"Non-Euclidean Mixture Model for Social Network Embedding"

Finally a model that understands social networks form through both birds-of-a-feather and popularity

NMM ((Non-Euclidean Mixture Model) combines spherical and hyperbolic spaces to better model how social networks actually form

https://arxiv.org/abs/2411.04876v1

🎯 Original Problem:

Social networks form links through two key factors - homophily (similar nodes connecting) and social influence (popular nodes attracting connections). Current models either focus on just one factor or use simple Euclidean spaces that can't capture the complex network structures.

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🔧 Solution in this Paper:

→ Introduces NMM (Non-Euclidean Mixture Model) that represents nodes in both spherical space (for homophily) and hyperbolic space (for social influence)

→ Uses spherical space to model cyclic connections between similar nodes and hyperbolic space to model hierarchical influence-based connections

→ Combines these two representations through a novel space unification loss that aligns the two geometric spaces

→ Enhances NMM with graph neural networks (NMM-GNN) using a variational autoencoder framework with non-Euclidean encoders and decoders

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💡 Key Insights:

→ Social network links form through both similarity and influence - need both spherical and hyperbolic spaces to model this effectively

→ Homophily creates cycles best captured in spherical space while influence creates hierarchies best captured in hyperbolic space

→ Unifying different geometric spaces through projection and alignment is key for coherent node representations

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📊 Results:

→ Significantly outperforms state-of-the-art baselines on social network generation tasks

→ Successfully tested on large-scale networks like LiveJournal (4.8M nodes) and Friendster (65.6M nodes)

→ More parameter efficient compared to existing models like RaRE