Spatial Clustering and the EM Algorithm

A clustering algorithm for spatial data is presented. It seeks a fuzzy partition which is optimal according to some criterion. We propose to penalize the energy function exhibited by Hathway (1986) with a term taking into account spatial contiguity constraints. The structure of the EM algorithm may be used for maximizing the proposed criterion. The Maximization step is then unchanged and the Expectation step becomes iterative.The efficiency of the new clustering algorithm has been tested with biological images and compared with other clustering techniques. 1 Introduction When classical clustering techniques are used for partitioning spatial data, the resulting classes will often be geographically very mixed. To avoid this phenomenon, the spatial information of the data has to be taken into account. Very different solutions to this problem have been proposed in the literature. A natural approach consists in using the geographical coordinates of the individuals, more or less heavily wei..