On the Benefits of Attribute-Driven Graph Domain Adaptation

Part 2/3

Regarding $k$NN, we follow existing works in the literature e.g., [4, 5, 6], which adopt it as a pre-processing step to construct the attribute view. Specifically, we note that the construction of attribute view using $k$NN is tied to the graph dataset itself, but does not rely on any specific algorithms or downstream tasks (i.e., we can obtain the attribute view prior to implementing our algorithm). In other words, it does not affect the computational complexity of the algorithm.

Q2

We would like to clarify that our paper specifically addresses the unsupervised domain adaptation (UDA) problem, where the model adapts knowledge from a source domain (with labeled data) to a target domain (without labeled data in line 161 target graph $G^T$) . Additionally, our target graph classification loss $\mathcal{L_T}$​ (Section 4.4, Eq. (4), line 339) does not rely on labels. $\hat{y}_i^T$​ is a pseudo-label that is obtained through dimensionality reduction. GAA focuses on aligning the node attributes and topological structures between the source and target graphs in the absence of labeled target data, which is a critical challenge in many real-world scenarios.

We believe that this unsupervised setting is highly important, as labeled data in the target domain is often unavailable or expensive to obtain. While our method does not rely on target labels, it employs novel techniques such as attribute alignment to achieve effective adaptation.

Q3

To address your concern, we have provided a detailed explanation of our hyperparameter selection strategy. Additionally, we discuss the optimal parameter settings in the context of our study. Furthermore, a comprehensive overview of the hyperparameter setting value for different datasets is provided in the revised manuscript Appendix D, Table 5.

$\alpha$, $\beta$, and $\tau$ are chosen from the set $\{0.005, 0.01, 0.1, 0.5, 1, 5\}$. These values provide flexibility for adjusting the relative importance of different loss terms. $k$(the number of neighbors for $k$-NN graph construction) is typically $k \in$ 1, \cdots, 10 $$ . The optimal value for k depends on the density and connectivity of the graph. The extremely large $k$ could also introduce noise that will deteriorate the performance [5]. Usually, our largest $k$ will be $6$ [4].

Airport Dataset: Often contains transportation networks with fewer nodes but complex edge relationships. Given the complexity of this dataset, $\alpha$, $\beta$, and $\tau$ should be set relatively higher to emphasize topology alignment and capture key structural relationships. $\alpha$, $\beta$ and $\tau$ is selected from $\{ 0.1, 0.5 \}$. A wide $k$ could be more effective due to the nature of these networks (containing both density and sparse). We select $k$ from $\{ 2, 3, 4\}$.

Citation Dataset: This dataset often has a higher node count and diverse structural characteristics. In such datasets, balancing the impact of node attributes and topology is important. $\alpha$, $\beta$ and $\tau$ is selected from $\{ 0.1, 0.5 \}$. A middle value of $k$ to capture relevant local structures could work well for this dataset. We select $k$ from $\{ 3, 4 \}$.

Social Network Dataset (Blog and Twitch): Social networks often contain a large number of nodes with rich attribute information but high variance in topology structure. Emphasize attribute consistency since social networks have distinctive attributes. Thus, attribute discrepancy is more sensitive to the values of $\alpha$, $\beta$, and $\tau$, which are selected from the set $\{0.01, 0.1, 0.5\}$. Small $k$ is recommended due to the dense connections in social networks. We select $k$ from $\{ 2, 3 \}$.

MAG Dataset: The MAG dataset is large and diverse, containing lots of classes with various relationships and rich metadata. Structural and attribute alignment are key factors. In this context, attribute shifts are both important to the values of $\alpha$, $\beta$, and $\tau$, which are selected from the set $\{0.1, 0.5\}$. The parameter $k$ works well when enabling the model to capture high-level local and global structural information within the graph. We select $k$ from $\{ 5, 6 \}$.

In summary, the weight of the loss function remains stable between 0.1 and 0.5, indicating that each loss function works well.

Part 3/3

Q4

To address your concern, we have included a comparison with the two latest state-of-the-art (SOTA) methods from 2024( Table 1-1, Table 1-2 and Table 3). Additionally, detailed descriptions of the experimental settings and an expanded comparison with other SOTA methods can be found in the revised manuscript ( Section 5.4, Table 2, Table 3, Table 4）.

[1] Liu, Shikun, et al. "Pairwise Alignment Improves Graph Domain Adaptation." International Conference on Machine Learning, 2024.

[2] Man, Wu, et al. "Unsupervised Domain Adaptive Graph Convolutional Networks." The Web Conference, 2020.

[3] Shi, Boshen, et al. "Improving Graph Domain Adaptation with Network Hierarchy." Conference on Information and Knowledge Management, 2023.

[4] Chen, Jie, et al. "Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection." Journal of Machine Learning Research, 2009.

[5] Wang, Xiao, et al. "AM-GCN: Adaptive Multi-channel Graph Convolutional Networks." SIGKDD International conference on knowledge discovery & data mining, 2020.

[6] Fang, Ruiyi, et al. "Structure-Preserving Graph Representation Learning." International Conference on Data Mining, 2022.

Part 1/3

Thank you for your constructive feedback! Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

We introduce Cross-view Similarity Matrix and Attention-based Attribute components to further boost the performance of GAA. This is essentially a tradeoff between algorithm performance and computational complexity. In light of your comments, we conducted additional experiments by removing the Cross-view Similarity Matrix and Attention-based Attribute, and the results are shown in Table 1-1 and Table 1-2. It can be observed that there is a slight performance drop after removing the Cross-view Similarity Matrix and Attention-based Attribute component. Specifically, we replace $att^S$ with $Z^S$ , $att^T$ with $Z^T$ , $att_f^S$ with $Z_f^S$ , and $att_f^T$ with $Z_f^T$. However, we note that it still outperforms other SOTA methods, such as recent 2024 work PA[1], which highlights the importance of attribute alignment in GAA.

Table 1-1. Cross-network node classification on the airport network and social network.

Table1-2. Cross-network node classification on the citation, blog network.

To further investigate the efficiency of GAAo, Table 2 reports the running time comparison across various algorithms. We also compared the training time and GPU memory usage of common baselines UDAGCN [2] and a recent SOTA method, JHGDA, which aligns graph domain discrepancy hierarchical levels [3]. As shown in Table 2, the evaluation results on U $\rightarrow$ B further demonstrate that, with tolerable computational and storage overhead, our method achieves superior performance.

Table2. Comparison of Training Time, Memory Usage, and Accuracy on U $\rightarrow$ B.

We also conduct one additional experiment on large-scale data MAG, and the results are shown in Table 3. It can be observed that GAA achieves state-of-the-art (SOTA) performance on large-scale datasets. Details of other baselines and dataset information are provided in the revised version (Table 4 and Table 1).

Table 3. Cross-network node classification on MAG datasets.

Dear Reviewer,

Thank you for your thoughtful feedback and for increasing the score of our manuscript. We sincerely appreciate your insightful questions, as addressing them has significantly strengthened our paper. We welcome any additional questions or suggestions you may have. Sincerely,

The Authors

Part 2/2

Q5

Following your suggestion, we also conduct one additional experiment on the hyperparameter analysis experiment in our revised manuscript Appendix D, Figure 5

To address your concern further, we have provided a detailed explanation of our hyperparameter selection strategy and discussed the optimal parameter settings in the context of our study. Furthermore, the revised manuscript includes a comprehensive overview of the hyperparameter selection process for different datasets, as outlined in Appendix D, Table 5.

$\alpha$, $\beta$, and $\tau$ are chosen from the set $\{0.005, 0.01, 0.1, 0.5, 1, 5\}$. These values provide flexibility for adjusting the relative importance of different loss terms. $k$ (the number of neighbors for $k$-NN graph construction) is typically $k \in$ 1, \cdots, 10 $$ . The optimal value for $k$ depends on the density and connectivity of the graph. The extremely large $k$ could also introduce noise that will deteriorate the performance [5]. Usually, our largest $k$ will be $6$ [4].

Airport Dataset: Often contains transportation networks with fewer nodes but complex edge relationships. Given the complexity of this dataset, $\alpha$, $\beta$, and $\tau$ should be set relatively higher to emphasize topology alignment and capture key structural relationships. $\alpha$, $\beta$ and $\tau$ is selected from $\{ 0.1, 0.5 \}$. A wide $k$ could be more effective due to the nature of these networks (containing both density and sparse). We select $k$ from $\{ 2, 3, 4\}$.

Citation Dataset: This dataset often has a higher node count and diverse structural characteristics. Balancing the impact of node attributes and topology is important in such datasets. $\alpha$, $\beta$ and $\tau$ is selected from $\{ 0.1, 0.5 \}$. A middle value of $k$ to capture relevant local structures could work well for this dataset. We select k from $\{ 3, 4 \}$.

Social Network Dataset (Blog and Twitch): Social networks often contain a large number of nodes with rich attribute information but high variance in topology structure. Emphasize attribute consistency since social networks have distinctive attributes. Thus, attribute discrepancy is more sensitive to the values of $\alpha$, $\beta$, and $\tau$, which are selected from the set $\{0.01, 0.1, 0.5\}$. Small $k$ is recommended due to the dense connections in social networks. We select $k$ from $\{ 2, 3 \}$.

MAG Dataset: The MAG dataset is large and diverse, containing lots of classes with various relationships and rich metadata. Structural and attribute alignment are key factors. In this context, attribute shifts are both important to the values of $\alpha$, $\beta$, and $\tau$, which are selected from the set $\{0.1, 0.5\}$. The parameter k works well when enabling the model to capture high-level local and global structural information within the graph. We select $k$ from $\{ 5, 6 \}$.

[1] Qiao, Ziyue, et al. "Information filtering and interpolating for semi-supervised graph domain adaptation." Pattern Recognition, 2024

Part 1/2

Thank you for your appreciated feedback. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

Thank you for your comment regarding the citation style. We apologize for the inconsistencies in our citations and have carefully reviewed and corrected them throughout the paper.

Q2

We acknowledge the importance of comparing our approach with recent advancements, including GIFI [1]. Although our method focuses on unsupervised graph domain adaptation, we recognize the value of benchmarking against semi-supervised methods for broader context. In our revised submission, we have incorporated this baseline into our experiments (see Section 5.4, Table 3 and Table 4). Our results demonstrate that while their method performs well in semi-supervised settings, our approach exhibits outperformance in unsupervised scenarios, highlighting its broader applicability. Additionally, we have clarified the distinctions between the two settings in Section 5.2.

Table1-1. Cross-network node classification on the airport network and social network.

Table1-1. Cross-network node classification on the Citation, Blog network.

Q3

Regarding the concern about masking node attributes and potential information loss, we would like to clarify that our method does not utilize node attributes masking. Our approach leverages full node attributes to preserve all available information. Although GAA is not designed to align in the embedding space, our approach achieves alignment by technically aligning graph node attributes and topology discrepancy in the embedding space. This ensures that representations in the embedding space are well-suited for domain adaptation without masking. We acknowledge the importance of exploring alignment in the embedding space as an independent strategy. This aligns with your suggestion and provides a promising avenue for future research. We will consider incorporating dedicated embedding alignment techniques in follow-up studies to further validate and improve our method.

Q4

We are pleased to provide additional T-SNE visualizations of citation datasets to demonstrate the effectiveness of our method. Detailed visualization results are in Appendix F of our updated manuscript. We observe from Appendix F compared with other SOTA methods. Firstly, nodes belonging to different classes are well-separated, demonstrating that GAA effectively distinguishes between classes in the embedding space. Secondly, nodes from the same class across different domains largely overlap, indicating that GAA significantly reduces domain discrepancies. The first observation highlights strong classification performance, while the second suggests effective domain adaptation.

Part 2/2

Q4

We introduce Cross-view Similarity Matrix and Attention-based Attribute components to further boost the performance of GAA. This is essentially a tradeoff between algorithm performance and computional complextity. In light of your comments, we conduct additional experiments by removing Cross-view Similarity Matrix and Attention-based Attribute and the results are shown in Table 1-1 and Table 1-2. It can be observed that there is a slight performacne drop after removing the Cross-view Similarity Matrix and Attention-based Attribute component. Specifically, we replace $att^S$ with $Z^S$, $att^T$ with $Z^T$, $att_f^S$ with $Z_f^S$, and $att_f^T$ with $Z_f^T$. However, we note that it still outperforms other SOTA methods, such as recent 2024 work PA[1], which highlights the importance of attribute alignment in GAA.

Table1-1. Cross-network node classification on the airport network and social network.

Table1-2. Cross-network node classification on the citation, blog network.

To further investigate the efficiency of GAAo, Table 2 reports the running time comparison across various algorithms. We also compared the training time and GPU memory usage of common baselines UDAGCN [2] and a recent SOTA method, JHGDA, which align graph domain discrepancy hierarchical levels [3]. As shown in Table2, the evaluation results on U $\rightarrow$ B further demonstrate that, with tolerable computational and storage overhead, our method achieves superior performance.

Table2. Comparison of Training Time, Memory Usage, and Accuracy on U $\rightarrow$ B.

Following your suggestion, we also conduct one additional experiment on large-scale data MAG, and the resutls are shown in Table 3. It can be observed that GAA achieves state-of-the-art (SOTA) performance on large-scale datasets. Details of other baselines and dataset information are provided in the revised version (Table 4 and Table 1).

Table3. Cross-network node classification on MAG datasets.

[1] Liu, Shikun, et al. "Pairwise Alignment Improves Graph Domain Adaptation." International Conference on Machine Learning, 2024.

[2] Man, Wu, et al. "Unsupervised Domain Adaptive Graph Convolutional Networks." The Web Conference, 2020.

[3] Shi, Boshen, et al. "Improving Graph Domain Adaptation with Network Hierarchy." Conference on Information and Knowledge Management, 2023.

Part 1/2

Thank you for your constructive feedback! Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

Thank you for your comment regarding the citation style. We apologize for the inconsistencies in our citations and have carefully reviewed and corrected this throughout the paper.

Q2

As mentioned in Line 187 of our manuscript, Theorem 1 indeed follows (Ma et al.,2021). On the other hand, we would like to note that Theorem 1 serves merely as a stepping stone for our theoretical analysis; our ultimate goal is to introduce Proposition 1, which highlights the role of attribute and topology divergence in GDA. On the algorithmic side, GAA minimizes both attribute and topology distribution shifts based on intrinsic graph property.

Q3

We appreciate your question, which gives us the opportunity to further validate the rationale behind our theoretical analysis and algorithm. Specifically, to investigate how the performance relates to the divergence, we have conducted an additional experiment, where we randomly generated 1000 pairs of graphs (source and target) varying attribute and topology values. At each time, the divergence of attribute and topology values between the source and target graphs was adjusted by utilizing make-blobs and stochastic block model (Details in Appendix F Section F1, Section F2). Figure 7 in Appendix F presents the normalized bound value divergence (calculated using Eq. (4) from Proposition 1) and loss value divergence $\mathcal{L}_A$ (defined in Eq. (12) on page 6) for both attribute and topology features as a function value divergence. It is evident that the theoretical values (blue dots) and actual loss values (red dots) exhibit highly consistent trends.

Furthermore, in each simulation, we first train a model using source values (either attribute or topology) and then evaluate its accuracy on the target graph (target accuracy). As shown in Figure 6, we observe that regardless of whether attributes or topology values are used, the target accuracy (green dots) consistently decreases as the divergence between the source and target domains increases. These empirical results highlight that both factors significantly influence the model's performance on the target domain, while the importance of attributes has long been overlooked in existing GDA studies. This further validates the rationale behind our work.

Part 2/2

Q3

$\mathcal{L}_D$ is a widely adopted unsupervised domain adaptation (UDA) loss in many graph domain adaptation (GDA) works [1, 2, 3], we include it to ensure a fair comparison. In Section 5.5 ablation study of our manuscript, the variant GAA_3 relies on the $\mathcal{L}_D$, which only leverages the topological information from the source and target graphs. Following your suggestion, we also conduct one additional experiment on the ablation experiment, including the performance of the model variant GAA_D, where $\mathcal{L}_D$ is excluded. We can observed that we observe that the model's performance is only slightly affected without $\mathcal{L}_D$, confirming that $\mathcal{L}_A$ plays a more important role.

Table3. Cross-network node classification on the airport network and social network.

Table4. Cross-network node classification on the Citation, Blog network.

[1] Wu, Jun, et al. "Non-IID Transfer Learning on Graphs." Annual AAAI Conference on Artificial Intelligence, 2023

[2] Man, Wu, et al. "Unsupervised Domain Adaptive Graph Convolutional Networks." The Web Conference, 2020.

[3] Shi, Boshen, et al. "Improving Graph Domain Adaptation with Network Hierarchy." Conference on Information and Knowledge Management, 2023.

Part 1/2

Thank you for your feedback. We would also appreciate your agreement on our method's novelty and effectiveness. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.

Q1

Our motivation is to make the attribute view matrix learnable. It selects essential attribute information to enable the model to obtain learnable attribute view information rather than relying on fixed attributes. This is essentially a tradeoff between algorithm performance and computional complextity to provide better performance.

Q2

The results from the $k$NN-GCN experiment (Tables 2 and 3) show that the Graph Convolutional Network (GCN) performs better when only relying on node attribute information. This finding highlights influence of attributes on model performance. We conducted ablation experiments focusing on this two specific terms: $||**att**^S - **att**^T||_2^2$ and $||**att**_f^S - **att**_f^T||_2^2$. The other loss functions used in model training are the same as those in GAA. Specifically, in the $\mathcal{L}_A$ function, GAA$_T$ employs $||**att**^S - **att**^T||_2^2$ but removes $||**att**_f^S - **att**_f^T||_2^2$, while GAA$_F$ utilizes $||**att**_f^S - **att**_f^T||_2^2$ but removes $||**att**^S - **att**^T||_2^2$. According to Table1. and Table2., we observe that GAA$_F$ generally outperforms GAA$_T$, suggesting that addressing attribute discrepancy is more beneficial for the performance of GDA. This is consistent with our observation that attributes discrepancy significantly larger than topology feature value discrepancy in our benchmarks. In addition, we discuss the impact of these two items separately in more detail in our revised manuscript Appendix F. In summary, while $||**att**_f^S - **att**_f^T||_2^2$ contributes more significantly to performance improvement, $||**att**^S - **att**^T||_2^2$ also plays a important role in enhancing the overall model.

Table1. Cross-network node classification on the airport network and social network.

Table2. Cross-network node classification on the Citation, Blog network.