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Fuzzy clustering to estimate the parameters of block mixture models

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Abstract

Finite mixture models are being increasingly used to provide model-based cluster analysis. To tackle the problem of block clustering which aims to organize the data into homogeneous blocks, recently we have proposed a block mixture model; we have considered this model under the classification maximum likelihood approach and we have developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. From the estimation point of view, classification maximum likelihood approach yields inconsistent estimates of the parameters and in this paper we consider the block clustering problem under the maximum likelihood approach; unfortunately, the application of the classical EM algorithm for the block mixture model is not direct: difficulties arise due to the dependence structure in the model and approximations are required. Considering the block clustering problem under a fuzzy approach, we propose a fuzzy block clustering algorithm to approximate the EM algorithm. To illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.

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Authors and Affiliations

  1. HEUDIASYC, UMR CNRS 6599, Université de Technologie de Compiègne, BP 20529, 60205, Compiègne Cedex, France

    G. Govaert

  2. IUT de Metz, LITA, Université de Metz, Ile du Saulcy, 57045, Metz Cedex, France

    M. Nadif

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  1. G. Govaert
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  2. M. Nadif
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Correspondence to G. Govaert.

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Govaert, G., Nadif, M. Fuzzy clustering to estimate the parameters of block mixture models. Soft Comput 10, 415–422 (2006). https://doi.org/10.1007/s00500-005-0502-z

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