这篇论文提出了cGAP，一个新框架，用HOMALS加热图来可视化高维分类数据，特别适合基因、生物医学等领域。能保持原数据矩阵，同时揭示聚类和结构。
cGAP（categorical Generalized Association Plots）提出了一种针对名义、有序和二值数据的可视化框架，通过同质性分析（HOMALS）将样本和类别嵌入三维欧几里得空间，并映射为RGB颜色表示相似模式。该框架集成三个协调视图：HOMALS引导的原始数据热图、样本邻近矩阵和变量邻近矩阵，并利用序列算法重排行列以揭示聚类、异常值和局部全局结构。在四个数据集（学生动物分类数据、哺乳动物齿廓、UCI蘑菇记录、COG数据库）上的应用展示了其透明探索性分析能力。cGAP还推导了重心可追溯性、投影失真和对比保持性质，说明嵌入几何如何传递到显示中。
cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data
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.