### Abstract

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 language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Statistics and Computing |

Volume | 7 |

Issue number | 1 |

Publication status | Published - 1 Dec 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Statistics and Computing*,

*7*(1), 1-10.

**Inference in model-based cluster analysis.** / Bensmail, Halima; Celeux, Gilles; Raftery, Adrian E.; Robert, Christian P.

Research output: Contribution to journal › Article

*Statistics and Computing*, vol. 7, no. 1, pp. 1-10.

}

TY - JOUR

T1 - Inference in model-based cluster analysis

AU - Bensmail, Halima

AU - Celeux, Gilles

AU - Raftery, Adrian E.

AU - Robert, Christian P.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - 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.

AB - 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.

KW - Bayes factor

KW - Eigenvalue decomposition

KW - Gaussian mixture

KW - Gibbs sampler

UR - http://www.scopus.com/inward/record.url?scp=0009038636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009038636&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0009038636

VL - 7

SP - 1

EP - 10

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 1

ER -