arXiv:2604.13816cs.LG2026-04

提出一种新聚类数判断方法,更好应对大小不一的簇。

Composite Silhouette: A Subsampling-based Aggregation Strategy

论文配图:Composite Silhouette: A Subsampling-based Aggregation Strategy
图 1 · 摘自论文原文
  • 通过多次抽样聚类,融合微均和宏均轮廓系数
  • 在合成与真实数据上准确恢复真实簇数
  • 适合处理簇大小不平衡的聚类任务

确定聚类数量是无监督学习中的核心挑战,因缺乏真实标签。轮廓系数是常用内部评估指标,但标准微均形式在簇大小不均衡时倾向于偏好大簇。宏均虽能缓解偏差,却可能过度强调少数簇的噪声。我们提出复合轮廓系数(Composite Silhouette),一种基于重复抽样聚类的簇数选择内部准则。对每个子样本,通过自适应凸权重结合微均与宏均轮廓分数,权重由其归一化差异决定,并经有界非线性平滑;最终得分通过对子样本级复合值取平均获得。我们建立了该准则的关键性质,并推导出其抽样估计的有限样本集中性保证。在合成与真实数据集上的实验表明,复合轮廓系数有效融合了微均与宏均的优势,更准确地恢复真实簇数。

原文摘要 · Abstract (English)

Determining the number of clusters is a central challenge in unsupervised learning, where ground-truth labels are unavailable. The Silhouette coefficient is a widely used internal validation metric for this task, yet its standard micro-averaged form tends to favor larger clusters under size imbalance. Macro-averaging mitigates this bias by weighting clusters equally, but may overemphasize noise from under-represented groups. We introduce Composite Silhouette, an internal criterion for cluster-count selection that aggregates evidence across repeated subsampled clusterings rather than relying on a single partition. For each subsample, micro- and macro-averaged Silhouette scores are combined through an adaptive convex weight determined by their normalized discrepancy and smoothed by a bounded nonlinearity; the final score is then obtained by averaging these subsample-level composites. We establish key properties of the criterion and derive finite-sample concentration guarantees for its subsampling estimate. Experiments on synthetic and real-world datasets show that Composite Silhouette effectively reconciles the strengths of micro- and macro-averaging, yielding more accurate recovery of the ground-truth number of clusters.

聚类分析轮廓系数无监督学习抽样策略

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