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\centerline{\bftwo REVIEW OF ICL CRITERION FOR CLUSTERING} 
\centerline{\bftwo IN MIXTURE MODELS}
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\centerline{\bfone{\it Nusrat Jahan}}
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\centerline{\bfone 
Department of Mathematics and Statistics}
\centerline{\bfone Mississippi State University}
\centerline{\bfone Mississippi State, MS 39762 USA}
\centerline{\bfone email:njahan@ra.msstate.edu}


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\centerline{\bfone ABSTRACT}
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\noindent

Statistical analysis of mixture models are of interest because it is an 
alternative to nonparametric density estimation and it is a powerful way of
modelling in cluster analysis. In case of density estimation, optimization 
of the Bayesian Information criterion (BIC) generally results in a good 
approximation of the density to be estimated. But in case of cluster analysis,
the BIC tends to overestimate the number of clusters when the data is a poor 
fit to the mixture model. In this context a modification of
BIC, integrated completed likelihood (ICL) criterion has been investigated.
In the ICL approach, the integrated completed likelihood is maximized to select
both a relevant form of model and  relevant number of clusters. In the BIC
approach, only the observed likelihood is maximized. Where as the integrated 
completed likelihood includes the estimated (using maximum a posteriori 
function) missing data. The ICL criterion penalizes for the complexity of the 
mixture model, thus ensuring the partitioning of data with the greatest 
evidence. This paper will focus on the computation of ICL, effectiveness and 
drawbacks of ICL in the context of cluster analysis. The differences between 
ICL and BIC will also be investigated.  
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