The Bag-and-Whisker Plot: A New Bagplot for Bivariate Data

2025-12-06

AI Summary

Traditional bagplots suffer from two key limitations: (1) outlier detection relies on a fixed inflation factor, hindering adaptability across varying sample sizes; and (2) the visualization fence is constructed via the convex hull, resulting in poor stability. This paper proposes the *bag-and-whisker plot*, a statistically adaptive bivariate outlier detection and visualization method. Our approach addresses these issues by: (1) formulating outlier detection as a multiple hypothesis testing problem to dynamically determine fence boundaries—ensuring sample-size adaptivity; and (2) replacing the convex hull with hierarchical granular whiskers, thereby enhancing plot stability and preserving fine-grained distributional structure. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed method significantly outperforms conventional bagplots in robustness, adaptability, and practical utility.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Ensemble Methods
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Security and Privacy: Data transparency and provenance

Abstract

The bagplot, also known as the "bag-and-bolster plot", is a notable extension of the boxplot from univariate to bivariate data. Although widely used, its practical application is hindered by two key limitations: the fixed inflation factor for outlier detection that does not adapt to the sample size, and the unstable convex hull used to visualize its fence. In this paper, we propose a new bagplot, namely the "bag-and-whisker plot'', as an improvement method to address these limitations. Our framework recasts outlier detection as a multiple testing problem, yielding a data-adaptive fence that controls statistical error rates and enhances the reliability of outlier identification. To further resolve graphical instability, we introduce a refined visualization that abandons the convex hull (the bolster) with a direct rendering of the statistical fence, complemented by granular whiskers that effectively illustrate the data's spread. Extensive simulations and real-world data analyses demonstrate that our new bagplot exhibits superior adaptivity and robustness compared to the existing standard, and thus can be highly recommended for practical use.

Problem

• Addresses fixed inflation factor in outlier detection
• Resolves unstable convex hull for fence visualization
• Enhances adaptivity and robustness of bivariate bagplot

Innovation

• Data-adaptive fence controls statistical error rates
• Direct rendering of fence replaces unstable convex hull
• Granular whiskers illustrate data spread effectively