🤖 AI Summary
Traditional boxplots struggle to detect bimodal or multimodal structures in univariate data and fail to reveal underlying subgroups or outliers. To address this, we propose the *bixplot*, a novel boxplot variant that integrates a univariate clustering algorithm with continuity constraints and a minimum cluster size requirement to automatically identify and visualize meaningful subgroups within multimodal distributions. The bixplot supports direct plotting of individual data points and enables gradient color mapping based on external variables, thereby enhancing interpretability of substructures. Crucially, it guarantees non-nested clusters and ensures each cluster contains a sufficient number of distinct observations. Implemented as open-source Python and R packages, the bixplot demonstrates superior performance over conventional boxplots across multiple real-world datasets—clearly exposing previously overlooked multimodal patterns and substantially improving the depth and practical utility of exploratory data analysis.
📝 Abstract
Boxplots and related visualization methods are widely used exploratory tools for taking a first look at collections of univariate variables. In this note an extension is provided that is specifically designed to detect and display bimodality and multimodality when the data warrant it. For this purpose a univariate clustering method is constructed that ensures contiguous clusters, meaning that no cluster has members inside another cluster, and such that each cluster contains at least a given number of unique members. The resulting bixplot display facilitates the identification and interpretation of potentially meaningful subgroups underlying the data. The bixplot also displays the individual data values, which can draw attention to isolated points. Implementations of the bixplot are available in both Python and R, and their many options are illustrated on several real datasets. For instance, an external variable can be visualized by color gradations inside the display.