Towards Multi-view Consistent Graph Diffusion

Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-07 10:11:00

Abstract: Facing the increasing heterogeneity of data in the real world, multi-view learning has become a crucial area of research. Many researchers favor using graph convolutional networks for their adeptness at modeling both the topology and the attributes. 
However, these approaches typically only consider the construction of static topologies within individual views, overlooking the potential relationships between views in multi-view data. Furthermore, there is a glaring absence of theoretical guidance for constructing topologies of multi-view data, leaving uncertainties about whether graph embeddings are progressing toward the desired state.
To tackle these challenges, we introduce a framework named energy-constrained multi-view graph diffusion. 
This approach establishes a mathematical correspondence between multi-view data and graph convolution via graph diffusion. It derives a feature propagation process with inter-view perception by considering both inter- and intra-view feature flows across the entire system, treating multi-view data as a holistic entity. Additionally, an energy function is introduced to guide the inter- and intra-view diffusion functions, ensuring that the representations converge towards global consistency.
The empirical research on several benchmark datasets substantiates the benefits of the proposed method and demonstrates its significant performance improvement.

Main paper: 
 related work: 
 This section briefly reviews the topics related to this work, including graph-based multi-view learning and graph diffusion models.Graph-based multi-view learning has emerged as a widely adopted learning paradigm. Its fundamental objective is to effectively propagate labels across different views of data by leveraging carefully constructed sample similarity matrics. Satchidanand et al. [28] introduced an approach by employing the extended uncertain random walk framework to facilitate reasoning about multi-relational data. Hao et al. [32] proposed to enhance the learning process of individual view graph matrices and unified graph matrices, ultimately leading to the development of a multi-view fusion technique. Fan et al. [6] proposed a task-directed One2Multi graph autoencoder clustering framework that effectively reconstructs multiple graph views by learning node embeddings using one infographic view and content data. Liang et al. [19] introduced a min-max formulation for graph-based multi-view clustering. Subsequently, they transformed this formulation into a convex and differentiable objective function, enabling the utilization of a simplified gradient descent algorithm to efficiently reach the global optimum. Huang et al. [11] introduced an attention allocation method to enhance the efficacy of graph-based multi-view clustering, utilizing both node attribute similarity and self-supervised information to comprehensively assess node relevance. These methods demonstrate that graph-based multi-view learning yields superior results compared to traditional approaches.Graph neural diffusion refers to a diffusion process that is guided by partial differential equations (PDEs). Eliasof et al. [5] drew inspiration from the numerical solution method of PDEs on manifolds to propose PDE-GCN which aimed at mitigating the oversmoothing phenomenon observed in graph convolutional networks. Chamberlain et al. [2] established a connection between layer structure and topology with discretized choices of time and space operators, addressing multiple challenges in graph learning including depth, oversmoothing, noise perturbations, and bottlenecks. Zhao et al. [42] put forward an approach to automatically learn the optimal neighborhood size from the data, challenging the traditional assumption that all GNN layers and feature channels should be propagated using the same neighborhood size. Song et al. [29] extensively investigated the use of thermal semigroups to delve into the enhanced robustness of graph neural PDEs against topological perturbations and introduced a generalized graph neural PDE framework to define a class of robust GNNs. Thorpe et al. [30] introduced graph neural diffusion with source terms, a novel method for deep learning on graphs with a limited number of labeled nodes and without oversmoothing. Huang et al. [9] pioneered the development of a comprehensive node diffusion model known as NDM which is adept at capturing the distinct attributes of individual nodes within the diffusion process, consequently facilitating the creation of top-notch node representations. Although graph neural diffusion models have garnered considerable success in various domains, their extension to complex multi-view learning fields remains challenging due to the intricate coupling among views that cannot be overlooked. 
method: 
 In this section, we elaborate on the proposed methodology, beginning with the graph diffusion process and expanding it to encompass multi-view graph diffusion. We propose an energy function for the multi-view data to guide the representations of views towards consistency. Figure 2 demonstrates the proposed model in detail.Let G = (A, X) represents the graph, whereA ∈ R 𝑁 ×𝑁 and X = [𝑥 1 ; • • • ; 𝑥 𝑁 ] ∈ R 𝑁 ×𝐷 .Here, 𝑁 corresponds to the number of samples and 𝐷 denotes the number of dimensions. Drawing inspiration from thermal diffusion on Riemannian manifolds, all instances are treated as a cohesive entity and propagated as a continuous flow of features. The smoothness of feature propagation between two instances is directly proportional to the disparity in their respective feature sets. Mathematically, this diffusion process can be formally described as follows:EQUATIONwhere H(𝑡) represents the feature representation at time 𝑡. The symbol ⊙ denotes Hadamard product, A 𝑖 𝑗 denotes the smoothness of feature propagation between instances 𝑖 and 𝑗, ∇ indicates the difference between instances, and 𝑑𝑖𝑣 (•) represents the cumulative feature flow. More specifically, for the 𝑖-th instance, the heat flow per unit of time into its interior corresponds to the summation of the heat changes over its space. Equation ( 1) can be written explicitly asEQUATIONSince Equation ( 2) represents continuous dynamics, practical implementation requires the utilization of numerical methods for its solution. We extend this process to encompass more intricate multi-view scenarios.Denote multi-view data as{X (𝑣) ∈ R 𝑁 ×𝐷 𝑣 } 𝑉 𝑣=1, where 𝐷 𝑣 is the dimensions of the 𝑣-th view. Denote heterogeneous graph data G = {A (1) , • • • , A (𝑉 ) , X}, where A (𝑣) ∈ R 𝑁 ×𝑁 represents the 𝑣th meta-path. Let Y ∈ R N×c be the label matrix and 𝑐 denotes the number of classes. || • || 2 denotes the Euclidean norm of vector and || • || 𝐹 represents the Frobenius norm of matrix. The proposed model begins with a diffusion process that considers the multi-view dataset as a unified entity, facilitating diffusion within and among views via the flow of features. Given that each view in the multiview data exhibits distinct dimensions, potentially impeding feature flow, we address this by independently mapping the features of each view into a shared space. The specifics are outlined below:EQUATIONwhere W (𝑣) ∈ R 𝐷 𝑣 ×𝑑 and b (𝑣) ∈ R 𝑑 are trainable weight matrices and bias. In heterogeneous graph data, there is no need for feature dimension alignment. Instead, information from multiple metapaths is fused into features to create the multi-view format. We can substitute formula (3) with the subsequent equation:EQUATIONwhere GNN(•) can be a simple GNN architecture, such as GCN.After undergoing the aforementioned process, we expand Equation (2) into the multi-view formulation. The details can be expressed as follows:EQUATIONwhereS (𝑣)𝑖 𝑗 (𝑡) denotes the diffusion flow coefficient between positions 𝑖 and 𝑗 within the 𝑣-th view at time 𝑡, while P 𝑣𝑚 (𝑡) denotes the diffusion flow coefficient between the 𝑣-th view and the 𝑚-th view at position 𝑖 at time 𝑡. The interpretation of Equation ( 5) is as follows: it represents the rate of change of feature at position 𝑖 for 𝑣-th view. This change is determined by the summation of feature fluxes entering position 𝑖 from other positions within the same view in space, as well as the feature fluxes from position 𝑖 of other views entering position 𝑖 of the given view. We rely on a variety of ODE solvers for solving differential equations, including the explicit Euler method, the modified Euler method, and the 4-th order Runge-Kutta (RK) method. For example, the explicit Euler method with step size 𝛼 is as follows:EQUATIONTheorem 3.1. Equation (6) converges iteratively when 0 < 𝛼 < 1.Proof. The updating rules defined in Equation ( 6) can be rewritten asEQUATIONwhere Q (𝑣,𝑘 ) and P (𝑘 ) are the intra-view and inter-view diffusion matrices, respectively. To ensure convergence, the spectral radius 𝜌 of the update matrix must satisfy 𝜌 (•) < 1. For the term involving Q (𝑣,𝑘 ) , with 𝜆 max (S (𝑣,𝑘 ) ) = 1, convergence requires:EQUATION)This ensures a contraction in the vector space. Given P (𝑘 ) is doubly stochastic with 𝜆 max (P (𝑘 ) ) = 1, it maintains the norm of H (𝑣,𝑘 ) , thus reinforcing the constraint on 𝛼 to keep 𝜌 of the overall update matrix below 1. □Given the distinct nature of multi-view data in comparison to graph data, it encompasses a broader spectrum of heterogeneous information yet does not inherently possess a topological structure. Hence, the development of intra-and inter-view diffusion coefficients is critical for facilitating a coherent diffusion process. We define a energy of the multi-view diffusion system as follows:EQUATIONwhere 𝜂 (•) and 𝛿 (•) denote the monotonically increasing concave functions. The first term quantifies the variance among nodes within the same view, where a minimal variance correlates with reduced energy levels. Similarly, the second term quantifies the disparity between nodes across different views, with the principle that a lesser disparity also results in decreased energy. This dual-term representation underlines the system's equilibrium, emphasizing the importance of minimizing both intra-and inter-view discrepancies to achieve optimal energy efficiency.EQUATIONAddressing the equation presented necessitates navigating through an extensive array of constraints, posing significant challenges in deriving appropriate values for S (𝑣,𝑘 ) and P (𝑘 ) . According to [35] we can learn that the proposed energy upper bound is:EQUATIONwhere η (•) and δ (•) correspond to the conjugate functions of 𝜂 (•) and 𝛿 (•). The upper bound is realized if and only if the conditions are satisfied:EQUATIONwhere S(𝑣)𝑖 𝑗 = S(𝑣) 𝑖 𝑗 𝑁 𝑗 =1 S(𝑣) 𝑖 𝑗. In this paper, we specify the function 𝜂 (𝑥) = 𝛿 (𝑥) = 𝑥 -2 log(𝑒 𝑥 2 -1 + 1), and then Equation ( 12) can be rewrite as:𝑖 𝑗 =EQUATIONwhere 𝑓 : R 𝑑 × R 𝑑 → R, 𝑔 : R 𝑁 ×𝑑 × R 𝑁 ×𝑑 → R. To ensure the inter-view diffusion matrix P retains symmetry and bi-randomness throughout the computation, we employ the differentiable projection algorithm as proposed by Chen et al. ( 2023) [4] :EQUATIONJ 1 ( P) = ReLU( P), (15)EQUATIONEQUATIONwhere 1 denotes all 1 vector. Equation ( 15) -( 17) undergoes iterative computations, necessitating a large number of iterations to satisfy the desired conditions. To expedite the convergence of this process, Equation ( 14) utilizes an initialization to approximate the constraintsatisfying matrix P. Ultimately, we obtain P = J 3 (J 2 (J 1 (J 0 ( P)))). By selecting both intra-view and inter-view diffusion functions, the energy function reaches its upper bound. We compute the energy function 𝐸 ({H (𝑣) } 𝑉 𝑣=1 ) partial derivative with respect to H (𝑣) . Following this computation, we implement a gradient descent algorithm in a step-wise manner, adopting a step size denoted by 𝛾, as delineated below:EQUATION)The detailed calculation process of Equation ( 18) is shown in Appendix A. Equation ( 18) reveals its structural similarity to Equation (6) , indicating that executing a single iteration of the update process effectively corresponds to a reduction in the overall system energy.After performing 𝐾 iterations, we attain the final potential representation for each view. Subsequently, we fuse the representation from all views, culminating in the final representation denoted as:EQUATIONwhere F (•) is a fuse function, typically implemented as sum, average, and concatenation. We ultimately employ a Multilayer Perceptron (MLP) to map the fused representation onto the probabilities of each category, as outlined below:EQUATION)where MLP is parameterized with W ∈ R 𝑑 ×𝑐 and b ∈ R 𝑐 . For a semi-supervised classification task, the proposed method employs a loss function defined by the cross-entropy errors:EQUATION)where Φ is the set of samples with labels. The procedural steps of the proposed method can be summarized in Algorithm 1.Input: Multi-view data X = {X (1) , • • • , X (𝑉 ) }, label set Y, the hyperparameters 𝐾 and 𝛼. Output: Predictive output Ỹ. for 𝑣 = 0 → 𝑉 do Compute S (𝑣,𝑘 ) and P (𝑘 ) by Equation (13); 7:Re-normalize P (𝑘 ) by Equation ( 14) - (17) 8:Compute H (𝑣,𝑘 ) by Equation (10);  
experiment: 
 In this section, we evaluate ECMGD for two tasks: 1) multi-view data comprising multiple observable modal feature matrices, and 2) heterogeneous graph data containing multiple heterogeneous graphs and one observable feature matrix. For each task, we benchmark ECMGD against a range of closely related competing models.We evaluate ECMGD on 8 real-world multi-view datasets and 4 heterogeneous graph datasets. Among them, BDGP, Flickr, and NUSWIDE are vision-language datasets; HW, GRAZ02, Caltech102, OutScene, NoisyMNIST, and Scene15 are digit image datasets; and YouTube consists of video games data. For the heterogeneous graph datasets, ACM and DBLP are citation networks; IMDB is a movie dataset; and YELP is a subset derived from a merchant review website. Table 1 illustrates a brief summary of these datasets. Additional details of the datasets can be found in Appendix B. For multi-view classification, HLR-M 2 VS [38] and ERL-MVSC [7] are traditional baseline, Co-GCN [18] , DSRL [33] , LGCN-FF [3] , IMVGCN [36] , PDMF [12] , and GEGCN [23] are networks-based methods. For heterogeneous graph classification, we employ GCN [15] , HAN [34] , DGI [31] , DMGI [26] , SSDCM [24] , MHGCN [39] . Details of the comparison algorithm can be found in Appendix C.All compared methods use the default parameters following the original paper. For the proposed method, we specify the following hyperparameters: The layers number 𝐾 = 3, step size 𝛼 = 0.1, MLP with neuron sizes [𝐷 𝑣 , 64, c], the learning rate is set as 5𝑒-3, training epoch is 200, weight decay set as 5𝑒-5, and random dropout is 0.5. In multi-view semi-supervised classification, ECMGD leverages a split of 10% supervised samples for the training and 90% unsupervised samples for the testing. Given the absence of a designated validation set, we adopt the strategy of utilizing the model from the final iteration for testing purposes. Conversely, for the semi-supervised classification of heterogeneous graph data, we employ a partitioning scheme of 20% for training, 10% for validation, and 10% for testing. Some experimental results are presented below, with additional results provided in Appendix D.Performance. The experimental results presented in Table 2 indicate that the proposed algorithm surpasses other algorithms across most datasets. Particularly noteworthy is its superior performance on datasets such as Flickr, Scene15, and Youtube, where it achieves accuracy improvements of 3.1%, 3.5%, and 3.7%, respectively, compared to the algorithm with the second-highest accuracy. The only exception is the BDGP dataset, where the proposed algorithm performs slightly lower than LGCN-FF. Furthermore, Table 3 illustrates the proposed method continues to demonstrate competitive performance even on large-scale multi-view datasets. Visualization. Figure 3 provides a visualization of the classification outcomes across various compared methods applied to the HW dataset. Observation of the figure shows that the proposed method significantly enhances inter-class separability within this dataset. This enhanced separability underscores the superiority of the proposed method in delineating between classes more distinctly. Figure 4 presents a visualization of the inter-view diffusion matrix P across varying numbers of layers, offering empirical evidence of the convergence of views with an increasing number of iterations. This Traing set size. Table 4 elucidates the performance accuracy achieved by various algorithms under differing levels of supervision. An observation from this data is that the proposed method not only excels under constrained supervision rates but also significantly surpasses the algorithm with the next highest accuracy by a margin of 8.3% at a 20% supervision rate. This substantial differential underscores the adaptability and efficiency of the proposed algorithm in semi-supervised learning contexts. Such findings compellingly argue in favor of the proposed algorithm's enhanced capability to leverage limited labeled data more effectively. Convergence. The convergence behavior of the proposed method is illustrated in Figure 5 , which depicts the convergence curves for various datasets. From this figure, there is a gradual decrease in training set loss as the number of epochs increases, alongside a corresponding gradual increase in the accuracy of the test/validation sets. Notably, for the multi-view datasets, satisfactory convergence is achieved at approximately 40 epochs. In contrast, the heterogeneous graph datasets demand a significantly longer duration to reach convergence, typically around 200 epochs. ACM DBLPIn this subsection, we extend the experimentation to heterogeneous graph data as shown in Table 5 . The results indicate that the proposed method achieves superior performance on datasets ACM, DBLP, and YELP. Notably, the proposed algorithm exhibits slightly lower performance compared to MHGCN on the IMDB dataset.Training Time. In addition, we evaluate the computational efficiency of various algorithms when applied to heterogeneous graph data, with the findings detailed in Figure 6 . The comparative analysis reveals that, while the proposed method exhibits a marginal delay in execution time relative to HAN, it nonetheless delivers superior performance outcomes. Significantly, it maintains This indicates that the proposed method achieves a clear balance between computational efficiency and performance.In this subsection, we evaluate the effectiveness of the proposed method by progressively removing the intra-view diffusion matrix S and the inter-view diffusion matrix P. For the intra-view diffusion process, we employ the 𝑘-nearest neighbor (𝑘NN) technique to construct the topology of each view. To assess the inter-view diffusion process, we conduct experiments using the identity matrix. The experiment results are shown in Figure 7 . Notably, the worst performance is observed when neither S nor P is used. Subsequently, the performance of the algorithm improves when either S or P is retained, with the highest performance observed when both S and P are used. However, an interesting phenomenon emerges: the impact of missing P on many datasets is much smaller than missing S. However, the absence of P significantly affects performance on the Flickr dataset. This observation suggests that views in the Flickr dataset may contain more disparate and inconsistent information, necessitating inter-view diffusion to integrate them effectively.In this subsection, we investigate the parameter sensitivity of the proposed model by examining the impact of different step sizes (𝛼) and varying numbers of layers (𝐾) on the performance of the proposed model. Figure 8 depicts the experimental results. The figure reveals a notable trend: as the value of 𝛼 increases, the performance of the proposed model decreases while the variance increases. This phenomenon arises from the resemblance of 𝛼 to the step size utilized in gradient descent. With larger values of 𝛼, the energy oscillation becomes more pronounced, especially as the number of layers (𝐾) grows. Consequently, this oscillation may lead to convergence toward suboptimal energy states, ultimately resulting in diminished performance.  
conclusion: 
 In this paper, we introduced a framework called ECMGD, which re-bridges multi-view learning with GCNs through the lens of graph diffusion. This approach effectively closed the gap between GCNs and the pursuit of multi-view consistency, addressing an existing disconnect. Additionally, we proposed an integrated energy function tailored for the multi-view framework as a theoretical basis. The function coordinates intra-and inter-view diffusion to promote cross-view consistency. Through rigorous mathematical derivations, we determined that the proposed iterative algorithm is equivalent to a one-step gradient descent on the energy of the multi-view system. Experimental evaluations on various multiview datasets and heterogeneous graph datasets confirmed the superiority of ECMGD. Moving forward, we aim to further refine ECMGD to improve its applicability in more complex scenarios. 
: 
 aging graphs to capture complex, irregular structures across diverse fields has garnered significant attention. Graphs excel in depicting intricate relationships, such as those observed among individuals in social networks [27, 43, 44] and the interactive forces between molecules [8, 22, 37] , and many other domains [17, 20, 36] . Accordingly, graph-based multi-view semi-supervised classification augments the model's potential by leveraging the similarity relationships within data. Among various graph-based multi-view semi-supervised classification algorithms, the graph convolutional network based approach meets researchers' needs for deep models. Graph Convolutional Networks (GCNs) have garnered considerable attention for their capacity to model both data topology and feature representation. These capabilities have rendered GCNs crucial in a diverse array of domains., including bioinformatics [10, 14, 40] , action recognition [21, 25, 41] , and traffic forecasting [1, 13, 16] . Researchers have integrated GCNs with multi-view learning by constructing inter-sample relationships directly from the data and extracting consistent representations across different views, as shown in Figure 1 (a) . Despite these promising advancements, these methods still face the following challenges: Building a static data dependency within individual view restricts interactions to samples within each view, overlooking potential cross-view information exchange. Additionally, there is still a lack of theoretical understanding regarding how constructing data dependencies can guide multi-view representations to achieve consistency.To address the outlined challenges, we establish a connection between multi-view learning and GCNs through the lens of graph neural diffusion. Initially, we conceptualize multi-view data as a multivariate heat diffusion system, where heat can freely propagate within each view and between corresponding points in different views. We model this process through a graph diffusion equation. We then propose a system energy function aimed at guiding interview and intra-view diffusion towards a consistent direction for multi-view representations, as demonstrated in Figure 1 (b). Therefore, we develop a framework called Energy Constrained Multi-view Graph Diffusion (ECMGD). Specifically, the proposed method extend graph diffusion to multi-view scenarios by introducing feature flow across views. We then numerically discretize the modeled diffusion equation to derive an updated formula representing each view. To achieve global consistency, we introduce a energy function for multi-view data as a regularization tool. This function ensures that diffusion paths maintain consistent feature propagation both within and across views. Through rigorous mathematical analysis, we demonstrate the intrinsic equivalence between the discretized form of the proposed multi-view diffusion equation and the dynamic minimization of the energy function. A defining characteristic of the proposed framework is its dual diffusion function, which is guided by the system energy. This includes an intra-view diffusion function that facilitates feature propagation within the same view for dynamic instance interactions, as well as an inter-view diffusion function specifically designed to enable precise feature transfer across different views of a particular instance. The contribution of this paper can be summarized as:• Propose the ECMGD framework to effectively address the deficiency in inter-view perception when constructing data dependencies in multi-view data.  
 
 Appendix:  


Decision: The paper received three  reviews,  all agreeing  - after the rebuttal phase – on the “accept” recommendation.
Reviewers all state to be confident, and highlight different positive aspects of this submission, thus my recommendation is to accept the paper for oral presentation.

Reviews: review: paper_summary: paper_summary: In this paper, the authors introduce a novel framework called Energy-Constrained Multi-View Graph Diffusion (ECMGD) to address the limitations of current multi-view learning approaches, particularly their lack of theoretical guidance in constructing multi-view data topologies. By modeling multi-view data as a unified entity and incorporating an energy function to guide both inter-view and intra-view diffusion, the proposed method ensures that representations converge towards global consistency. This framework extends graph diffusion processes to multi-view scenarios, enabling more effective feature propagation across views. Empirical results on various benchmark datasets demonstrate significant performance improvements over state-of-the-art methods.
strength_weakness: strength_weakness: 1. This paper is well-written and easy to follow. The authors' keen observations drive their motivation, which is clearly illustrated.
2. The introduction of an energy function to guide the diffusion process is mathematically demonstrated to enhance the consistency of the representations.
3. The paper's effectiveness is validated through extensive experiments on multiple benchmark datasets, showing superior performance compared to existing methods.
4. Thorough ablation studies further support the robustness and superiority of the proposed method over all baselines.
limitations: limitations: 1. Section 3.2 is a bit confusing overall; it would be helpful if it could be divided for clarity.
2. The experiments in the paper primarily focus on evaluating semi-supervised classification tasks on several public datasets. However, the method has not been thoroughly assessed for its performance on different data characteristics, such as missing views.
paper_summary: paper_summary: To address the limitation of existing methods that only consider static data dependencies within a single view and overlook potential relationships between views, the authors propose a graph diffusion-based multi-view learning approach. Unlike current methods, this approach establishes a mathematical correspondence between multi-view data and Graph Convolutional Networks (GCNs) through graph diffusion. It treats multi-view data as a unified entity and designs a propagation process that is aware of inter-view relationships. Extensive experiments demonstrate the effectiveness of the proposed method.
strength_weakness: strength_weakness: 1, The authors propose a graph diffusion method for multi-view learning and conduct extensive theoretical analysis, demonstrating that this method can achieve consistency across different views.
2, The authors conducted extensive quantitative and qualitative experiments on multiple datasets, demonstrating the effectiveness of the proposed method.
limitations: limitations: 1, The authors claim that existing methods overlook potential information exchange between views, but the necessity of addressing this issue is not clearly articulated.

2, The authors use a graph diffusion approach to propagate information both within and between views, thereby achieving inter-view information consistency. However, there is a lack of discussion and explanation on whether this process effectively balances the utilization of differential information across the various views.

3, In Equation (9), the energy function of the multi-view diffusion system defined by the authors assigns a weight of 1/2 to the term quantifying intra-view differences, and a weight of 1/4 to the term quantifying inter-view differences. This discrepancy raises the question of whether it results in differing levels of emphasis on intra-view versus inter-view information.

4, Reproducibility is limited. Although the paper presents extensive theoretical proofs, the authors have not provided the corresponding code or implementation details.
paper_summary: paper_summary: The authors establish a mathematical correspondence between multi-view data and GCNs via graph diffusion. This approach treats multi-view data as a cohesive entity and devises a feature propagation process that is aware of inter-view interactions, incorporating both inter- and intra-view feature flows across the system. Furthermore, an energy function is introduced to guide this diffusion process, ensuring that the resulting representations achieve global consistency.
strength_weakness: strength_weakness: 1). An innovative approach involves treating multi-view data as a cohesive entity and designing a feature propagation process that sensitively integrates interactions between views, encompassing both inter- and intra-view feature flows throughout the system.

2). This is an extremely comprehensive set of baselines to test against, and the performance of ECMGD holds up impressively.

3). The code is concise and clear, and the results can be reproduced.
limitations: limitations: 1). Equations 14-17 describe the iterative process; how many iterations are selected for this paper?

2). The meta-path mentioned by the authors in line 281-line 283 requires further explanation.

3). What does the symbol 'S' represent in Section 4.6? If I understand correctly, does it refer to {S^(v)}_{v=1}^V?

4). I am curious about the computational time complexity of the proposed model due to the added diffusion among views.

5). If the value of alpha is made learnable, I believe it could significantly benefit the proposed model.

6). There seems to be some jumps in the derivation of Equation 12- 13. I think it is helpful to detail this process.