提出可快速生成多种新聚类层次结构的方法
Ultrametric Cluster Hierarchies: I Want 'em All!
- 基于任意合理聚类树，快速求解中心型聚类目标
- 所得聚类结果均为层级结构，且计算极快
- 适合需要多视角聚类分析的研究者使用
层次聚类是探索性数据分析的强大工具，将数据组织成一系列嵌套的聚类树，从中可选择任意划分。本文证明：对于任意合理的聚类层次结构，均可高效求解所有中心型聚类目标（如k-means），且解本身也必然为层级结构。因此，给定一个聚类树后，可快速获得大量新的、同样有意义的层次结构。如同标准层次聚类，研究者可从中任选所需划分。实验在多个数据集、聚类树和划分方案上验证了所提方法的有效性。
原文摘要 · Abstract (English)
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one can optimally solve any center-based clustering objective over it (such as $k$-means). Moreover, these solutions can be found exceedingly quickly and are themselves necessarily hierarchical. Thus, given a cluster tree, we show that one can quickly access a plethora of new, equally meaningful hierarchies. Just as in standard hierarchical clustering, one can then choose any desired partition from these new hierarchies. We conclude by verifying the utility of our proposed techniques across datasets, hierarchies, and partitioning schemes.
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