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On Total Number of Candidate Component Cluster Centers and Total Number of Candidate Mixture Models in Model Based Clustering

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Author(s): Tayfun Servi | Hamza Erol

Journal: Sel├žuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 8;
Issue: 2;
Start page: 57;
Date: 2007;
Original page

Keywords: Multivariate normal mixture model | Mixture model based clustering | Model selection | Total number of candidate component cluster centers | Total number of candidate mixture models | Number of possible mixture models.

ABSTRACT
Determining the number of component clusters for a multivariate normal mixture model is the most important problem in model based clustering and determining the number of candidate mixture models is the most interesting problem in multivariate normal mixture model based clustering using model selection criteria. In this study; first, the concept of the total number of candidate component cluster centers is introduced and an interval is constructed by using the number of partitions in each variable in multivariate data. Second, an equation is given for the total number of candidate mixture models in multivariate normal mixture model based clustering. The number of candidate mixture models is defined as the sum of the number of possible mixture models with different number of component clusters.
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