Large Scale Clustering of Dependent Curves

In this paper, we introduce a model-based method for clustering multiple curves or functionals under spatial dependence specified up to a set of unknown parameters. The functionals are decomposed using a semi-parametric model where the fixed effects account for the large-scale clustering association and the random effects for the small scale spatialdependence variability. The clustering model assumes the clustering membership as a realization from a Markov random field. Within our estimation framework, the emphasis is on a large number of functionals/spatial units with sparsely sampled time points. To overcome the computational cost resulting from large dependence matrix operations, the estimation algorithm includes a two-stage approximation: low-ranked kernel-based decomposition of the dependence matrix and Incomplete Choslesky Factorization of the kernel matrix. We assess the performance of our clustering approach within a simulation study. The simulation results show enhanced clustering estimation accuracy of our method compared with other existing model-based clustering methods under a series of settings: small number of time points, low signal-to-noise ratio and different spatial dependence structures. Many case studies will fall within our clustering framework, but we focus on obtaining fine-grid spatial clusters for demographics trends including ethnicity and income for five southern states of US over the past 11 years.