针对相关性聚类设计了结构类型验证方法，发现部分指标在特定数据结构下失效。
Establishing Validity for Distance Functions and Internal Clustering Validity Indices in Correlation Space
- 基于23种典型相关模式构建理论最优聚类，用可控扰动数据评估指标有效性
- 发现SWC和DBI在相关性结构下有效，而VRC和PBM不适用，且相关距离函数无效
- 提出结构类型专属验证框架，为其他聚类结构提供可复用的方法模板
内部聚类有效性指数（ICVI）可在无真实标签情况下评估聚类质量。现有研究普遍发现，没有单一指数在所有数据集上表现最优，导致实践者缺乏选择依据。我们指出，此前研究将人类标注作为标准，但忽略了数据内在结构类型对有效性的影响。结构类型指聚类试图发现的数据数学组织形式。有效性理论要求基于结构类型定义聚类质量。本文首次对相关性模式这一结构类型进行有效性评估，将23种典型相关模式作为理论最优聚类，使用含可控扰动的合成数据，在内容、准则、构念和外部有效性四个维度进行全面检验。结果表明：轮廓系数（SWC）与戴维斯-布尔丁指数（DBI）在相关性模式下有效，而卡林斯基-哈拉巴兹（VRC）与帕赫拉-班达亚-莫利克（PBM）指数失效；简单Lp范数距离有效，而相关性专用距离函数在结构、准则和外部有效性上均失败。该结果与以往研究不同，证明有效性依赖于结构类型。本研究提出的结构类型专属验证方法，不仅提供实际判据（SWC>0.9，DBI<0.15），也为其他结构类型的有效性建立提供了方法模板。
原文摘要 · Abstract (English)
Internal clustering validity indices (ICVIs) assess clustering quality without ground truth labels. Comparative studies consistently find that no single ICVI outperforms others across datasets, leaving practitioners without principled ICVI selection. We argue that inconsistent ICVI performance arises because studies evaluate them based on matching human labels rather than measuring the quality of the discovered structure in the data, using datasets without formally quantifying the structure type and quality. Structure type refers to the mathematical organisation in data that clustering aims to discover. Validity theory requires a theoretical definition of clustering quality, which depends on structure type. We demonstrate this through the first validity assessment of clustering quality measures for correlation patterns, a structure type that arises from clustering time series by correlation relationships. We formalise 23 canonical correlation patterns as the theoretical optimal clustering and use synthetic data modelling this structure with controlled perturbations to evaluate validity across content, criterion, construct, and external validity. Our findings show that Silhouette Width Criterion (SWC) and Davies-Bouldin Index (DBI) are valid for correlation patterns, whilst Calinski-Harabasz (VRC) and Pakhira-Bandyopadhyay-Maulik (PBM) indices fail. Simple Lp norm distances achieve validity, whilst correlation-specific functions fail structural, criterion, and external validity. These results differ from previous studies where VRC and PBM performed well, demonstrating that validity depends on structure type. Our structure-type-specific validation method provides both practical guidance (quality thresholds SWC>0.9, DBI<0.15) and a methodological template for establishing validity for other structure types.
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