Kybernetika

An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method described here applies in a binary setup a recently proposed algorithm, called Neighborhood EM, which seeks a partition that is both well clustered in the feature space and spatially regular \cite{AmbroiseNEM1996}. This approach is derived from the EM algorithm applied to mixture models \cite{Dempster1977}, viewed as an alternate optimization method \cite{Hathaway1986}. The criterion optimized by EM is penalized by a spatial smoothing term that favors classes having many neighbors. The resulting algorithm has a structure similar to EM, with an unchanged M-step and an iterative E-step. The criterion optimized by Neighborhood EM is closely related to a posterior distribution with a multilevel logistic Markov random field as prior \cite{Besag1986,Geman1984}. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions \cite{Govaert1990}. Experiments on simulated spatial binary data yield encouraging results.