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：图表示学习已成为刻画和理解网络结构的重要工具，尤其在社会网络分析中。此类表示学习方法通常将网络嵌入低维空间，使每个个体的作用可通过其潜在位置进行表征。当前社交网络面临的核心问题之一是极化现象与过滤气泡的涌现，它们助长了"我们 vs. 他们"的对立思维模式，这种由极端立场定义的极化态势被认为最终可能引发政治暴力并侵蚀民主制度。此类极化网络通常通过反映好恶关系的符号链接进行刻画。本文提出潜在符号关系距离模型（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，将模型扩展至不同极端立场的表征。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，准确预测友好与敌对关系，同时在将嵌入空间限制为多面体时，提供由极端立场定义的可解释可视化结果。