Statistical Variability Networks: Transforming Statistical Summaries into Network Representations

Cluster analysis is widely used to identify groups of similar observations, but conventional cluster representations provide limited information about the statistical variability associated with these groups. This article introduces {red}{Statistical Variability Networks} (hereafter referred to as STAT Networks), a network-based framework for representing statistical descriptions of clustered data. For each cluster, a representative centroid and additional variability vectors are constructed by replacing individual centroid values with lower and upper statistical bounds. These vectors are then represented as nodes in a weighted \((k)\)-nearest-neighbor network, where connections reflect statistical proximity between the resulting vectors. The framework supports several statistical representations, including 95% confidence intervals (CI), one and two standard deviations (1SD and 2SD), interquartile range (IQR), and interquartile whisker range (IWR). The proposed framework is demonstrated on the E. coli, Iris, and Yeast datasets to examine how different statistical representations affect the resulting network structure and relationships between cluster profiles. The results show that the number and structure of inter-cluster connections vary across the statistical representations, with broader variability ranges generally revealing additional statistical proximity between cluster profiles. The results also demonstrate cases where cluster profiles that appear separated in the original network become connected when their statistical variability is represented. STAT Networks therefore provide a complementary representation for exploring relationships between cluster profiles and their statistical variability alongside conventional statistical visualizations.