Inference in model-based cluster analysis

Halima Bensmail, Gilles Celeux, Adrian E. Raftery, Christian P. Robert

Research output: Contribution to journalArticle

119 Citations (Scopus)


A new approach to cluster analysis has been introduced based on parsimonious geometric modelling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classification, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be specified by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. Here, we propose a new approach which overcomes all these difficulties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace-Metropolis estimator. It works well in several real and simulated examples.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalStatistics and Computing
Issue number1
Publication statusPublished - 1 Dec 1997
Externally publishedYes



  • Bayes factor
  • Eigenvalue decomposition
  • Gaussian mixture
  • Gibbs sampler

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Statistics and Probability
  • Theoretical Computer Science

Cite this

Bensmail, H., Celeux, G., Raftery, A. E., & Robert, C. P. (1997). Inference in model-based cluster analysis. Statistics and Computing, 7(1), 1-10.