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Some Comments on the Performance of Information Ratios for Assessing Numbers of Components in Finite Mixtures

Athanase Polymenis

Abstract



Information-based methods have been found useful for providing alternative ways in order to address the difficult problem of estimating the number of components in finite mixture models. In the present study we focus on a specific information-based method called minimum information ratio (MIR) criterion. Since simulation results presented in earlier research work showed in general a nice performance of this criterion in cases of good data clustering the aim of the present study will be to investigate reasons underlying such behavior. Our approach is motivated by the fact that a high MIR value computed during implementation of this criterion when a model with true number of components k is fitted can be considered as a natural indicator for good data clustering, whereas a small MIR value indicates poor data clustering. Simulations show that the more data clustering is improved the more the magnitude of this indicator exceeds corresponding magnitudes of MIR values obtained from fitted models with g(≠k) components. These results account in turn for a nice performance of the MIR criterion in cases of good data clustering.

Keywords


Mixture, EM algorithm, data clustering.

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