Clustering Spatially Correlated Functional Data With Multiple Scalar Covariates

We propose a probabilistic model for clustering spatially correlated functional data with multiple scalar covariates. The motivating application is to partition the 29 provinces of the Chinese mainland into a few groups characterized by the epidemic severity of COVID-19, while the spatial dependence and effects of risk factors are considered. It can be regarded as an extension of mixture models, which allows different subsets of covariates to influence the component weights and the component densities by modeling the parameters of the mixture as functions of the covariates. In this way, provinces with similar spatial factors are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. Further, the identifiability of the proposed model is analyzed, and sufficient conditions to guarantee “generic” identifiability are provided. An
$L_{1}$
-penalized estimator is developed to assist variable selection and robust estimation when the number of explanatory covariates is large. An efficient expectation-minimization algorithm is presented for parameter estimation. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Finally, it is worth noting that the proposed model has a wide range of practical applications, e.g., health management, environmental science, ecological studies, and so on.