Graph representation learning has become a prominent tool for the characterization and understanding of the structure of networks in general and social networks in particular. Typically, these representation learning approaches embed the networks into a low-dimensional space in which the role of each individual can be characterized in terms of their latent position. A major current concern in social networks is the emergence of polarization and filter bubbles promoting a mindset of "us-versus-them" that may be defined by extreme positions believed to ultimately lead to political violence and the erosion of democracy. Such polarized networks are typically characterized in terms of signed links reflecting likes and dislikes. We propose the latent Signed relational Latent dIstance Model (SLIM) utilizing for the first time the Skellam distribution as a likelihood function for signed networks and extend the modeling to the characterization of distinct extreme positions by constraining the embedding space to polytopes. On four real social signed networks of polarization, we demonstrate that the model extracts low-dimensional characterizations that well predict friendships and animosity while providing interpretable visualizations defined by extreme positions when endowing the model with an embedding space restricted to polytopes.

翻译：图表示学习已成为表征和理解网络结构（特别是社交网络）的重要工具。通常，这些表示学习方法将网络嵌入到低维空间中，使得每个个体的角色可通过其潜在位置进行刻画。当前社交网络面临的主要挑战之一是极化现象与过滤气泡的涌现，其助长了"我们vs他们"的二元对立思维模式——这种思维往往由极端立场定义，并被认为最终会导致政治暴力与民主侵蚀。此类极化网络通常通过反映喜恶关系的符号链接进行表征。本文提出符号关系隐距离模型（SLIM），首次将Skellam分布作为符号网络的似然函数，并通过将嵌入空间约束为多面体来扩展模型以刻画不同极端立场。在四个真实社交符号极化网络上，我们证明该模型能够提取低维表征，有效预测友谊与敌意关系；当将嵌入空间约束为多面体时，还能提供由极端立场定义的可解释性可视化结果。