Clustering Spatially Correlated Functional Data With Multiple Scalar Covariates.

Area of Science:

• Statistics
• Spatial Analysis
• Epidemiology

Background:

• Clustering spatially correlated functional data with covariates presents analytical challenges.
• Existing mixture models may not fully capture complex spatial dependencies and covariate effects.

Purpose of the Study:

• To develop a probabilistic model for clustering spatially correlated functional data, incorporating multiple scalar covariates.
• To apply the model to partition Chinese provinces based on COVID-19 epidemic severity, accounting for spatial and risk factor influences.

Main Methods:

• The proposed model extends mixture models by allowing covariates to influence component weights and densities.
• Identifiability is analyzed, and an L1-penalized estimator is developed for variable selection with numerous covariates.
• An expectation-maximization algorithm is used for efficient parameter estimation.

Main Results:

• The model effectively clusters provinces by integrating spatial correlation and covariate effects.
• Identifiability conditions are established, and the L1-penalized estimator aids in handling high-dimensional covariates.
• Simulation studies and real-data analysis demonstrate the method's empirical performance.

Conclusions:

• The developed probabilistic model offers a robust framework for clustering spatially correlated functional data.
• It provides a method to analyze disease severity patterns while considering geographical and risk factor influences.
• The model has broad applicability in fields such as public health, environmental science, and ecological studies.