Dr. Kenneth S. Berenhaut published in PNAS 

A social perspective on perceived distances reveals deep community structure

The WFU News Service has published an article, Where mathematics and a social perspective meet data, about the paper. The article was written by Kim McGrath.

Significance

Community structure arising through relationships and interactions is essential to our understanding of the world around us. Leveraging social concepts of conflict and support, we introduce a method to transform input dissimilarity comparisons into output pairwise relationship strengths (or cohesion) and resulting weighted networks. The introduced perspective may be particularly valuable for data with varying local density such as that arising from complex evolutionary processes. Mathematical results, together with applications in linguistics, genetics, and cultural psychology as well as to benchmark 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.

Abstract

Community structure, including relationships between and within groups, is foundational to our understanding of the world around us. For dissimilarity-based data, leveraging social concepts of conflict and alignment, we provide an approach for capturing meaningful structural information resulting from induced local comparisons. In particular, a measure of local (community) depth is introduced that leads directly to a probabilistic partitioning conveying locally interpreted closeness (or cohesion). A universal choice of threshold for distinguishing strongly and weakly cohesive pairs permits consideration of both local and global structure. Cases in which one might benefit from use of the approach include data with varying density such as that arising as snapshots of complex processes in which differing mechanisms drive evolution locally. The inherent recalibrating in response to density allows one to sidestep the need for localizing parameters, common to many existing methods. Mathematical results together with applications in linguistics, cultural psychology, and genetics, as well as to benchmark clustering 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.

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