Model selection for mixture model via integrated nested Laplace approximation

To cluster or partition data/signal, expectation-and-maximisation or variational approximation with a mixture model (MM), which is a parametric probability density function represented as a weighted sum of K̂ densities, is often used. However, model selection to find the underlying K̂ is one of the key concerns in MM clustering, since the desired clusters can be obtained only when K̂ is known. A new model selection algorithm to explore K̂ in a Bayesian framework is proposed. The proposed algorithm builds the density of the model order which information criterion such as AIC and BIC or other heuristic algorithms basically fail to reconstruct. In addition, this algorithm reconstructs the density quickly as compared with the time-consuming Monte Carlo simulation using integrated nested Laplace approximation.