发表机构
Eindhoven University of Technology（埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Gap指数，一种度量降维散点图空白区域失真的质量指标，对高视觉影响的小结构变形敏感，计算快速且可解释。
AI 中文摘要
质量指标对于降维投影在高维数据可视化分析中的正确应用至关重要，它们量化了投影与高维数据相比的失真程度，为用户对生成布局中结构的置信度提供可靠指示。然而，大多数流行指标聚焦于捕捉点之间的直接关系（如距离或邻域），却忽略了布局空白区域的失真，尽管这些空白区域常构成二维布局中视觉相关的特征。本文提出Gap指数（GI），这是一种用于二维投影的质量指标，通过测量投影空白区域的空间失真来捕捉视觉失真。具体做法是将空间分解为空白三角形，再将其与高维对应物比较以计算变形；这种逐三角形变形可聚合为单个标量值，或叠加在投影上以可视化区域失真模式。结果表明，与流行质量指标不同，GI对具有高视觉影响的小结构变形敏感，且计算快速、可解释性强。
英文摘要
Quality metrics play a crucial role in the proper use of dimensionality reduction projections for visual analysis of high-dimensional data. They quantify the degree of distortion of a projection compared to the high-dimensional data and provide a reliable indication of how confident users can be in the structures they see in the resulting layouts. However, most popular metrics focus on capturing direct relationships between points (e.g., distances or neighborhoods) while neglecting distortions in empty areas of the layout, even though these often compose visually relevant features of a 2D layout. In this paper, we introduce the Gap Index (GI), a quality metric for 2D projections that captures visual distortion by measuring spatial distortion in empty areas of a projection. It does so by decomposing the space into empty triangles, which are then compared to their high-dimensional counterparts to compute the deformation. This per-triangle deformation can be aggregated into a single scalar value or overlaid on a projection to visualize regional distortion patterns. Results show that, contrary to popular quality metrics, the GI is sensitive to small structural deformations that have high visual impact. It is also fast to compute and interpretable.
Comments11 pages, 13 figures
