cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data

2026-07-16

AI Summary

This study addresses the lack of visualization methods for high-dimensional categorical data that simultaneously preserve structural information and ensure interpretability. The authors propose cGAP, a novel framework that uniquely maps the geometric embedding from HOMALS directly into RGB color space, thereby fully retaining the original data matrix within a heatmap. By integrating row/column reordering with a coordinated tri-view layout, cGAP concurrently reveals clusters, outliers, and hierarchical structures. The method is theoretically grounded in properties such as centroid traceability, enabling full-matrix provenance. Empirical validation across diverse datasets—including student–animal classifications, mammalian dental formulas, mushroom attributes, and orthologous gene clusters—demonstrates its effectiveness in significantly enhancing the transparency and interpretability of exploratory analysis for categorical data.

Abstract

High-dimensional categorical data arise in genetics, biomedicine, and the social sciences, yet visualization tools for such data remain far less developed than those for continuous variables. Existing methods either scale poorly, rely heavily on low-dimensional displays detached from the original data matrix, or prioritize predictive accuracy over interpretability. To address this gap, we introduce categorical Generalized Association Plots (cGAP), a visualization framework for nominal, ordinal, and binary data that preserves the original data matrix while augmenting it with interpretable geometric structure. cGAP uses Homogeneity Analysis (HOMALS) to embed subjects and category levels in a three-dimensional Euclidean space and maps the embedding to red-green-blue coordinates so that similar patterns receive similar colors. The framework integrates three coordinated views: a HOMALS-guided heatmap of the raw data matrix, a subject proximity matrix, and a variable proximity matrix. Seriation algorithms are then used to reorder rows and columns to reveal coherent clusters, outliers, and local-to-global structure. We also derive barycentric traceability, projection-distortion, and contrast-preservation properties that clarify how embedding geometry is transferred to the display. We demonstrate the versatility of cGAP through applications to student-animal classification data, mammalian dentition profiles, mushroom records from the UCI Machine Learning Repository, and the Clusters of Orthologous Genes database. These examples show that cGAP supports transparent exploratory analysis by maintaining traceability between derived visual structure and the original categorical observations. cGAP provides a full-matrix, heatmap-based visualization environment for investigating complex categorical datasets across scientific domains.

Problem

• high-dimensional categorical data
• visualization
• interpretability
• data matrix preservation
• exploratory analysis

Innovation

• cGAP
• HOMALS
• categorical data visualization
• heatmap
• seriation