Multi-View Graph Clustering via Node-Guided Contrastive Encoding

Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.

Q1: Time Complexity Concerns
A1: We appreciate the reviewer’s attention to computational efficiency. While generating V views iteratively introduces additional complexity, this design aligns with state-of-the-art late-fusion multi-view clustering methods (e.g., DualGR), where view-specific processing precedes fusion. As detailed in Section 4.3.4 (Complexity Analysis), NGCE’s complexity remains comparable to prior works, as the incremental cost arises solely from a parallel GNN module (for node-guided encoding, the part from $\tilde{X}$ to $\overline{X}^n$ in Figure 1).

Q2: Incremental Contribution
A2: While NGCE builds on contrastive learning principles, its node-guided encoding mechanism represents a novel contribution by unifying homophilic and heterophilic interactions within a single framework. Unlike prior works that treat these as separate tasks or rely on heuristic aggregation, NGCE explicitly models their interplay through adaptive weight learning and noise-augmented recovery (Section 3.1.2). This design enables superior performance on both homogeneous and heterogeneous graphs.

Q3: Applicability to Purely Structural Graph and Functionality Without Node Features

A3: We fully acknowledge your concern regarding the method's reliance on node features, which indeed limits its applicability in datasets with limited or no node feature information. In the revised Limitations subsection in Discussion section, we clarify that NGCE’s current implementation assumes the availability of node features. Specifically, we will acknowledge that the current implementation struggles in scenarios where node features are absent. However, we believe that this limitation is not insurmountable. There are potential solutions to extend our approach to such datasets, and we intend to explore them in future work. Possible strategies include:

• Random Walk-based Feature Generation: Random Walks could be employed to generate node embeddings by capturing structural information from the graph, an approach often used in graph embedding techniques such as DeepWalk.
• Learned Node Features: We could also incorporate a dedicated encoder to generate node features directly from the graph structure, thereby enabling the method to function even in the absence of explicit node attributes.

Both strategies might allow us to retain the benefits of our node-guided contrastive encoding approach while extending its applicability to a wider range of datasets. We will present these potential solutions in the Limitations subsection to provide a more comprehensive view of possible extensions to our work.

Q4: Typos and Redundant Definitions
A4: In response, we have carefully reviewed the entire manuscript and addressed all identified issues to improve clarity, consistency, and overall presentation.

We sincerely appreciate your thorough review and constructive feedback, which have greatly improved the quality of our manuscript.

Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.

Q1: Delayed Definition of Mathematical Symbols
A1: We sincerely apologize for the oversight in deferring symbol definitions to the appendix. In the revised manuscript, all mathematical symbols (e.g., adjacency matrices, node features, and operators) are now explicitly defined when they first appear in the main text. For example, all parameters related to GNNs are now clearly introduced within their corresponding equations.

Q2: Ambiguity in Equation (11)
A2: We thank the reviewer for identifying this ambiguity. The GCN architecture in Equation (11) shares the same structural design as the GCN in Equation (8) and operates with independent parameters (i.e., no weight sharing). This distinction ensures that the node recovery module learns distinct patterns from the graph encoding process. We have clarified this in the revised manuscript by explicitly stating that in Equation (11).

We greatly appreciate your careful evaluation and thoughtful recommendations, which have significantly improved the rigor and clarity of our work.

Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.

Q1: Theoretical Validation or Detailed Experimental Evidence of Section 3.1.2

A1: Thank you for your valuable feedback. In the current version, we have provided a detailed algorithmic description and conducted extensive ablation studies to empirically validate the effectiveness of our proposed mechanism. We fully acknowledge the importance of theoretical analysis and plan to incorporate rigorous theoretical examinations (including convergence analysis and generalization capability analysis) in future extensions of this work.

As shown in the following tables, removing the node recovery component ("NGCE w/o node recovery") leads to significant performance degradation across both homogeneous and heterogeneous graphs.

This table reports clustering performance metrics in the order of NMI/ARI/ACC/F1. These results suggest that the recovery mechanism plays a critical role in capturing both local and global structural patterns, especially in heterogeneous datasets.

Q2: Typographical Revisions

A2: In response, we have carefully reviewed the entire manuscript and addressed all identified issues to improve clarity, consistency, and overall presentation.

Q3: Equation (9) Clarification

A3: We have revised the explanation surrounding this equation to provide clearer context and interpretation. Specifically, the first term minimizes the agreement between the reconstructed node features and the features of the masked nodes in the encoder graph, since there is no valid information correlation in these nodes; the second term drives the GCN with graph joint encoding embeddings to retain critical unmasked node information.

The whole process requires the GCN to identify and preserve the correct unmasked features from the masked non-adjacent nodes in the graph structure, where the graph joint encoding embeddings are forced to learn the essential patterns of node feature distribution in the encoding stage.

Q4: First-Order Neighborhood Superiority (Figure 2)

A4: We believe that the superior performance under first-order neighborhood aggregation is due to the graph encoding mechanism proposed in our framework. This phenomenon suggests that our learning paradigm enables the encoded graph to directly integrate valuable edges, thereby substantially reducing the necessity for higher-order neighborhood processing in subsequent GNN operations. Specifically, when the order is set to 1 or some other low number, the model effectively captures direct neighborhood relationships within the encoded graph while minimizing noise interference. In contrast, although higher-order aggregation introduces redundancy and can theoretically provide additional information, the induced noise becomes particularly difficult to mitigate in unsupervised learning scenarios due to the lack of explicit supervisory signals. A discussion of this trade-off, along with the inherent limitations of our model, will be provided in the Discussion section.

Q5: 2024 Baseline Comparisons.

A5: We added comparisons with VGMGC [TNNLS 25], BMGC [ACM MM 24], and SMVC [Neural Networks 24]. Among these, VGMGC and BMGC are open-source and can be evaluated across all datasets, while SMVC, though not yet open-sourced, shares our homogeneous dataset selection. The comparison results are shown in the table below. For open-source baselines, we used the results reported in the original paper where available; otherwise, we evaluated them using default parameters or settings from similar datasets. The following table reports clustering performance metrics in the order of NMI/ARI/ACC/F1.

These experimental results show that our method consistently achieves superior performance compared to methods in recent publications.

We greatly appreciate your rigorous evaluation and suggestions, which have significantly strengthened our manuscript.