Location dependent Dirichlet process mixture model for clustering spatially correlated time series

Abstract

Dirichlet process mixture model has been widely used as a Bayesian nonparametric model for clustering. However, the exchangeability assumption of Dirhclet process is not valid for clustering spatially correlated time series because these data are spatially and temporally indexed. In the analysis of spatially correlated time series, the correlations between observations at proximal times and locations must be appropriately considered. In this study, we propose a location-dependent Dirichlet process mixture model, which is an extension of the traditional Dirichlet process mixture model, for clustering spatially correlated time series. We model the temporal pattern as an infinite mixture of Gaussian processes while considering spatial dependency using a location-dependent Dirichlet process prior over mixture weights, which encourages observations from proximal locations to be assigned to the same cluster. At the same time, because global mixture weights and mixture atoms for modelling temporal patterns are shared across space, observations with similar temporal patterns can be still grouped together even if they are far away. The proposed model also allows the number of clusters to be automatically determined during the clustering procedure. We validate the proposed model using simulated examples. Moreover, in a real case study, we detect the clusters of daily confirmed number of COVID-19 for each county in the USA according to their spatial and temporal similarities, and analyze the mean temporal pattern of each cluster.