Spatial Clustering for Carolina Breast Cancer Study.

In the Carolina Breast Cancer Study (CBCS), clustering census tracts based on spatial location, demographic variables, and socioeconomic status is crucial for understanding how these factors influence health outcomes and cancer risk. This task, known as spatial clustering, involves identifying clusters of similar locations by considering both geographic and characteristic patterns. While standard clustering methods such as K-means, spectral clustering, and hierarchical clustering are well-studied, spatial clustering is less explored due to the inherent differences between spatial domains and their corresponding covariates. In this paper, we introduce a spatial clustering algorithm called Gaussian Process Spatial Clustering (GPSC). GPSC leverages the flexibility of Gaussian Processes to cluster unobserved functions between different domains, extending traditional clustering techniques to effectively handle geospatial data. We provide theoretical guarantees for GPSC's performance and demonstrate its capability to recover true clusters through several empirical studies. Specifically, we identify clusters of census tracts in North Carolina based on socioeconomic and environmental indicators associated with health and cancer risk.