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.

Transcriptome studies which provide temporal information can be valuable for identifying groups of similarly-behaving transcripts and provide insight into overarching gene regulatory networks. Nevertheless, inferring meaningful biological conclusions is challenging, in part because it is difficult to holistically consider both local relationships and global structure of these complex and overlapping transcriptional responses. To address this need, we employed the recently-developed method, Partitioned Local Depth (PaLD), which reveals community structure in large data sets, to examine four time-course transcriptomic data sets generated using the model plant Arabidopsis thaliana. As this is the first paper in systems biology to implement the PaLD approach, we provide a self-contained description of the method and show how it can be used to make predictions about gene regulatory networks based on temporal responses of transcripts. The analysis provides a global network representation of the data from which graph partitioning methods and neighborhood analysis can reveal smaller, more well-defined groups of like-responding transcripts. These groups of transcripts that change in response to hormone treatment (auxin and ethylene) and salt treatment were shown to be enriched in common biological function and/or binding of transcription factors that were not identified with prior analyses of this data using other clustering methods. These results reveal the potential of PaLD to predict gene regulatory networks within large transcriptomic data sets.

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