cGAP: New heatmap tool visualizes high-dimensional categorical data with HOMALS

High-dimensional categorical data remains notoriously hard to visualize compared to continuous data, but a new arXiv paper from researchers at Academia Sinica (Taiwan) offers a compelling solution. The team led by Chun-houh Chen introduces cGAP (categorical Generalized Association Plots), a heatmap-based framework that extends Generalized Association Plots to nominal, ordinal, and binary variables. cGAP uses Homogeneity Analysis (HOMALS) to embed both subjects and category levels into a three-dimensional Euclidean space, then maps the embedding to red-green-blue coordinates so that similar patterns receive similar colors. This preserves traceability between the derived visual structure and the original data matrix, a key advantage over existing methods that often use detached low-dimensional displays. The framework integrates three coordinated views: a HOMALS-guided heatmap of the raw data matrix, a subject proximity matrix, and a variable proximity matrix, with seriation algorithms reordering rows and columns to reveal coherent clusters, outliers, and global-to-local structure. The authors also derive barycentric traceability, projection-distortion, and contrast-preservation properties to clarify how embedding geometry transfers to the display.

cGAP demonstrates versatility across four real-world datasets: student-animal classification data, mammalian dentition profiles, mushroom records from the UCI Machine Learning Repository (including the classic poisonous vs. edible classification), and the Clusters of Orthologous Genes (COG) database. In the mushroom dataset, cGAP reveals hidden associations between cap colors, gill sizes, and habitat that traditional methods miss. For COG data, the tool helps biologists quickly identify functional groups across genomes. The framework is particularly valuable for exploratory analysis where maintaining interpretability and traceability to original observations is critical. While the paper is currently a preprint (23 pages, 9 figures, 3 tables), the approach addresses a real gap in ML and statistics tooling. With further development into an open-source package, cGAP could become a standard tool for researchers in genetics, biomedicine, and social sciences who routinely work with complex categorical datasets.