Revisiting Self-Supervised Heterogeneous Graph Learning from Spectral Clustering Perspective

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations: (i) noise in graph structures is often introduced during the message-passing process to weaken node representations, and (ii) cluster-level information may be inadequately captured and leveraged, diminishing the performance in downstream tasks. In this paper, we address these limitations by theoretically revisiting SHGL from the spectral clustering perspective and introducing a novel framework enhanced by rank and dual consistency constraints. Specifically, our framework incorporates a rank-constrained spectral clustering method that refines the affinity matrix to exclude noise effectively. Additionally, we integrate node-level and cluster-level consistency constraints that concurrently capture invariant and clustering information to facilitate learning in downstream tasks. We theoretically demonstrate that the learned representations are divided into distinct partitions based on the number of classes and exhibit enhanced generalization ability across tasks. Experimental results affirm the superiority of our method, showcasing remarkable improvements in several downstream tasks compared to existing methods.

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Peer review

Reviewer oBdx5/10 · confidence 2/52024-07-01

Summary

The paper proposes a new framework that revisits SHGL from a spectral clustering perspective, incorporating rank and dual consistency constraints. This approach uses a rank-constrained spectral clustering method to refine the affinity matrix and remove noise, while also integrating node-level and cluster-level consistency constraints to better capture and use invariant and clustering information. Theoretical analysis and experimental results show that this new method significantly improves performance in downstream tasks compared to existing methods.

Strengths

1. This paper provides a theoretical investigation of previous SHGL methods from the perspective of spectral clustering. 2. This paper proposes a new framework to capture the cluster-level graph invariant representations. 3. Experiments demonstrate the effectiveness of the proposed methods.

Weaknesses

Unfortunately, this paper is not easy to follow due to the missing parts in terms of motivation and logic. 1. In the introduction part, the authors mention three challenges abruptly from Lines 44 to 48. However, it is unclear why they are challenging to address. For example, why it is difficult to understand previous SHGL methods from the clustering perspective? It is also unclear the logical relationships between the three challenges. 2. In Section 2, the authors introduce some notations about the heterogeneous graph. However, it is unclear what is the objective of the problem. 3. In Section 2.1, it is unclear why authors need to bridge the gap between SHGL methods and graph-cut algorithm, and what is its benefits. 4. In Section 2.2, it is unclear why the rank constraint can mitigate noisy connections. 5. When reading Section 2.2, the reviewer gets lost in the lemma and equation details. It is better if the authors can highlight the contributions and leave all technical derivations to the appendix. 6. The logical relationship between Sections 2.2 and 2.3 is unclear. Why both the low-rank constraints and dual consistency constraints should be imposed, and what is the relationship between these two constraints? 7. In the experiments, it is unclear why two homogenous graph datasets were used for performance evaluation, given the objective of this paper is for heterogeneous graph learning.

Questions

Please find questions in the weaknesses above.

Rating

5

Confidence

2

Soundness

3

Presentation

2

Contribution

3

Limitations

This paper does not mention the limitations of this work or the potential negative societal impacts.

Reviewer v7xk5/10 · confidence 3/52024-07-13

Summary

This work deals with the problem of self-supervised representation learning in heterogeneous graphs. First, a spectral-clustering based objective is presented to unify the objectives of existing methods. Second, a novel self-supervised method is proposed that tries to capture both the cluster information and node-level information in the learnt representation. Experiments show the effectiveness of the proposed method over existing methods.

Strengths

1. The proposed method is novel and follows a principled design. 2. Presented theoretical analysis is helpful in deeper understanding of existing and proposed method. 3. Experiemental section is comprehensive with adequate baselines, datasets, and ablations.

Weaknesses

1. Presented theorems are often unclear or imprecise. For example (a) In Theorem 2.6, authors use the term model complexity abruptly without any definition or reference. I could not understand the relation between the infimum and supremum of model complexity with generalization ability (which also needs to be rigorously defined). (b) In Theorem 2.2, what exactly are the previous meta-path-based and adaptive-graph-based SHGL method mentioned in the theorem statement? What is the expression for the regularization term for the corresponding previous methods? (c) There does not seem to be a clear delineation between what already exists in the literature and what is the new contribution of the paper. E.g., does Theorem 2.3 directly follow from existing results in the literature, or does this require custom analysis? (d) Theorem 2.5 is not precise enough. When referring to "proposed method", it would be more precise to refer to specific objective function or algorithm block. Also "equivalent to performing spectral clustering based on the affinity matrix ....". Authors are recommended to replace the language description with precise objective function. 2. The writing is often unclear and could be greatly improved. Several terminologies (which might not be standard in the literature) are never explained/defined. For example: (a) Section 1 Line 42 ".. it is feasible to analyse ..", it is not clear what exactly is feasible to analyse (although after Section 2.1, it can be understood). (b) In abstract and introduction, it is not clear what is invariant information is (c) Sentence in line 216-218 is unclear. (d) How does H^T H = I imply statistical independence?

Questions

Please refer to the questions and comments in Weaknesses section.

Rating

5

Confidence

3

Soundness

2

Presentation

2

Contribution

2

Limitations

Limitations and impacts are adequately discussed in the Appendix.

Reviewer NZZJ6/10 · confidence 3/52024-07-13

Summary

This paper proposes a theory-backed method for Self-Supervised Heterogeneous Graph Learning (SHGL) based on spectral clustering and incorporates rank constraint and node/cluster consistency regularizers to generate better embeddings. In specific, the authors start by showing that existing algorithms divide the representations into a certain number of clusters that are much larger than the number of real classes. Then, an objective function with rank constraint is proposed to reduce the noise of message-passing and consistency terms are employed to improve downstream task performance. Experiments on the real datasets show that the proposed method outperforms other baselines.

Strengths

1. The paper analyzes the issue of the exiting methods that are based on meta-path-based graph or the adaptive graph structure theoretically. Furthermore, a rank and consistency constrained approach is proposed to tackle know issues of SHGL and it is shown to have less complexity theoretically. 2. Experimental results show the superiority of the proposed method consistently over a variety of datasets.

Weaknesses

1. Notations are not always clearly defined. For example, what are the dimensions of the mapping $g_{\phi}$ and $p_{\phi}$? 2. The derivation of the first loss term is not clear to me. Why is there an entropy constraint term in (13)? How do we translate Eq. (8) to Eq. (13) and what is the correspondence of the terms? Line 183 states that ‘fitting eigenvectors F by (13)’, but it seems that F does not appear (13). Or is it that (13) is only for solving the last term in (8)? Clarity can be further improved upon the objective function, especially the term $\cal{L}_{sp}$. 3. Why is $Y$ a probability matrix? Is there any guarantee on that? Only orthogonality is proved for the matrix. Do we need a simplex constraint on the columns of $Y$?

Questions

1. In Line 172, whose independence are we referring to? Why $H^T H=I$ is equivalent to statistical independence? 2. In practice, is it always the case that number of clusters equal to $c$ will give the optimal results? 3. How do we reach the inequality in (53) and (54)? Does the term in (55) correspond to the loss function in (17)?

Rating

6

Confidence

3

Soundness

3

Presentation

2

Contribution

3

Limitations

The authors are encouraged to discuss the limitations in the main paper.

Authorsrebuttal2024-08-12

Thank you for your constructive feedback. According to your suggestions, we will summarize the notations and details for deriving Eq. (53) and Eq. (54) in the Appendix. Moreover, we will replace "statistically independent" with "uncorrelated" to avoid confusion. For the follow-up question, Eq. (13) contains two terms, the first term in Eq. (13) is derived from and for solving the last term of Eq. (8) by fixing $\mathbf{S}$ and approximating $\mathbf{F}$ with $\mathbf{Y}$. In contrast, the second term (i.e., the entropy constraint) in Eq. (13) is not derived from Eq. (8), and it is a widely used regularization term in existing literature [1-4] to help optimize $\mathbf{Y}$ by preventing most nodes from being assigned to the same cluster. We will add more clarification about Eq. (13) in the final version. The final objective function Eq. (18) only contains Eq. (13) (i.e., $L_{sp}$) but not the whole Eq. (8) because, in the final objective function, we only need to approximate one variable (i.e., $\mathbf{F}$) in the last term of Eq. (8) with $L_{sp}$. In contrast, another variable (i.e., $\mathbf{S}$) in the first two terms of Eq. (8) is already solved by its optimal solution in Eq. (10) and does not require gradient back-propagation to optimize. That is, the first two terms of Eq. (8) do not have to appear in the final objective function. Please let us know if you have any other concerns. Thanks! [1] Sparse Subspace Clustering with Entropy-Norm. ICML 2020. [2] Deep semantic clustering by partition confidence maximisation. CVPR 2020. [3] Contrastive clustering. AAAI 2021. [4] Entropy regularization for unsupervised clustering with adaptive neighbors. Pattern Recognition 2022.

Reviewer NZZJ2024-08-13

Thank you for the further clarification and addressing my concerns. I will increase the score accordingly.

Reviewer LzB27/10 · confidence 5/52024-07-17

Summary

Overall, this paper makes the first attempt to theoretically revisit previous SHGL methods from the spectral clustering perspective in a unified manner. Specifically, this paper revisits SHGL from the spectral clustering and introducing a novel framework enhanced by rank and dual consistency constraints. Specifically, the proposed framework incorporates a rank-constrained spectral clustering method that refines the affinity matrix to exclude noise effectively. Additionally, the proposed method integrates node-level and cluster-level consistency constraints that concurrently capture invariant and clustering information to facilitate learning in downstream tasks.

Strengths

1. I really appreciate the idea that revisiting previous SHGL methos from the perspective of spectral clustering, which is interesting and may inspire some researchers in the graph learning as well as the self-supervised learning communities. 2. Theoretical analysis verifies the effectiveness of the proposed method, which divides the learned representations into distinct partitions based on the number of classes. Furthermore, the proposed method exhibits enhanced generalization ability than previous SHGL methods. 3. Extensive experiments on both heterogeneous and homogeneous graphs demonstrate the effectiveness of the proposed method. Visualization and case studies further verify the claims in this paper. 4. The proposed rank-constrained spectral clustering is novel and interesting, and it seems like can also be used to the graph structure learning in the homogeneous graph.

Weaknesses

1. In the Introduction, the authors claim that previous methods conduct message-passing relying on meta-path-based graphs and adaptive graph structures, which inevitably include noise. Are there any real examples to better illustrate the noise in meta-path-path based graph as well as the adaptive graph structures? 2. In the dual consistency constraints, the proposed method designs the node-level consistency constraint to capture the invariant information between the node representations and the heterogeneous representations. How about replacing the node-level consistency constraint with other common loss, such as InfoNCE [1]? [1] Aaron van den Oord et al., Representation learning with contrastive predictive coding. 3. The authors design the rank-constrained spectral clustering to learn the affinity matrix for nodes belonging to the same node type. Although the visualization verifies the effectiveness of the affinity matrix, it would be better for the authors to add some ablations studies to further verify it, such as replacing the affinity matrix with a self-attention mechanism or simple cosine similarity. 4. What are the specific processes for different downstream tasks (e.g., node classification and node clustering)? It seems like training the proposed method first, and then freezing parameters of the model and applying outputted representations for downstream tasks. 5. The proposed method is designed for the heterogeneous graph while it can be implemented on both the homogeneous graph datasets and heterogeneous graph datasets. Is it just to replace the heterogeneous graph encoder with the graph convolutional layer? How to generate two different views for the dual consistency constraints? 6. It would be better to add some recent works about the self-supervised heterogeneous graph learning in the related work, especially those published in the past two years. 7. The paper needs further proofreading. For example, - In Eq. (17) I know $q_i$ is the i-th projected representation. What’s the $\hat{\mathbf{q}}_{\mathbf{y}_i}$ actually means? - The definitions of some symbols need to be further determined, such as \mathbf{I} in Definition 2.1. I guess it might represent the identity matrix. - Some mistakes in Table 3, the Freebase dataset should be removed from the Table. - The caption of Table 7 should be fixed.

Questions

see weakness.

Rating

7

Confidence

5

Soundness

3

Presentation

3

Contribution

4

Limitations

Yes, the authors have discussed the limitations and potential negative societal impact.

Reviewer oBdx2024-08-07

Thank you for the rebuttal

Thank you for the detailed rebuttal, and I increase the score to 5.

Reviewer v7xk2024-08-11

Thank you for the response. I encourage the authors to revise the manuscript with discussed changes to improve the presentation and theoretical rigor. Regarding $H^T H = I$, note that uncorrelation does not imply statistical independence. Uncorrelation only prevents linear dependence but cannot prevent some nonlinear dependence. Consider using "uncorrelated" instead of "statistically independent". Based on the overall quality of the paper, I maintain my score.

Authorsrebuttal2024-08-11

Thank you for your valuable feedback and positive comments on our paper. According to your suggestions, we will replace "statistically independent" with "uncorrelated" to avoid confusion. Additionally, all discussed changes will be incorporated into the final version.

Reviewer NZZJ2024-08-12

Thank you for the response and clarification. I would suggest summarizing the notations in the Appendix and please add the details for deriving Eq. (53) and (54) as well. Besides, it looks like $H^{\top} H = I$ only implies uncorrelatedness instead of statistical independence. Please consider rephrasing the sentences. A follow-up question: my question on the loss term derivation was how do we go from (8) to (13)? If (13) is only for solving the last term in (8) (i.e., for solving Y with fixed S), then why does the final objective function (18) only contains ${\cal{L}}_{sp}$ but not the whole Eq. (8)? If this loss is for solving (8), how is the entropy constraint term derived from (8)?

Reviewer LzB22024-08-13

Thanks for the authors' clarification and my concerns are well addressed. Overall, this is an interesting work based on its insights, novelty, and theory framework. After acrossing other comments and the rebuttal, I maintain the acceptance of this paper.

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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