Adversarial enhanced representation for link prediction in multi-layer networks

W1. The relationship between the present work with the body of works on link prediction in heterogeneous graphs (multiple edge types) is never established in the paper. As a result, GNN-based models for heterogeneous graphs (e.g., R-GCN, HIN) were never included in the comparison. It is worth mentioning that these models do capture correlations between different edge types, which are arguably analogous to edges in different layers.

W2. The problem tackled in the paper is also likely related to embeddings for knowledge graphs (e.g., DGL-KE). This is also missing in the related work and in the experimental section.

W3. The combination of an adversarial loss with a binary classification loss (three sets of parameters to be optimized) can pose several challenges to the training, requiring a delicate balance between the two losses. Yet, there is no hyperparameter in $Loss_{final}$ (Eq. 12) to control this balance. There are no plots showing the evolution of the loss components.

W4. No study or empirical results regarding the method scalability. Networks are relatively small.

W5. It is hard to determine whether the comparison with the baselines is fair.

W6. Some design choices in the proposed method are not well-justified. Additional experiments need to be included in the ablation study.

W7. Notation and typesetting need improvement. Spelling must be reviewed.

W8. The results are not reproducible based on the information provided in the submission. Appendix was not used.

1. Missing baseline models. Although this paper proposes an interesting research question and a promising model architecture, it fails to mention two highly related works, MANE [1] and MLHNE [2]. These two works both work on multi-layer network embedding and both propose intra-layer and inter-layer concept to integrate information of different network layers. This submitted work lacks the discussion and comparison with these two papers.

[1] Li, J., Chen, C., Tong, H., & Liu, H. (2018, May). Multi-layered network embedding. In Proceedings of the 2018 SIAM International Conference on Data Mining (pp. 684-692). Society for Industrial and Applied Mathematics.

[2] Zhang, D. C., & Lauw, H. W. (2021). Representation Learning on Multi-layered Heterogeneous Network. In Machine Learning and Knowledge Discovery in Databases. Research Track: European Conference, ECML PKDD 2021, Bilbao, Spain, September 13–17, 2021, Proceedings, Part II 21 (pp. 399-416). Springer International Publishing.

2. Insufficient experiment tasks. For network embedding area, if the proposed model is unsupervised, both link prediction and node classification are important evaluation tasks. Node classification has been a standard evaluation task in network embedding area and has been used in various papers, including the above mentioned two missing papers, but this submitted paper contains link prediction but not node classification.

3. Small datasets. The datasets in the paper contain <2K vertices, which is much smaller than real-world scenarios. Thus it's difficult to say if the proposed model can scale to large networks efficiently. I expect to see experiments on larger datasets, say 100K vertices.

1. Multi-layer GNNs or multiplex GNNs are not new topics, but the paper does not comprehensively review the existing literature in this topic. In addition to the literature review, the authors did not include these works as baselines for experimental comparisons. For example, existing related works include: [1] Mitra, Anasua, et al. "Semi-supervised deep learning for multiplex networks." Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 2021. [2] Zhang, Weifeng, et al. "Multiplex graph neural networks for multi-behavior recommendation." Proceedings of the 29th ACM international conference on information & knowledge management. 2020. [3] Li, Jundong, et al. "Multi-layered network embedding." Proceedings of the 2018 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2018.

2. The proposed approach is not well-motivated and the writings need a lot of improvements. For example, it is not clear why CNNs are applied after GCNs for inter- and intra-layer node embeddings. In addition, it looks to me that layer discriminator and link predictor serve for a similar purpose, but the uniqueness of these components is not further highlighted.

3. The datasets used in this work are quite small. The largest dataset only contains ~1500 nodes. The authors are suggested to use the datasets from the above mentioned works to conduct more comprehensive experimental evaluations.

4. Minor: The notations are not very readable. Many notations are named a bit long (e.g., IR, TR, SR, etc.).

W1: The novelty of AER is insufficient. Many of the components used in AER are traditional and widely known models or operators (e.g., GCN, CNN). Authors do not explain clearly about the motivation for combining them. And in my opions, many of the operations represented in this paper seem to be basic to existing methods. W2: The experiment is insufficient and the baslines maybe lacking. First, the old-fashioned link prediction baselines are missing, including but not limited to common neighbors (CN), Jaccard, preferential attachment (PA), Adamic-Adar (AA), resource allocation (RA), Katz, PageRank (PR), and SimRank (SR). (2) Some SOTA models are also needed such as SEAL (Link Prediction Based on Graph Neural Networks). W3: The writing of the paper needs to be improved. In particular, the third paragraph of the introduction is not well understood and lacks citations to support points. There is no need to introduce too many details of the experimental parameters in the methods section. And the description in the algorithm section is rather redundant and does not fit the form of the algorithm.