Scalable Link Prediction in Dynamic Networks via Non-Negative Matrix Factorization (1411.3675v3)

Abstract: We propose a scalable temporal latent space model for link prediction in dynamic social networks, where the goal is to predict links over time based on a sequence of previous graph snapshots. The model assumes that each user lies in an unobserved latent space and interactions are more likely to form between similar users in the latent space representation. In addition, the model allows each user to gradually move its position in the latent space as the network structure evolves over time. We present a global optimization algorithm to effectively infer the temporal latent space, with a quadratic convergence rate. Two alternative optimization algorithms with local and incremental updates are also proposed, allowing the model to scale to larger networks without compromising prediction accuracy. Empirically, we demonstrate that our model, when evaluated on a number of real-world dynamic networks, significantly outperforms existing approaches for temporal link prediction in terms of both scalability and predictive power.

• The paper proposes a temporal latent space model that predicts dynamic links with a temporal smoothness constraint ensuring realistic node transitions.
• The authors develop scalable BCGD algorithms, including local and incremental variants, to efficiently optimize the model for large networks.
• Empirical results demonstrate that the model outperforms existing methods, achieving an average AUC score of 0.81 in real-world networks.

Temporal Latent Space Inference for Link Prediction in Dynamic Networks

The paper under examination presents a temporal latent space model designed to predict links in dynamic social networks. By leveraging a sequence of historical graph snapshots, the model aims to infer the evolving network structure over time. It posits that each user resides within a latent space, with links between users more likely when they occupy proximate positions within this space. Distinctively, the user positions are allowed to evolve dynamically as the network changes.

Key Contributions

1. Model Proposal: A temporal latent space model is proposed for dynamic link prediction. The model incorporates a temporal smoothness constraint, ensuring realistic transitions of latent positions over time.
2. Algorithmic Framework: The authors present a comprehensive optimization framework to infer the temporal latent space. This includes a global optimization algorithm and two alternative local and incremental variants, each designed with scalability in mind to handle large networks efficiently.
3. Computational Efficiency: Two fast BCGD algorithms, local and incremental, are developed. These allow for efficient handling of large graphs, with the incremental approach particularly designed to efficiently update only the affected nodes with graph changes, significantly reducing computation time.
4. Empirical Validation: Through extensive experimentation on real-world networks, the proposed model outperformed existing temporal link prediction methods concerning both predictive accuracy and scalability. The results highlight an average AUC score of 0.81 for the global BCGD approach, which is notably promising.

Methodological Advances

The paper explores the challenge of predicting dynamic links via a temporal latent space model, extending beyond static graphs where nodes have fixed latent positions. The temporal model aligns with the homophily principle by positioning nodes as close in the latent space based on similar attributes, thereby enhancing the link prediction accuracy. The application of block-coordinate gradient descent (BCGD) for learning such latent representations marks a methodological advancement, showing quadratic convergence rates—a substantial contribution to optimization in temporal networks.

The paper also addresses the inherent NP-hardness of non-negative matrix factorization within its theoretical framework, providing a compelling argument for using BCGD to achieve a tractable solution. Additionally, by introducing constraints on the dimensionality of the latent space, the model provides handles for balancing between computational cost and representational accuracy, thereby offering practical advantages for real-world applications.

Implications and Future Directions

The implications of this research are manifold, impacting both theoretical understanding and practical applications in dynamic network analysis. The model's robustness in capturing temporal dynamics offers a tool that transcends static assessments, capable of real-time link predictions that align closely with actual network evolutions. This has considerable implications for recommendation systems like suggesting new acquaintances in social networks or predicting partnership in collaborative networks.

Future research directions may include extending these models to capture more complex temporal non-linearities, potentially accommodating abrupt shifts due to external events. Moreover, adapting the framework to accommodate weighted and directed graphs could broaden its applicability. Continuous-time models could also overcome some limitations inherent to discrete snapshots, providing even more precise predictions.

Lastly, by exploring reductions in computational load through parallelization techniques or stochastic approximation methods, further efficiency gains may be realized. The combination of theoretical elegance and empirical validation provides a robust foundation for further exploration in network dynamics and link prediction methodologies.

Overall, this paper significantly advances the field of dynamic network analysis with its introduction of scalable temporal latent space inference, facilitating new insights into how networks grow and evolve over time.