  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.
