Geodesic
Fuzzy clustering of spatial binary data
Kybernetika, Tome 34 (1998) no. 4, p. [393]

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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 [AmbroiseNEM1996]. This approach is derived from the EM algorithm applied to mixture models [Dempster1977], viewed as an alternate optimization method [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 [Besag1986,Geman1984]. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions [Govaert1990]. Experiments on simulated spatial binary data yield encouraging results.
Classification : 62H30, 62H86, 62M40, 65C60
Keywords: mixture models 
@article{KYB_1998__34_4_a6,
     author = {Dang, M\^o and Govaert, G\'erard},
     title = {Fuzzy clustering of spatial binary data},
     journal = {Kybernetika},
     pages = {[393]},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {1998},
     zbl = {1274.62418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998__34_4_a6/}
}
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Dang, Mô; Govaert, Gérard. Fuzzy clustering of spatial binary data. Kybernetika, Tome 34 (1998) no. 4, p. [393]. http://geodesic.mathdoc.fr/item/KYB_1998__34_4_a6/