The aim of the work is to identify a clustering structure for the 20 Italian regions according to the main variables related to COVID-19 pandemic. Data are observed over time, spanning from the last week of February 2020 to the first week of February 2021. Dealing with geographical units observed at several time occasions, the proposed fuzzy clustering model embedded both space and time information. Properly, an Exponential distance-based Fuzzy Partitioning Around Medoids algorithm with spatial penalty term has been proposed to classify the spline representation of the time trajectories. The results show that the heterogeneity among regions along with the spatial contiguity is essential to understand the spread of the pandemic and to design effective policies to mitigate the effects.

这项工作的目的是根据与 COVID-19 大流行相关的主要变量确定意大利 20 个地区的聚类结构。随着时间的推移观察数据，从 2020 年 2 月的最后一周到 2021 年 2 月的第一周。处理在多个时间场合观察到的地理单位，所提出的模糊聚类模型嵌入了空间和时间信息。适当地，已经提出了一种基于指数距离的具有空间惩罚项的围绕中心点的模糊分区算法来对时间轨迹的样条表示进行分类。结果表明，区域之间的异质性以及空间连续性对于了解大流行的传播和设计有效的政策来减轻影响至关重要。