cGAP：用于高维分类数据可视化的带HOMALS引导热图的广义关联图
cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data
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中文总结 AI 辅助
研究针对高维分类数据可视化工具不足的问题，提出cGAP框架，利用HOMALS嵌入数据并集成多视图，经序列化算法揭示数据结构，推导相关属性，通过多领域应用展示其多功能性，为研究复杂分类数据集提供可视化环境。
中文摘要 AI 辅助
高维分类数据出现在遗传学、生物医学和社会科学中，但此类数据的可视化工具远不如连续变量的发达。现有方法要么扩展性差，严重依赖与原始数据矩阵分离的低维显示，要么优先考虑预测准确性而非可解释性。为填补这一空白，我们引入分类广义关联图（cGAP），这是一种用于名义、有序和二元数据的可视化框架，在保留原始数据矩阵的同时，用可解释的几何结构对其进行扩充。cGAP使用同质性分析（HOMALS）将对象和类别级别嵌入三维欧几里得空间，并将嵌入映射到红-绿-蓝坐标，使相似模式获得相似颜色。该框架集成了三个协调视图：原始数据矩阵的HOMALS引导热图、对象接近度矩阵和变量接近度矩阵。然后使用序列化算法对行和列进行重新排序，以揭示连贯的聚类、异常值和局部到全局的结构。我们还推导了重心可追溯性、投影失真和对比度保持属性，以阐明嵌入几何结构如何转移到显示中。我们通过将cGAP应用于学生-动物分类数据、哺乳动物牙列轮廓、UCI机器学习库中的蘑菇记录和直系同源基因数据库集群，展示了cGAP的多功能性。这些例子表明，cGAP通过保持派生视觉结构与原始分类观察之间的可追溯性，支持透明的探索性分析。cGAP为跨科学领域研究复杂分类数据集提供了一个基于全矩阵热图的可视化环境。
英文摘要
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.
发表机构
- Institute of Statistical Science, Academia Sinica（学术院统计研究所）
- Department of Statistics, National Taipei University（台北国立大学统计系）
- Holistic Education Center, Mackay Medical University（Mackay医学院整体教育中心）
- Department of Statistics and Data Science, Tamkang University（淡江大学统计与数据科学系）
- Institute for Information Industry（资讯产业研究院）
- Department of Applied Mathematical and Graduate Institute of Statistics, National Chung Hsing University（中正大学应用数学及统计研究所）
- Department of Statistics, National Chengchi University（中正大学统计系）
机构由 AI 辅助整理，请以论文原文为准。
