Converting Spatial to Social: Using Persistent Homology to Understand Social Groups

In social settings, people display sophisticated spatial behaviors—for example, one might naturally enter into a conversation by sidling up to a group. Artificial agents will need the ability to reason about spatial representations of social information to understand not only how social groups form, but also how to interact within and around them. Leveraging the insight that people reason about shared space topologically rather than geometrically, we employ techniques from applied topology to introduce a new method for social group analysis that improves quantifiability and enables rigorous analysis of social group structure. We present a novel topological mathematical formalism called the social simplicial complex that provides an equivalence relation for socially analogous configurations of people and is provably robust against small perturbations and noise. Moreover, this formalism suggests quantifiable metrics to assess the confidence of social group existence and the social closeness of people within groups. We further use this formalism to introduce an open-source toolkit for evaluating possible models of social relationships, which we name the Social Topological Analysis (SoTA) Toolkit. Finally, we explore algebraic topology’s potential to serve more generally as a powerful tool for multi-modal social data processing, and its possibilities for further applications in social-spatial analysis.