Model-Based Clustering With Dissimilarities: A Bayesian Approach

• Published in: Journal of computational and graphical statistics Vol. 16; no. 3; pp. 559 - 585
• Main Authors: Oh, Man-Suk, Raftery, Adrian E
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.09.2007; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Coordinate systems; Covariance; Datasets; Euclidean space; Gaussian distributions; Hierarchical model; Leukemia; Markov chain Monte Carlo; Mixture models; Modeling; Monte Carlo simulation; Multidimensional scaling; Normal distribution; Parametric models; Studies; Yeasts
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1198/106186007X236127

A Bayesian model-based clustering method is proposed for clustering objects on the basis of dissimilarites. This combines two basic ideas. The first is that the objects have latent positions in a Euclidean space, and that the observed dissimilarities are measurements of the Euclidean distances with error. The second idea is that the latent positions are generated from a mixture of multivariate normal distributions, each one corresponding to a cluster. We estimate the resulting model in a Bayesian way using Markov chain Monte Carlo. The method carries out multidimensional scaling and model-based clustering simultaneously, and yields good object configurations and good clustering results with reasonable measures of clustering uncertainties. In the examples we study, the clustering results based on low-dimensional configurations were almost as good as those based on high-dimensional ones. Thus, the method can be used as a tool for dimension reduction when clustering high-dimensional objects, which may be useful especially for visual inspection of clusters. We also propose a Bayesian criterion for choosing the dimension of the object configuration and the number of clusters simultaneously. This is easy to compute and works reasonably well in simulations and real examples.