4.3 Article

Spatiotemporal clustering using Gaussian processes embedded in a mixture model

Journal

ENVIRONMETRICS
Volume 32, Issue 7, Pages -

Publisher

WILEY
DOI: 10.1002/env.2681

Keywords

clustering; community ecology; Gaussian process; Laplace approximation; mixture; regions of common profiles; spatial; spatiotemporal

Funding

  1. Academy of Finland [317255]
  2. Data Analytics Program of Data61 (CSIRO)
  3. Research Funds of the University of Helsinki [465/51/2014]
  4. Academy of Finland (AKA) [317255, 317255] Funding Source: Academy of Finland (AKA)

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This study introduces a finite mixture model for spatial and spatiotemporal clustering that incorporates spatial and spatiotemporal autocorrelation and environmental covariates using Gaussian processes. Bayesian inference through approximation methods, including Laplace approximation and Markov chain Monte Carlo approaches, is employed for efficient and accurate analysis of large datasets. Results suggest that the Laplace approximation is a useful alternative to MCMC methods for spatial and spatiotemporal clustering.
The categorization of multidimensional data into clusters is a common task in statistics. Many applications of clustering, including the majority of tasks in ecology, use data that is inherently spatial and is often also temporal. However, spatiotemporal dependence is typically ignored when clustering multivariate data. We present a finite mixture model for spatial and spatiotemporal clustering that incorporates spatial and spatiotemporal autocorrelation by including appropriate Gaussian processes (GP) into a model for the mixing proportions. We also allow for flexible and semiparametric dependence on environmental covariates, once again using GPs. We propose to use Bayesian inference through three tiers of approximate methods: a Laplace approximation that allows efficient analysis of large datasets, and both partial and full Markov chain Monte Carlo (MCMC) approaches that improve accuracy at the cost of increased computational time. Comparison of the methods shows that the Laplace approximation is a useful alternative to the MCMC methods. A decadal analysis of 253 species of teleost fish from 854 samples collected along the biodiverse northwestern continental shelf of Australia between 1986 and 1997 shows the added clarity provided by accounting for spatial autocorrelation. For these data, the temporal dependence is comparatively small, which is an important finding given the changing human pressures over this time.

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