  Biological systems often exhibit a heterogeneous arrangement of objects, such
as assorted nuclear chromatin patterns in a tumor, assorted species of bacteria
in biofilms, or assorted aggregates of subcellular particles. Principle
Component Analysis (PCA) and Multiple Component Analysis (MCA) provide
information about which features in multidimensional data aggregate, but do not
provide in situ spatial information about these aggregations. This paper
outlines the Numericized Histogram Score (NHS) algorithm, which converts the
histogram distribution of shortest distances between objects into a continuous
variable that can be represented as a spatial heatmap. A histogram can be
transformed into an intensity value by assigning a weighting factor to each
sequential bin. Each object in an image can be replaced by its NHS value, which
when calibrated to a color scale results in a heatmap. These spatial heatmaps
reveal regions of aggregation amid heterogeneity that would otherwise mask
loco-regional spatial associations, which will be especially useful in the
field of digital pathology. In addition to visualizing aggregations as
heatmaps, the ability to calculate degrees of recurring patterns of aggregation
allows investigators to stratify samples for further insights into clinical
outcome, response to treatment, or omic subtypes (genomic, transcriptomic,
proteomic, metabolomic, etc.).
