Bayesian Mixture Labeling and Clustering

Label switching is one of the fundamental issues for Bayesian mixture modeling. It occurs due to the nonidentifiability of the components under symmetric priors. Without solving the label switching, the ergodic averages of component specific quantities will be identical and thus useless for inference relating to individual components, such as the posterior means, predictive component densities, and marginal classification probabilities. The author establishes the equivalence between the labeling and clustering and proposes two simple clustering criteria to solve the label switching. The first method can be considered as an extension of K-means clustering. The second method is to find the labels by minimizing the volume of labeled samples and this method is invariant to the scale transformation of the parameters. Using a simulation example and the application of two real data sets, the author demonstrates the success of these new methods in dealing with the label switching problem.