On Fitting Mixture Models

Consider the problem of tting a nite Gaussian mixture, with an unknown number of components, to observed data. This paper proposes a new minimum description length (MDL) type criterion, termed MMDL (formixtureMDL), to select the number of components of the model. MMDL is based on the identi cation of an \equivalent sample size", for each component, which does not coincide with the full sample size. We also introduce an algorithm based on the standard expectationmaximization (EM) approach together with a new agglomerative step, called agglomerative EM (AEM). The experiments here reported have shown that MMDL outperforms existing criteria of comparable computational cost. The good behavior of AEM, namely its good robustness with respect to initialization, is also illustrated experimentally.