Spatial Fuzzy Clustering using EM and Markov Random Fields

AbstractMethods are investigated in order to partition in k groups a set of n multivariate observation vectorslocated at neighboring geographic sites; applications include image segmentation, ecological or soil datacartography. In this perspective,the deterministic variant of the EM procedure described in Zhang (1992)for hiddenMarkov randomfieldsis shownto beequivalentto the optimization ofa spatialfuzzyclusteringcriterion using the so-called Neighborhood EM algorithm (Ambroise, Dang & Govaert 1997, Ambroise1996). The obtained fuzzy partition can be interpreted as the (nk) posterior probabilities that theobservations belong to the K groups, computed by an efficientiterative method based on the mean fieldapproximationprinciple. Theresulting algorithm maybeviewedas anextensionof thek-meansalgorithmto fuzzy clustering and spatial data.Keywords: Fuzzyclustering,spatialdata,unsupervisedimagesegmentation,hiddenMarkovrandomfields,EM algorithm, mean field approximation. 1 INTRODUCTION Spatial clustering goals. In exploratory data analysis, clustering techniques aim to summarize a set of

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