Coupling Category Alignment for Graph Domain Adaptation

We are truly grateful for the time you have taken to review our paper, your insightful comments and support. Your positive feedback is incredibly encouraging for us! In the following response, we would like to address your major concern and provide additional clarification.

Q1: The idea of this paper, especially category-level alignment, may be neglected by graph domain adaptation (eg. [1]), but it is not new in domain adaptation. I think the novelty of this paper is ok for me, but not very high.

A1: Thank you for your constructive feedback. While category-level alignment is indeed an idea present in broader domain adaptation literature, we believe our work contributes uniquely to graph domain adaptation by specifically addressing this underexplored aspect within the graph setting.

Highlighting the Novel Contributions in Graph Domain Adaptation: Our work tailors the category-level alignment to the unique challenges of graph data, such as structural complexity and domain-specific topological differences. Besides, we clarify how our approach integrates multi-branch architecture and iterative pseudo-label refinement, making it particularly effective for addressing category-level shifts in graph domain adaptation.

Methodology: The proposed Coupling Category Alignment (CoCA) framework focuses on category-level alignment, an underexplored area in Graph Domain Adaptation (GDA). By employing a dual-branch structure—one branch capturing explicit structural features (SP branch) and the other learning implicit graph embeddings (MP branch)—CoCA effectively bridges the gap between feature space alignment and category-level alignment, addressing unique challenges in graph data.

Theoretical Contributions: CoCA provides theoretical guarantees for its performance. For example, Theorem 2 establishes an upper bound on target domain error. Furthermore, CoCA introduces a theoretical framework for iterative pseudo-label refinement, highlighting how category alignment progressively reduces domain error.

Experimental Validation: Extensive experiments on real-world datasets such as DD, COX2, COX2_MD, BZR, and BZR_MD validate the effectiveness of CoCA (Table 1). The results show that our method consistently outperforms state-of-the-art (SOTA) GDA methods.

Table 1: Graph classification accuracy (in %) on PROTEINS, COX2, and BZR (source->target).

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we address your comments in the following.

Q1: The paper makes ambitious claims about CoCA’s effectiveness across multiple datasets; however, the lack of a rigorous ablation study to dissect each component’s contribution weakens the evidence of its effectiveness. Without such analysis, it’s unclear if the improvements stem from the method itself or merely the combination of existing techniques.

A1: Thanks for your feedback. I’d like to clarify that we have conducted a rigorous ablation study in Section 5.4, where we analyze the impact of each component in the CoCA model. This section specifically breaks down how individual modules contribute to performance, providing evidence that the improvements are due to CoCA’s unique components rather than simply a combination of existing techniques.

Q2: The theoretical guarantees provided seem somewhat underdeveloped for the complexity of the task. While the paper introduces bounds, the assumptions and conditions for these bounds are not well-explained, which limits their practical relevance and could make it difficult for others to validate or build upon this work

A2: Thanks for your important feedback. To strengthen the theoretical guarantees and improve their clarity and practical relevance, we will revise the paper with detailed explanation of assumptions. We will clearly state all assumptions required for deriving the theoretical bounds, such as the properties of the underlying data distributions, the structural aspects of the graphs, and the behavior of the alignment mechanisms.

Q3: The paper's presentation could be more accessible; currently, it assumes a high level of familiarity with domain-specific jargon and concepts. A broader contextualization of the problem in simpler terms would make the work more approachable for a wider audience.

A3: Thanks for your question. Making our work accessible to a broader audience is essential, and we will take the following steps to improve readability:

Simplified Problem Context in the Introduction: We’ll start with a straightforward explanation of the problem, including a brief description of domain adaptation and category-level alignment, and their significance for graph data. This will set the stage in a way that readers outside the immediate field can follow.

Glossary of Key Terms: We will introduce key domain-specific terms when they first appear, with concise definitions to ensure that readers new to the topic understand the terminology.

Conceptual Overviews of Methodology: Each section introducing a complex method or theoretical result will start with a plain-language overview to frame the detailed content that follows. This will make the sections easier to approach and understand before delving into technical specifics.

By adding these clarifications, we aim to make the paper more accessible and ensure that the contributions are clear to a diverse audience.

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we address your comments in the following.

Q1: Experimental analyses are insufficient.

A1: We appreciate your feedback. To address the concern, we have conducted experiments on the real-world benchmark datasets DD, COX2, COX2_MD, BZR, and BZR_MD, as suggested. These datasets are widely recognized in graph domain adaptation research and were also used in CoCo and DEAL, ensuring comparability.

Table 1: Graph classification accuracy (in %) on PROTEINS, COX2, and BZR (source->target).

Our results show that our proposed method consistently outperforms other state-of-the-art methods, including those in CoCo and DEAL. This demonstrates the effectiveness of our strategies across various real-world datasets.

Q2: Besides, the new processed dataset is also not publically available, from the paper I can't get a sufficient understanding of this specific setting.

A2: Thank you for clarifying. Since the dataset is publicly available and the partitioning method is thoroughly detailed in the experimental section, we will emphasize these points clearly in the manuscript to ensure readers are fully informed.

Highlighting Dataset Availability: We introduce the dataset in Section 5.1, noting that all datasets can be freely accessed via the TUdataset website.

Clarifying Dataset Partitioning Details: In the experimental section, we briefly describe the partitioning method for each dataset. Additionally, we will provide a more detailed explanation of dataset construction in the appendix.

Q3: Although the results in Table 1 and Table 2 are impressive, it is unclear if the comparison is completely fair. Specifically, this paper compares their results with other works on the conventional graph network backbone. The authors exploit a new GMT graph network as the MPbranch while many methods in Table 1 and 2 do not use a new graph network. Comparing previous methods with the proposed attention-based method on conventional graph network is not fair.

A3: Thanks for your feedback. By including experiments with GMT as the backbone and demonstrating that our method still outperforms others under the same backbone, we have ensured a fair and robust comparison. The results are shown in Table 2. From the results, we can validate the superiority of the proposed CoCA.

Table 2: The classification results (in %) on Mutagenicity under edge density domain shift (source→target). M0, M1, M2, and M3 denote the sub-datasets partitioned with edge density. Bold results indicate the best performance.

We are truly grateful for the time you have taken to review our paper, your insightful comments and support. Your positive feedback is incredibly encouraging for us! In the following response, we would like to address your major concern and provide additional clarification.

Q1: The motivation of this manuscript is not clear. The authors should clearly claim the challenging issues in previous methods.

A1: Thanks for your valuable comment. We will clearly explain the motivation from different perspectives:

Motivation: The primary motivation of our work is to address the category-level domain alignment challenges in graph domain adaptation, where previous methods often struggle to accurately align domain distributions at the category level. This misalignment can result in poor classification performance, especially in scenarios with significant structural and categorical shifts between source and target domains.

Challenging Issues in Previous Methods:

(1) Lack of Category-Level Alignment: Previous methods typically focus on aligning the overall domain distribution without effectively addressing category-level alignment. This can lead to category confusion, where classes in the target domain are misclassified due to insufficient discrimination at the category level. As a result, these methods are prone to performance degradation in tasks requiring precise category alignment.

(2) Inadequate Handling of Structural Shifts: Traditional domain adaptation techniques for graphs rely primarily on message-passing neural networks (MPNNs) or single-branch architectures, which often fail to capture higher-order structural information explicitly. This limitation affects their ability to handle structural shifts between domains, leading to suboptimal performance in tasks where topological differences are critical.

(3) Insufficient Exploitation of Reliable Samples in Target Domain: Many existing approaches do not fully utilize reliable samples within the target domain. When pseudo-labels are generated, significant domain shifts often result in error accumulation, which degrades the adaptation process and leads to subpar performance.

Our Approach to Addressing These Issues: To overcome these challenges, our method introduces a Coupling Category Alignment (CoCA) framework with dual-branch architecture, which:

(1) Ensures category-level consistency by alternating reliable sample selection between branches to iteratively refine the alignment across categories.

(2) Utilizes both implicit (MPNN-based) and explicit (shortest-path-based) topological features to handle structural shifts more effectively.

(3) Integrates multi-view and cross-domain contrastive learning to minimize domain discrepancies at the category level, reducing error accumulation in pseudo-labels through a theoretically grounded process.

By addressing these challenges, our approach achieves more robust and accurate performance in graph domain adaptation tasks.

In light of these responses, we hope we have addressed your concerns, and hope you will consider raising your score. If there are any additional notable points of concern that we have not yet addressed, please do not hesitate to share them, and we will promptly attend to those points.

We are truly grateful for the time you have taken to review our paper, your insightful comments and support. Your positive feedback is incredibly encouraging for us! In the following response, we would like to address your major concern and provide additional clarification.

Q1: The novelty of this paper appears incremental.

A1: Thank you for your comment. It’s important to recognize that while the graph convolutional network (GCN) and graph kernel network branches in our framework may resemble the structure of the branches in the referenced work [1], our approach introduces a distinct focus on achieving category-level domain alignment. Specifically, our methodology centers on Coupling Category Alignment (CoCA), which systematically iterates between branches to select reliable samples, thereby facilitating cross-branch adjustments that mitigate potential domain shifts in an unsupervised manner. This iteration enhances the model’s capacity to address category-level alignment with theoretical backing, a differentiation from prior methods.

Moreover, the multi-view and cross-domain contrastive learning in our framework differs from typical cross-branch contrastive approaches. Our method leverages a unique alignment strategy to reduce classification error in target domains while establishing consistency between domains at the category level. The resulting theoretical generalization bounds for category alignment present a novel contribution that is empirically supported by extensive experimentation.

In essence, while there are surface similarities to the branches and contrastive approaches of [1], our work provides unique theoretical and practical innovations that address unsupervised domain adaptation challenges in graph classification. This distinct focus on category alignment and iterative optimization exemplifies our contribution beyond incremental improvements.

Q2: This paper lacks self-containment. Many mathematical symbols are used without definition; for example, in line 139, it is unclear what Z, h, and \hat{h} represent.

A2: We are sorry for the confusing. We add the definition of each symbols: $Z$ represents the space of graph representations, and $h$ represents the learned hypothesis, or the model’s decision function, in the source domain, and $\hat{h}$ is the corresponding decision function applied in the target domain. We will revise the manuscript to provide precise definitions for all mathematical symbols upon their first usage.

Q3: Some theorem definitions lack rigor. For instance, "Theorem 2" is not a true theorem but rather a corollary inferred from Theorem 1, as also stated in [2]. Similarly, "Theorem 4" should not be classified as a theorem, as it is also a corollary based on an existing theorem.

A3: Thanks for your question. We rename Theorem 2 to Corollary 1 and explicitly clarify that it follows directly from Theorem 1. Similarly, Theorem 4 will be renamed Corollary 2, reflecting its basis on an existing theoretical result rather than a novel, standalone theorem.