提出新指标CADI，评估降维后聚类排列是否真实可信。
Class Angular Distortion Index for Dimensionality Reduction
- 用点三元组内角衡量聚类组织的保真度
- 在真实与合成数据上验证，传统指标失效时CADI仍有效
- 可微分，适合用于优化降维过程
降维技术常被分为保持全局结构或局部邻域结构两类。此区分在可视化中至关重要：全局方法可能掩盖聚类，而局部方法可能过度强调聚类。即使聚类在投影中看似分明，其相对排列也可能任意或误导，t-SNE和UMAP等方法普遍存在此问题。现有聚类质量指标仅衡量聚类可分性，或假设原始空间中聚类为球形。本文提出类角畸变指数（CADI），通过点三元组间的内部角来判断投影中聚类组织的保真度。我们在真实与合成数据上展示了现有指标失效的案例，而CADI给出可解释结果。由于依赖角度计算，CADI具有可微性，可支持优化。我们进一步展示基于CADI的降维方法。
原文摘要 · Abstract (English)
Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure clusters while local methods can over-emphasize them. Yet, even when clusters appear distinct, their relative arrangement in the projection may be arbitrary or misleading, a common issue in techniques such as t-SNE and UMAP. Existing cluster quality metrics either only measure cluster separability or assume spherical, globular clusters in the original space. We introduce the Class Angular Distortion Index (CADI), a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection. We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result. Since it relies on computing angles, CADI is also differentiable, enabling optimization. We demonstrate this with a CADI-based DR technique.
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