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Fuzzy clustering of spatial binary data. (English) Zbl 1274.62418
Summary: An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method 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. This approach is derived from the EM algorithm applied to mixture models [A.P. Dempster, N.M. Laird and D.B. Rubin, J. R. Stat. Soc., Ser. B 39, 1–38 (1977; Zbl 0364.62022)], viewed as an alternate optimization method [R.J. Hathaway, Stat. Probab. Lett. 4, 53–56 (1986; Zbl 0585.62052)]. 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. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions. Experiments on simulated spatial binary data yield encouraging results.
MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H86 Multivariate analysis and fuzziness
62M40 Random fields; image analysis
65C60 Computational problems in statistics (MSC2010)
Keywords:
mixture models
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