提出新评估方法,平衡聚类信息量与简洁性。
External Clustering Validation by the Homogeneity-Parsimony Trade-off

- 基于信息瓶颈原理,定义同质性与简洁性得分
- 得分随聚类细化单调变化,更符合直觉
- 可统一多种评估指标,适合算法比较与特征选择
常用标量指标评估聚类结果时,常忽略一个根本权衡:聚类应充分反映真实类别,又不能过度细分。本文提出归一化的同质性与简洁性得分,量化这一权衡。该方法基于信息瓶颈原理改进,不鼓励有损压缩。通过实例和数学证明,说明所提得分在聚类细化过程中单调变化,优于已有方案。进一步拓展信息论框架,推导出基于集合匹配与成对匹配的同质性-简洁性得分,统一了常见评估标准。在成对设定下,该权衡等价于二分类器的受试者工作特征曲线。实验证明该框架可用于特征选择与算法比较,联合分析得分可明确聚类性能点并识别帕累托最优解。
原文摘要 · Abstract (English)
Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.
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