Bayesian Mixture Labeling and Clustering

• Published in: Communications in statistics. Theory and methods Vol. 41; no. 3; pp. 403 - 421
• Main Author: Yao, Weixin
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.02.2012; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Bayesian mixtures; Clustering; Exact sciences and technology; General topics; K-means; Label switching; Labeling; Markov chain Monte Carlo; Markov processes; Mathematics; Monte Carlo simulation; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Studies; Invariant; Statistical distribution; Cluster analysis (statistics); Multivariate analysis; Stochastic method; Markov chain; Probability density; Scale parameter; Markov chain Monte Carlo; Marginal distribution; Approximation theory; Posterior distribution; Bayes estimation; Mixed distribution; K-means; Monte Carlo method; Label switching; Discriminant analysis; Data analysis; Prior distribution; Bayesian mixtures; Average; Statistical estimation; Clustering; Mean estimation; Statistical method; Numerical analysis; Simulation; 62F10; 62F15
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2010.526741

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.