Spatial Clustering Using the Likelihood Function

Clustering has been widely used as a tool to group multivariate observations that have similar characteristics. However, there have been few attempts at formulating a method to group similar multivariate observations while taking into account their spatial location (R.T. Ng and J. Han, 1994), (J. Cuzick and R. Edwards, 1990), (G.C. Simbahan and A. Dobermann, 2006). This paper proposes a method to spatially cluster similar observations based on their likelihoods. The geographic or spatial location of the observations can be incorporated into the likelihood of the multivariate normal distribution through the variance-covariance matrix. The variance-covariance matrix can be computed using any specific spatial covariance structure. Therefore, observations within a cluster which are spatially close to one another will have a larger likelihood than those observations which are not close to one another. This results in spatially close observations being placed into the same cluster.