Estimating the Number of Components in Gaussian Mixture Models Adaptively ⋆

An important but difficult problem of mixture model is estimating the number of components, k, by model selection criterion. We investigate the sum of weighted real and imaginary parts of all LogCharacteristic Functions (LCF) for Gaussian Mixture Model (GMM) and propose a new method to estimate k, adaptively. Our method defines the Sum of Weighted Real parts of all LCFs (SWRLCF) as a new convergent function and propose a new model selection criterion based on it. Our new model criterion makes use of the stability of the SWRLCF when k is larger than the true number of components. The univariate acidity and simulated 2D datasets are used to test. Experiment results suggest that our method without any priori is more suited for large sample applications than Akaike’s Information Criterion (AIC), AIC3, Bayesian Information Criterion (BIC) and the Stepwise Split and-merge EM (SSMEM) methods.