Spatial Fuzzy Clustering using EM and Markov Random Fields

Methods are investigated in order to partition in k groups a set of n multivariate observation vectors located at neighboring geographic sites; applications include image segmentation, ecological or soil data cartography. In this perspective, the deterministic variant of the EM procedure described in Zhang (1992) for hidden Markov random fields is shown to be equivalent to the optimization of a spatial fuzzy clustering criterion using the so-called Neighborhood EM algorithm (Ambroise, Dang & Govaert 1997, Ambroise 1996). The obtained fuzzy partition can be interpreted as the (n k) posterior probabilities that the n observations belong to the K groups, computed by an efficient iterative method based on the mean field approximation principle. The resulting algorithm may be viewed as an extension of the k-means algorithm to fuzzy clustering and spatial data.