Non-Euclidean Mixture Model for Social Network Embedding

Summary

This paper proposes NMM-GNN, a non-Euclidean mixture model that captures both homophily and hierarchies in social networks for embedding.

Strengths

1.The paper is well-structured, clearly written, and easy to follow. 2.In the experiments section, the author compared baselines from different categories on multiple tasks (classification and link prediction). The results show that the NMM-GNN proposed in the paper consistently achieves the best performance.

Weaknesses

1. The related work section does not cover most existing social embedding works. For example, many works, in addition to RaRE, also consider both the similarities and the social impact of nodes. 2. There is no clear proof or at least empirical experiments to demonstrate that it is more reasonable to embed both node similarity and social impact in spherical space instead of Euclidean space.

Questions

1. My main concern is that social network embedding algorithms considering social impact are not novel. For example, when performing edge prediction, one can directly assume the probability of the edge is proportional to the degree of both nodes. I hope the author could further explain why the proposed method is novel enough in terms of encoding both similarity and impact. 2. Despite the experimental results and ablation study in the main article showing the good performance of the proposed method, I want to know how the speed of the method compares with existing baselines.

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

2

Limitations

The author discussed the potential limitations of the paper in detail in the appendix.

Summary

The authors understand why links are generated through node-embedded representations of social networks. Specifically, spherical space is utilized to represent the homogeneity of nodes and hyperbolic space is utilized to represent the hierarchy and influence of nodes. By mixing these two spaces together, the corresponding link representation is finally obtained.

Strengths

1.The writing is clear and easy to understand. 2.The experiments were adequate and demonstrated the power of the models

Weaknesses

1.The idea of the article is not novel. Both hyperbolic and spherical spaces are geometric models that are very commonly used in the field of social networking.[1] 2.Although the authors are trying to explain linking relationships in terms of homogenization and hierarchy, however the learning of the model embedding is still unknown, which does not explain the emergence of social networks. 3.There has been much better work on embedding methods in hybrid spaces. [2]The authors don't contribute as much to this as their article suggests. [1]Network geometry. Nature physics [2]Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning AAAI 2024 [3]Product Manifold Learning. AISTATS 2021

Questions

1.How to analyze the reasonable causes of social network link generation from complex feature representations? 2.Can this model explain small-world networks in complex networks?

Rating

5

Confidence

5

Soundness

4

Presentation

4

Contribution

3

Limitations

1.The model does not really give an adequate explanation of links in complex networks, but only from the perspectives of homogeneity and hierarchy.

Summary

This paper proposes a new Graph-based non-Euclidean mixture model for social networks. Under the assumptions that social network links are formed due to either homophily or social influence, the homophily factor is modeled in spherical space and the social influence factor is in hyperbolic space. The homophily regulated nodes lie on the surface of the spherical ball and the social influence-regulated nodes lie on the open Poincare ball. The projection to align these two spaces is also proposed. The non-Euclidean GraphVAE is also integrated into the model. Experiments show the proposed model outperforms other baselines.

Strengths

- The proposed framework models both the homophily and social influence factors for social network generation. - It is integrated into the non-Euclidean graph-based VAE to further improve performance. - Experiments show the proposed model outperforms other SOTA baselines.

Weaknesses

- The motivation of the space unification is unclear (See the questions below).

Questions

- Why is the space unification necessary? Each node has two coordinates, in the spherical and the hyperbolic space. The link between nodes i and j is generated either from the spherical or hyperbolic proximity (it is the "explaining away" situation as explained in the RaRE paper [6] ). The homophily and social influence relationships may be unrelated or may even contradict to each other (you may hate your boss). Therefore the two coordinates may not necessarily be aligned. It would be appreciated if the authors would elaborate on this. - The $\kappa$-GCN proposed in [39] also deals with spherical and hyperbolic spaces. I would like to know the similarities and/or differences between the two approaches as the two coordinates in the proposed model can also be regarded as a coordinate in the product space. The authors do not discuss them. They just compare the experimental performance. - What is $i$ in the definition of $\log_0^H$ and $\exp_o^H$ ?

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

As for the computational efficiencies, more formal and quantitative comparisons would be necessary in the main texts.

Summary

This work addresses the embedding of social networks with downstream tasks such as link prediction in mind. In this manuscript the authors propose to model the link as the mixture of two factors of node embedding, Spherical and Hyperbolic. Concretely, two kinds of node embedding are unified into a single loss by projecting from hyperbolic space into spherical space, and jointly trained in the framework of VAE on Graaph. The authors also conduct experiments against a wide range of baseline methods to highlight the capacity of the proposed method.

Strengths

The idea is novel. Overall things are good. The idea of bridging both is novel, and according to experiments performance better than purely hyperbolic embedding. Writing is overall clear and, although there are many details, it’s generally feasible to follow. Extensive comparison with a wide range of baselines from different categories. Good discussion of limitations.

Weaknesses

The major issue is on limited datasets in experiments. I would suggest the authors consider other datasets used in previous works, such as synthetic datasets, citation networks (PubMed, wikipedia citation, DBLP, Microsoft Academic Graph ) and other social networks (e.g. Twitter). Also another factor limiting the impact of the proposed method is that the proposed method does not work on the whole-graph level, and thus only applies to node classification and link prediction tasks. If by any extension the embeddings could be aggregated to the whole-graph leve, there could be more significance (e.g. tasks like molecular classification, protein-to-protein interactions)

Questions

N/A

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

Well addressed.

Response to Rebottal

Thanks for your response! I have known the contribution and novelty of your work. At last, I have raised my score.