cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data
Machine Learning
Summary
The authors developed a new way to visualize complex categorical data, like survey answers or genetic traits, that keeps the original data intact while adding helpful geometric patterns. Their method, called categorical Generalized Association Plots (cGAP), places data points and categories into a 3D space and assigns colors based on similarity. This helps reveal groups, outliers, and relationships through coordinated heatmaps and matrices, making it easier to explore and understand big categorical datasets. They tested cGAP on examples from biology, education, and machine learning to show how it works across different fields.
Authors
Chun-houh Chen, Shun-Chuan Chang, Chiun-How Kao, Yi-Ju Lee, Shang-Ying Shiu, Yin-Jing Tien, ShengLi Tzeng, Han-Ming Wu
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.