Generalized Partitioned Local Depth

In this paper, we provide a generalization of the concept of cohesion as introduced recently by Berenhaut et al. (Proc Natl Acad Sci 119:2003634119, 2022). The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information.