Graph-Theoretic Insights into Bayesian Personalized Ranking for Recommendation

Graph self-supervised learning (GSL) is essential for processing graph-structured data, reducing the need for manual labeling. Traditionally, this paradigm has extensively utilized Bayesian Personalized Ranking (BPR) as its primary loss function. Despite its widespread application, the theoretical analysis of its node relations evaluation have remained largely unexplored. This paper employs recent advancements in latent hyperbolic geometry to deepen our understanding of node relationships from a graph-theoretical perspective. We analyze BPR's limitations, particularly its reliance on local connectivity through 2-hop paths, which overlooks global connectivity and the broader topological structure.