Spatial Clustering Techniques: An Experimental Comparison

Abstract

This study considers the problem of clustering spatially located observations, which arises in various fields like unsupervised image segmentation, quantitative biogeography, or mapping of soil properties. In those applications, it is often reasonable to assume that the partition changes slowly in the geographic space. This assumption is taken into account in a recently proposed fuzzy clustering method, the so-called Neighbourhood EM algorithm (Ambroise, 1996; Ambroise et al., 1997) : this method optimizes a criterion containing on the one hand the fuzzy sum of within-cluster inertia exhibited by Hathaway (1986), and on the other hand a spatial smoothing function of the classification. At each iteration of the resulting algorithm, the class memberships of the observations are updated based both on their fitness to the class parameters and on the class of the neighbours. This procedure is interpretable as an application of the Expectation-Maximization (EM) principle to a hidden Markov random field (Dang & Govaert, 1998) . Alternatively, prior to applying traditional clustering techniques, the data may be preprocessed by filtering techniques in order to reduce the noise (Cocquerez et al., 1995) . Post-smoothing of the classification is also tested as an alternative approach to take into account the assumption of spatial regularity of the partition.