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

2026-07-20 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Life Sciences & Biology, Research Methodology & Innovation · Depth: Expert, extended

Summary

Categorical Generalized Association Plots (cGAP) is a novel visualization framework designed for high-dimensional nominal, ordinal, and binary data, addressing the limitations of existing tools that often scale poorly or detach from the original data matrix. cGAP employs Homogeneity Analysis (HOMALS) to embed subjects and category levels into a three-dimensional Euclidean space, mapping these embeddings to red-green-blue coordinates to ensure similar patterns receive similar colors. The framework integrates three coordinated views: a HOMALS-guided heatmap of the raw data, a subject proximity matrix, and a variable proximity matrix. Seriation algorithms reorder rows and columns to reveal coherent clusters, outliers, and local-to-global structure. The method maintains traceability between derived visual structure and original observations. Its versatility is demonstrated through applications including student-animal classification, mammalian dentition profiles (66 mammals, 8 variables), mushroom records (8,124 samples, 22 variables), and the Clusters of Orthologous Genes database (2,296 genomes, 5,061 variables).

Key takeaway

For Data Scientists or Research Scientists analyzing complex high-dimensional categorical datasets, cGAP offers a powerful visualization approach to uncover hidden structures. You should consider integrating cGAP to maintain traceability between visual patterns and original observations, especially when identifying clusters, outliers, or variable associations. This framework helps you move beyond simple dimension reduction by providing coordinated views that reveal both local and global data characteristics, enabling more transparent exploratory analysis.

Key insights

cGAP visualizes high-dimensional categorical data by linking raw matrices to HOMALS-derived color and proximity, ensuring traceability.

Principles

• Similar embedded patterns receive similar colors.
• Subject coordinates are barycenters of selected categories.
• Low-dimensional displays only underestimate full-space distances.

Method

cGAP uses HOMALS for 3D embedding, maps coordinates to RGB, generates raw-data heatmaps, subject/variable proximity matrices, then applies seriation.

In practice

• Identify clusters and outliers in complex categorical datasets.
• Distinguish globally weak from locally decisive variables.
• Audit data for systematic missingness or substructure.

Topics

• Categorical Data Visualization
• Homogeneity Analysis
• Seriation Algorithms
• Exploratory Data Analysis
• High-Dimensional Data
• Genomic Data Analysis

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.