An Efficient Model Selection for Gaussian Mixture Model in a Bayesian Framework

In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of K̂ Gaussian component densities. However, model selection to find underlying K̂ is one of the key concerns in GMM clustering, since we can obtain the desired clusters only when K̂ is known. In this paper, we propose a new model selection algorithm to explore K̂ in a Bayesian framework. The proposed algorithm builds the density of the model order which any information criterions such as AIC and BIC basically fail to reconstruct. In addition, this algorithm reconstructs the density quickly as compared to the time-consuming Monte Carlo simulation.