Comonotonic-Based Time Series Clustering With Constraints: A Review and a Conceptual Framework

Time series clustering is a widely used unsupervised learning approach that identifies groups of similar time series to uncover hidden patterns in complex datasets. In recent years, this technique has gained traction in the analysis of geo-referenced time series, where spatial information must be incorporated into the dissimilarity measure to achieve meaningful results. This paper offers a thorough review of dissimilarity-based clustering methods with soft spatial constraints, i.e., approaches that integrate spatial context into the clustering process without enforcing strict spatial proximity within clusters. Our focus is on copula-based clustering techniques, which effectively capture comovements among time series without requiring explicit modeling of their marginal distributions. We first introduce a general framework for copula-based time series clustering and then explore how spatial constraints can be embedded into the clustering process. Finally, we propose a general framework, called Triple-C, which provides two comprehensive model architectures that address this challenge through either a dissimilarity fusion step or a copula aggregation approach.