标题： 多变量时间序列聚类验证的典型相关模式 显示英文标题

标题： Canonical Correlation Patterns for Validating Clustering of Multivariate Time Series

摘要： 基于相关性的多变量时间序列聚类方法揭示了健康、金融和工业应用中变量之间关系的制度变化。 然而，验证发现的聚类是否代表不同的关系而非任意分组仍然是一个基本挑战。 现有的聚类有效性指数是为欧几里得数据开发的，它们在相关模式中的有效性尚未经过系统评估。 与欧几里得聚类不同，欧几里得聚类中几何形状提供了离散的参考目标，而相关性存在于连续空间中，没有等效的参考模式。 我们通过引入数学定义的典型相关模式作为验证目标来填补这一验证空白，这些目标将无限的相关空间离散化为有限且可解释的参考模式。 使用在受控条件下具有完美真实标签的合成数据集，我们证明典型模式提供了可靠的验证目标，其中L1范数用于映射，L5范数用于轮廓宽度准则和Davies-Bouldin指数表现出优越性能。 这些方法对分布偏移具有鲁棒性，并能正确检测相关结构退化，从而提供实际实施指南。 这项工作为高风险领域中的严格相关性聚类验证建立了方法基础。 显示英文摘要

摘要： Clustering of multivariate time series using correlation-based methods reveals regime changes in relationships between variables across health, finance, and industrial applications. However, validating whether discovered clusters represent distinct relationships rather than arbitrary groupings remains a fundamental challenge. Existing clustering validity indices were developed for Euclidean data, and their effectiveness for correlation patterns has not been systematically evaluated. Unlike Euclidean clustering, where geometric shapes provide discrete reference targets, correlations exist in continuous space without equivalent reference patterns. We address this validation gap by introducing canonical correlation patterns as mathematically defined validation targets that discretise the infinite correlation space into finite, interpretable reference patterns. Using synthetic datasets with perfect ground truth across controlled conditions, we demonstrate that canonical patterns provide reliable validation targets, with L1 norm for mapping and L5 norm for silhouette width criterion and Davies-Bouldin index showing superior performance. These methods are robust to distribution shifts and appropriately detect correlation structure degradation, enabling practical implementation guidelines. This work establishes a methodological foundation for rigorous correlation-based clustering validation in high-stakes domains.