提出新指标衡量降维图空区域扭曲，更贴合人眼视觉感知。
Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index
- 通过空三角形对比高低维空间变形，量化空域扭曲程度。
- 相比传统指标，对细微但显著的视觉结构变形更敏感。
- 计算快、结果可可视化，适合数据探索与交互分析。
质量度量在高维数据降维投影的可视化分析中至关重要，它们量化投影与原始高维数据之间的失真程度，帮助用户判断所见结构的可信度。然而，多数主流度量关注点间直接关系（如距离或邻域），忽视了布局中空区域的失真，而这些区域常构成二维布局中重要的视觉特征。本文提出间隙指数（Gap Index, GI），一种针对二维投影的质量度量，通过分解空间为若干空三角形，并与高维对应结构比较，计算其形变程度。该每三角形形变可聚合为单一标量值，或叠加至投影图上以可视化区域失真模式。实验表明，与流行度量不同，GI 对具有高视觉影响的小型结构形变极为敏感，且计算高效、结果可解释。
原文摘要 · Abstract (English)
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.
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