to make reconstruction graphs more adaptable to neighborhood aggregation mechanisms.
strength_weakness: strength_weakness: (1) The application of mutual information theory to validate the dual optimization strategy provides a robust theoretical foundation for the proposed method.

(2) Experimental results show the superiority of the proposed method on a number of real-world and synthetic datasets.
limitations: limitations: (1) The specific details for training the baseline methods/models are not fully explained.

(2) In Section 3.1, the notation of v is not defined, yet it is directly used as a superscript in lines 287-289.

(3) It is better to add illustrations (e.g., toy example) to explain the motivation of the proposed model.
paper_summary: paper_summary: The paper proposes a novel multi-view graph clustering method named Dual-Optimized Adaptive Graph Clustering (DOAGC). This approach leverages adaptive graph reconstruction and a dual optimization strategy to address the heterophilous graph issue while maintaining the benefits of traditional GNNs.
strength_weakness: strength_weakness: - The introduction of a dual-optimized adaptive graph reconstruction mechanism is innovative and addresses the limitations of existing GNNs on heterophilous graphs effectively.
- The authors provide extensive experimental results on both real-world and synthetic datasets, showcasing the method's robustness and effectiveness across different scenarios.
- The paper is well organized and well written.
limitations: limitations: - It seems that the proof of mutual information for the dual optimization strategy in the appendix is somewhat confusing. I suggest simplifying the notation for clarity.
paper_summary: paper_summary: The authors introduce a novel DOAGC method tailored for multi-view graph clustering (MVGC), specifically addressing the challenges posed by heterophilous graphs. The primary objective of DOAGC is to reconfigure the graph structure to better align with conventional Graph Neural Networks (GNNs). It features an adaptive graph reconstruction mechanism utilizing a dual optimization strategy.
strength_weakness: strength_weakness: - The methodology is illustrated in detail, with clear explanations of the adaptive graph construction and dual optimization strategy.
- Experimental results demonstrate DOAGC's effectiveness in addressing issues related to heterophilous graphs, outperforming other baseline methods on various widely used datasets.
- The inclusion of theoretical justifications, such as mutual information theory, adds depth to the understanding of why the proposed method is effective.
limitations: limitations: - The authors should explain how to determine the number of views to be utilized.
- In Table 1, the authors mention the "homophily degree" of the analyzed graphs; however, they do not provide a clear explanation of this term.
- Discussing some recent works on multi-view GNNs in Related Work would be helpful.