arXiv:2501.13093cs.ITcs.AI2025-01

提出可保证恢复无歧义聚类的新算法,解决密度不均导致的聚类模糊问题。

Guaranteed Recovery of Unambiguous Clusters

  • 基于信息论定义聚类歧义,识别可唯一确定的簇结构。
  • 通过密度种子+贪心扩展,实现对非凸簇的准确恢复。
  • 对重叠簇鲁棒,参数少,性能优于主流方法。

聚类常因正确划分标准的内在模糊性而困难,即使已知簇数 $K$,当不同簇间密度差异大或单个簇存在多个分离的高密度区时,歧义仍普遍存在。本文提出一种信息论框架,用于判断 $K$-聚类是否具有歧义,并设计一个在无歧义时可保证恢复的算法。该框架形式化了簇内两个高密度区若足够分离,则可能被误认为两个独立簇的情况。算法先用密度方法识别 $K$ 个部分簇(或‘种子’),再以贪心策略将未分配点加入,形成完整聚类。我们实现并测试了适用于重叠簇的改进版本,发现其参数选择极少,在多个数据集上表现优于广泛使用的非凸聚类算法。

原文摘要 · Abstract (English)

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation in density among different clusters, and clusters have multiple relatively separated regions of high density. In this paper we propose an information-theoretic characterization of when a $K$-clustering is ambiguous, and design an algorithm that recovers the clustering whenever it is unambiguous. This characterization formalizes the situation when two high density regions within a cluster are separable enough that they look more like two distinct clusters than two truly distinct clusters in the $K$-clustering. The algorithm first identifies $K$ partial clusters (or "seeds") using a density-based approach, and then adds unclustered points to the initial $K$ partial clusters in a greedy manner to form a complete clustering. We implement and test a version of the algorithm that is modified to effectively handle overlapping clusters, and observe that it requires little parameter selection and displays improved performance on many datasets compared to widely used algorithms for non-convex cluster recovery.

聚类无歧义密度聚类非凸聚类

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