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

Abstract

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 may improve the evaluation of group structure in projected data. We compared the use of confidence ellipses and Voronoi tessellation as visualization tools for two-dimensional data projections 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 projections overlapping the opposite group and revealed internal group heterogeneity. In datasets with moderate or absent group separation, Voronoi tessellation more effectively exposed the lack of meaningful structure. Meanwhile, 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 projected biomedical data and supports hypothesis validation and exploratory analyses in dimensionality reduction and clustering.