Title: UGC: Universal Graph Coarsening
Venue: NeurIPS 2024
Accepted: yes
Keywords: Graph Coarsening

Graph Neural Networks

Locality sensitive hashing

Heterophilic Graph

Scaling Graph Learning
Abstract: In the era of big data, graphs have emerged as a natural representation of intricate relationships. However, graph sizes often become unwieldy, leading to storage, computation, and analysis challenges. A crucial demand arises for methods that can effectively downsize large graphs while retaining vital insights. Graph coarsening seeks to simplify large graphs while maintaining the basic statistics of the graphs, such as spectral properties and $\epsilon$-similarity in the coarsened graph. This ensures that downstream processes are more efficient and effective. Most published methods are suitable for homophilic datasets, limiting their universal use. We propose **U**niversal **G**raph **C**oarsening (UGC), a framework equally suitable for homophilic and heterophilic datasets. UGC integrates node attributes and adjacency information, leveraging the dataset's heterophily factor. Results on benchmark datasets demonstrate that UGC preserves spectral similarity while coarsening. In comparison to existing methods, UGC is 4x to 15x faster, has lower eigen-error, and yields superior performance on downstream processing tasks even at 70% coarsening ratios.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nGraph coarsening aims at scaling an original large graph into a small graph. This paper proposes a graph coarsening method which was designed to be equally suitable for homophilic and heterophilic datasets, specifically, aggregating node clusters identified by a hash function. This paper is one of the pioneering works exploring graph coarsening in heterophilic graph datasets, and the proposed solution seems promising. However, the current formulation of the proposed method and some of the claims in the paper are not rigorous and solid enough.\n\nSTRENGTHS:\n-\tThis paper is one of the pioneering works exploring graph coarsening in heterophilic graph datasets.\n-\tAggregating hypernodes through a hash function instead of neighbors is a promising solution to perform heterophilic graph coarsening.\n\nWEAKNESSES:\n-\tThe presentation of this paper is unclear. Check out `Questions’.\n-\tThe current formulation of the proposed `Hash functions’ is ambiguous and biased. Check out `Questions’.\n-\tSome claims were in fact wrong. Check out `Questions’.\n\nQUESTIONS:\n-\tLine 4. `vital insights’, `essential features’ in line 5. and ‘vital information’ in line 20. are too vague. I suggest being more specific and keeping the phrasing unchanged.\n-\tLine 67-68. `The Graph Coarsening(GC) problem \\bf{may be} thought of as learning a coarsening matrix….’ Is it or is it not? A formal definition of the Graph Coarsening problem is required whether cited from others or by you.\n-\tLine 128-129. `Due to this, these methods are extremely computationally demanding and defeat the purpose of reducing the original graph.’ This statement suggests that ‘GNN-based Graph Condensation’ is useless. I suggest being more objective.\n-\tLine 143-144.` The concepts of homophily and heterophily in graphs are primarily concerned with whether the edges between two nodes align with their respective features.’ is not correct. Recall that homophily and heterophily are defined by whether edges align with labels, not features. You need to state a hypothesis or experimentally verify that: `the same labels imply similar features’.\n-\tLine 155-160. The current formulation hash function is biased to node degree distribution since you concat the adj with node feature. Consider this example that a graph has 1 node whose degree is 999 and other 999 nodes’ degree is 1 (a radial graph). In this case, the hash value of the degree 999 node will be significantly larger than the other nodes, e.g. 90-99 to 1-10, and setting `r’ parameter only makes it worse. Meanwhile, the 11-89’th hypernode is empty. This is an extreme case of long-tail distribution of node degrees, however, simple concatenation inevitably causes the number of aggregated nodes in the hypernode to be uneven, specifically strongly correlated with the node distribution.\n-\tAgain, concat the adj with node feature is ambiguous. Considering that the hash result will change w.r.t. the change of index order of nodes.\n-\tWhat is ‘|||’ in the proof of Theorem 3.1 in line 575? Moreover, the derivation in the proof is speculative. You need to explain clearly why each step of the inequality holds.\n-\tLine 180-181. `It means that the adjacency matrix A~ has a substantially smaller number of non-zero elements than A.’ is not correct. Consider a chain graph with N nodes, N-1 edges, and if the head node and the tail node were aggregated, it became a circle with N-1 nodes and N-1 edges, where the number of edges remains unchanged.\n-\tWhere is the introduction of baselines from `Var.Neigh.’ to ` Kron’? If somewhere else, I suggest moving to Chap experiments.\n-\tFigure 7 is confusing. Present `actual time saved’ (time by downstream task on original graph – time by downstream task on coarsened graph + time by coarsening the graph) together with downstream task performance loss/gain by your method and baselines will be more meaningful.\n\nLIMITATIONS:\nThe authors have adequately addressed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-06-18"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new Universal Graph Coarsening (UGC) framework designed to handle both homophilic and heterophilic graphs. The UGC framework is capable of retaining important spectral properties, including eigenvalue error, hyperbolic error, and 𝜖-similarity measure. Experimental results demonstrate significant improvements in both performance and effectiveness with the UGC framework.\n\nSTRENGTHS:\n* Derive the coarsening matrix over graphs with heterophily property is an interesting idea, and Locality Sensitive Hashing (LSH) technique significantly reduces the algorithm's complexity.\n* UGC offers significant speed improvements and is capable of handling both homogeneous and heterogeneous graphs.\n* The experiments has demonstrated UGC’s limitations and possibility to improve the effectiveness across datasets.\n* The paper is also very clear with thorough experiments and analysis.\n\nWEAKNESSES:\n1. Although the LSH strategy is much faster than other methods, the memory space overhead is non-negligible. Could you please measure the space complexity and provide a further empirical evaluation of the method? Additionally, how is the number of hash functions (𝑙) configured?\n2. The paper lacks a detailed description of the experimental setup, including software and hardware environments, as well as the parameters used for different algorithms.\n3. From Figure 5, we can see that UGC does not exhibit lower errors (RRE and HE) at lower Coarsening Ratios. I think it questions the claimed advantage of preserving spectral properties. Can the authors give a detail explanation?\n4. Figure 5 illustrates that the methods (e.g., VAE, VC) do not maintain a monotonic relationship between the Coarsening Ratio and RRE/HE Error. Additionally, UGC does not exhibit a clear advantage across the overall Coarsening Ratio. Can the authors make a further clarify?\n5. Table 3 does not prove the claim of “UGC (features) method achieves substantial accuracy enhancements” over GCN, GraphSAGE, GIN and GAT. Can the authors utilize UGC to more recent models, e.g., 3WL-GNNs, heterogeneous graph neural networks?\n6. Minor issues：\n    * In Figure 2, the specific meanings of a, b, and c are not labeled in the diagram.\n\nQUESTIONS:\nPlease see the weakness section.\n\nLIMITATIONS:\nThe authors have adequately addressed the limitation of the potential negative societal impact of their work.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

comments: SUMMARY:
The authors propose a novel Universal Graph Coarsening (UGC) framework, which is suitable for both homophilic and heterophilic datasets. UGC integrates node attributes and adjacency information to leverage dataset heterogeneity effectively. The results demonstrate that UGC is significantly faster (4x to 15x), maintains spectral similarity, and outperforms existing methods in terms of computational efficiency, eigen-error, and downstream processing tasks, especially at 70% coarsening ratios. The key contributions highlight UGC's universal applicability, efficiency, and information preservation.

STRENGTHS:
1. The approach is intuitive and easy to understand.
2. The approach has a lower computational cost than most common method (Var.Neigh. etc,.)

WEAKNESSES:
For ScalableTrainingof Graph Neural Networks section, there are no detailed discussion on GNN models except GCN.

QUESTIONS:
For Table 4, why only GCN results are shown? I also expected results for GIN GAT and GraphSage.

LIMITATIONS:
Limitation is discussed in detail in papers.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-14

comments: SUMMARY:
This paper present a framework UGC for graph coarsening to reduce a larger graph to a smaller graph. It uses Locality Sensitive Hashing (LSH) of augmented node features, and works on both homophily and heterophilic graphs. Experiments could verify its effectiveness in original graph property perservation and efficiency in coarsening speed.

STRENGTHS:
S1: This work proposes to use hashing method to graph coarsening and works well on universal homophilic and heterophilic graphs, which is interesting and rational to me.


S2: The overall logic, problem definition, and the solution, are well described and clearly illustrated. The presentation is good and not hard to follow.

S3: UGC is faster compared to existing methods. It achieves a reduction in graph size with lower computational time, making it suitable for large datasets.

WEAKNESSES:
Here are some questions need to be further addressed:

W1: In lines 149-150, it claims that the augmented feature vector is calculated by dot product and concatenation, it is not very clear that how to concate A with node features X?


W2: Some figures, e.g., figure 1 and figure 4, is not very clear for visualization.

W3: In table 4, for comparisons in GNN classification accuracy, it would be better to involve some other graph size reduction methods, like GCOND, SFGC to show the performance.

W4: Is there any ablation study to show the effectiveness of the proposed augmented feature vector?

W5: More detailed explanations and analysis of whether the proposed method could adapt heterophilic graph well are expected. Is there any specific design targeting for heterophily?

QUESTIONS:
See Weaknesses.

LIMITATIONS:
Yes.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-15