Generalized partitioned local depth
This work extends foundational ideas in data analysis to handle uncertain and conflicting information, but it is incremental as it builds directly on prior research.
The paper generalizes the concept of cohesion from partitioned local depth by introducing local relevance and support division, extending earlier results and applying it to reveal communities in uncertain data.
In this paper we provide a generalization of the concept of cohesion as introduced recently by Berenhaut, Moore and Melvin [Proceedings of the National Academy of Sciences, 119 (4) (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.