Alessia Benevento

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.

Sequential sampling methods are often used to estimate functions describing models subjected to time‐intensive simulations or expensive experiments. These methods provide guidelines for point selection in the domain to capture maximum information about the function. However, in most sequential sampling methods, determining a new point is a time‐consuming process. In this paper, we propose a new method, named Sieve, to sequentially select points of an initially unknown function based on the definition of proper intervals. In contrast with existing methods, Sieve does not involve function estimation at each iteration. Therefore, it presents a greater computational efficiency for achieving a given accuracy in estimation. Sieve brings in tools from computational geometry to subdivide regions of the domain efficiently. Further, we validate our proposed method through numerical simulations and two case studies on the calibration of internal combustion engines and the optimal exploration of an unknown environment by a mobile robot.

The clustering of time series with geo-referenced data requires a suitable dissimilarity matrix interpreting the comovements of the time series and taking into account the spatial constraints. In this paper, we propose a new way to compute the dissimilarity matrix, merging both types of information, which leverages on the Wasserstein distance. We then make a quasi-Gaussian assumption that yields more convenient formulas in terms of the joint correlation matrix. The method is illustrated in a case study involving climatological data.