A social perspective on perceived distances reveals deep community structure

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Importance

The community structure resulting from relationships and interactions is essential to our understanding of the world around us. By leveraging the social concepts of conflict and support, we introduce a method to transform input dissimilarity comparisons into output pairwise relationship strengths (or cohesion) and the resulting weighted networks. The perspective introduced can be particularly valuable for data with varying local density such as those resulting from complex evolutionary processes. Mathematical results, as well as applications in linguistics, genetics and cultural psychology as well as reference data, have been included. Together, these demonstrate how meaningful community structure can be identified without additional inputs (e.g. number of clusters or neighborhood size), optimization criteria, iterative procedures, or distributional assumptions.

Summary

Community structure, including relationships between and within groups, is fundamental to our understanding of the world around us. For dissimilarity-based data, leveraging social concepts of conflict and alignment, we propose an approach to capture meaningful structural information resulting from induced local comparisons. In particular, a measure of local (community) depth is introduced which leads directly to a probabilistic partitioning conveying locally interpreted proximity (or cohesion). A universal choice of threshold to distinguish between strongly and weakly cohesive pairs allows both local and global structure to be considered. Cases in which one might benefit from using the approach include data of varying density such as those that present themselves as snapshots of complex processes in which different mechanisms drive evolution locally. The inherent recalibration in response to density avoids the need for localization parameters, common to many existing methods. Mathematical results as well as applications in linguistics, cultural psychology and genetics, as well as reference grouping data have been included. Together, these demonstrate how meaningful community structure can be identified without additional inputs (e.g. number of clusters or neighborhood size), optimization criteria, iterative procedures, or distributional assumptions.

Footnotes

    • Accepted November 30, 2021.
  • Author contributions: KSB and RLM collaborated on the early development of local depth; KSB and KEM developed PaLD; and KSB and KEM drafted the document.

  • The authors declare no competing interests.

  • This article is a direct PNAS submission.

  • This article contains additional information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2003634119/-/DCSupplemental.

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