用精确率与召回率评估降维是否真实保留了聚类结构
Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation
- 将降维分为关系建模与映射两阶段，用标签指导评估关系阶段
- 精确率与召回率量化模型对预期聚类结构的保留程度
- 帮助调参、发现投影错误，适合想验证聚类结果的研究者
降维技术常用于可视化高维数据并揭示预期聚类结构，但投影中常无法显现该结构。现有指标或评估投影可靠性，或衡量聚类质量，却无法解释为何预期结构缺失。视觉分析虽有效，但因超参数空间大而耗时。本文基于降维分两阶段的最新框架——关系阶段建模相似性，映射阶段进行投影——提出两个监督型评估指标：精确率与召回率，用于衡量关系阶段中建模关系与预设标签所代表聚类结构的一致性。通过 t-SNE 与 UMAP 的实验验证，该方法可指导超参数调优，识别投影伪影，并判断预期结构是否已保留在关系建模中，显著提升降维过程的速度与可靠性。
原文摘要 · Abstract (English)
Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure. However, such a structure may not always appear in the projections. Existing DR quality metrics assess projection reliability (to some extent) or cluster structure quality, but do not explain why expected structures are missing. Visual Analytics solutions can help, but are often time-consuming due to the large hyperparameter space. This paper addresses this problem by leveraging a recent framework that divides the DR process into two phases: a relationship phase, where similarity relationships are modeled, and a mapping phase, where the data is projected accordingly. We introduce two supervised metrics, precision and recall, to evaluate the relationship phase. These metrics quantify how well the modeled relationships align with an expected cluster structure based on some set of labels representing this structure. We illustrate their application using t-SNE and UMAP, and validate the approach through various usage scenarios. Our approach can guide hyperparameter tuning, uncover projection artifacts, and determine if the expected structure is captured in the relationships, making the DR process faster and more reliable.
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