Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.

翻译：现有函数型数据聚类方法常优先考虑划分准确性而忽视可解释性，当数据生成过程遵循特定底层结构且聚类间存在序数关系时，难以提取有意义的洞察。本文提出K-Models这一新颖框架，通过整合序数约束并估计生成观测函数型轮廓的随机过程关键底层要素，同时提升可解释性与结构识别能力。所提方法通过模拟实验和实际应用进行验证。特别地，该方法在感兴趣区域（ROI）曲线上进行测试——该曲线表征反射式传感器监测抗原-抗体结合等生物分子相互作用时的反应轮廓。这些曲线记录了分析物暴露期间，固定有抗原的多个测量点位反射光强度随时间的变化，捕捉系统的结合动力学特征。由于仅需从观测动力学中识别内在信号模式，该数据集成为评估所提方法增强可解释性的理想基准。通过将结构假设融入聚类过程，K-Models在保持与前沿技术相当性能的同时增强可解释性，为分析具有底层序数结构的函数型数据提供了宝贵工具。