Voronoi tessellation as a complement or replacement for confidence ellipses in the visualization of data projection and clustering results

Visualizing two-dimensional data projections with group-wise coloring and confidence ellipses is a standard approach in biomedical data analysis. However, this method can obscure subtle group overlaps or atypical cases. Voronoi tessellation, which is widely used in crystallography to analyze local structure, offers a parameter-free geometric alternative that can improve the evaluation of group structure in raw or projected data. We implemented Voronoi tessellation as a plot type for two-dimensional biomedical data and compared it with confidence ellipses on three artificial datasets and three biomedical datasets. For datasets with well-separated classes, both visualization techniques effectively delineated groups. Voronoi tessellation more clearly highlighted cases with points overlapping the opposite group, revealed internal group heterogeneity, and enabled quantification of structural discordance via a Voronoi island count as a visualization-intrinsic metric with no equivalent in confidence ellipse approaches. In datasets with moderate or absent group separation, Voronoi tessellation more effectively exposed the lack of meaningful structure, whereas confidence ellipses more clearly indicated distant outliers. Voronoi tessellation also facilitated the identification of clustering failures. Thus, Voronoi tessellation enhances the detection of deviations from expected group patterns and provides geometric insights that complement statistical summaries from confidence ellipses. Therefore, integrating Voronoi tessellation into standard data analysis workflows is a valuable addition for visualizing biomedical data and supports hypothesis validation and exploratory analyses in both raw data visualization and dimensionality reduction or clustering. An R library “VoronoiBiomedPlot” is available at the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/package=VoronoiBiomedPlot.