WISE-GNN: Enhancing GNNs with Wise Embedding and Topological Encoding

Method

1. The wise-gnn obtains new features by measuring the distance between nodes and multiple cluster centers, making the representations of similar initial nodes more alike. Node representations are updated through a message-passing mechanism. If a node has a high degree of heterophilic, the message-passing approach will still influence the final node representation.

2. The introduction of the topology module does not effectively interact with the wise embedding, but rather functions as a simple combination.

Experiment

1. The dataset used in the paper is too small.
2. The method lacks comparision with the strong baselines for heterophilic graphs.
3. The performance of GCN on Cora is too low on the public split.

1. Unclear Objective Function: The objective function and the overall process for integrating Wise embeddings into the GNN model are insufficiently explained, which hinders understanding of how these embeddings work in the training framework.
2. Limited Motivation for Wise Embeddings: While capturing information from distant nodes is valuable, the use of classWISE benchmarks as an effective means of encoding this information lacks sufficient justification. It’s unclear why this specific method would be more beneficial than alternative strategies, such as clustering approaches, which may offer richer structural context.
3. Restricted Novelty: The Topological Module is primarily adopted from established work in persistent homology, offering limited originality in its formulation or integration. The Wise embedding concept also appears somewhat incremental rather than ground-breaking.
4. Experimental Ambiguity: The experimental setup and results need more clarity, particularly concerning the T-H2GCN performance and whether the results fully validate the claimed improvements. Additionally, comparisons with clustering-based methods would strengthen the case for Wise embeddings as a distinct improvement.

1. The novelty is limited considering that class landmark (or prototypes) has been extensively used in node representation learning and clustering in the literature.
2. The wise embedding seem to be handcrafted. This could be time-consuming. The authors did not discuss the runtime of the method.
3. It is unclear why wise embedding is used for GNN input while the betti vector is processed through MLP.
4. The Chameleon and Squirrel datasets used in the study are known to be problematic[1]. It is recommended to use the filtered versions of these datasets to ensure more reliable results.
5. The heterophilous datasets used for evaluation are all relatively small. To validate the claims more robustly, it is essential to conduct experiments on large-scale heterophilous datasets[1][2].
6. More recent heterophilous baselines are needed for performance comparison.
7. Reproducibility is poor. No code released, and no hyperparameters specified.

References

[1] Platonov, O., Kuznedelev, D., Diskin, M., Babenko, A., & Prokhorenkova, L. (2023). A critical look at the evaluation of GNNs under heterophily: Are we really making progress?. arXiv preprint arXiv:2302.11640.

[2] Derek Lim, Felix Hohne, Xiuyu Li, Sijia Linda Huang, Vaishnavi Gupta, Omkar Bhalerao, and Ser Nam Lim. Large scale learning on non-homophilous graphs: New benchmarks and strong simple methods. Advances in Neural Information Processing Systems, 34, 2021.

1. The motivation of this paper is very unclear. In the abstract and introduction, the authors mention that they want to address the issues of GNNs in oversmoothing, oversquashing, and underreaching. However, what are these problems are not introduced in detail. In this work, a method of topology embedding is proposed. It's very unclear why this can solve these many problems of GNNs. Moreover, in the experiments, the authors majorly evaluate the performance on heterophilic graphs, which make the objective of this work more confusing.

2. The technical contributions are limited. The core idea of this method is to learn a topology embedding to benefit the classification with GNNs. Similar ideas have already been well explored. For example, LinkX utilizes an MLP to learn the topology embedding from the adjacency matrix. Position embeddings are also clearly investigated for graph transformer [1].

3. The experiments are not convincing. For example, in table 2, the GCN only has 59% accuracy, which is in conflict with the widely reported results (around 72%). Hence, the improvements are not convincing. In addition, experiments are only conducted on several small datasets which only contain several thousand nodes.

4. The paper is poorly written. The details of building the wise embedding is difficult to follow. Why this method can be effective for heterophilic graphs is not discussed. The paper is not cited is a right way, which makes the paper very difficult to follow.

[1] Ying, Chengxuan, et al. "Do transformers really perform badly for graph representation?." Advances in neural information processing systems 34 (2021): 28877-28888.