将聚类差异的杰卡德距离分解为影响与质量指标，揭示变化本质。
Decomposing the Jaccard Distance and the Jaccard Index in ABCDE
- 通过分解杰卡德距离和指数，提出影响与质量新指标。
- 新指标数学性质良好，且相互间有简单方程关联。
- 适用于调试聚类变化、分析质量提升，适合数据科学家使用。
ABCDE是一种用于评估大规模聚类差异的复杂技术。其核心度量是杰卡德距离，该度量在固定项目集（带权重）的聚类空间中为真距离度量。杰卡德指数是互补度量，表征两个聚类的相似性，两者关系为：杰卡德距离 + 杰卡德指数 = 1。本文进一步分解杰卡德距离与杰卡德指数，每项分解产生‘影响’与‘质量’两类指标。影响指标衡量聚类差异的规模特征，质量指标则通过人工判断评估聚类变化对质量的改进程度。该分解提供对聚类变化更深入的洞察，并开启新的调试与探索方法。新指标数学上行为良好，彼此间以简单方程关联。尽管可视为ABCDE的替代框架，但更宜视为互补。它为聚类变化的幅度与质量提供了不同视角，用户可结合两种方法获得更全面理解。
原文摘要 · Abstract (English)
ABCDE is a sophisticated technique for evaluating differences between very large clusterings. Its main metric that characterizes the magnitude of the difference between two clusterings is the JaccardDistance, which is a true distance metric in the space of all clusterings of a fixed set of (weighted) items. The JaccardIndex is the complementary metric that characterizes the similarity of two clusterings. Its relationship with the JaccardDistance is simple: JaccardDistance + JaccardIndex = 1. This paper decomposes the JaccardDistance and the JaccardIndex further. In each case, the decomposition yields Impact and Quality metrics. The Impact metrics measure aspects of the magnitude of the clustering diff, while Quality metrics use human judgements to measure how much the clustering diff improves the quality of the clustering. The decompositions of this paper offer more and deeper insight into a clustering change. They also unlock new techniques for debugging and exploring the nature of the clustering diff. The new metrics are mathematically well-behaved and they are interrelated via simple equations. While the work can be seen as an alternative formal framework for ABCDE, we prefer to view it as complementary. It certainly offers a different perspective on the magnitude and the quality of a clustering change, and users can use whatever they want from each approach to gain more insight into a change.
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