Model-based Gaussian and non-Gaussian clustering.

*(English)*Zbl 0794.62034Summary: The classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms, including those based on the sum of squares criterion and on the criterion of H. P. Friedman and J. Rubin [J. Am. Stat. Assoc. 62, 1159-1178 (1967)]. However, as currently implemented, it does not allow the specification of which features (orientation, size, and shape) are to be common to all clusters and which may differ between clusters. Also, it is restricted to Gaussian distributions and it does not allow for noise.

We propose ways of overcoming these limitations. A reparameterization of the covariance matrix allows us to specify that some, but not all, features be the same for all clusters. A practical framework for non- Gaussian clustering is outlined, and a means of incorporating noise in the form of a Poisson process is described. An approximate Bayesian method for choosing the number of clusters is given.

The performance of the proposed methods is studied by simulation, with encouraging results. The methods are applied to the analysis of a data set arising in the study of diabetes, and the results seem better than those of previous analyses. A magnetic resonance image (MRI) of the brain is also analyzed, and the methods appear successful in extracting the main features of anatomical interest. The methods described here have been implemented in both Fortran and S-PLUS versions, and the software is freely available through StatLib.

We propose ways of overcoming these limitations. A reparameterization of the covariance matrix allows us to specify that some, but not all, features be the same for all clusters. A practical framework for non- Gaussian clustering is outlined, and a means of incorporating noise in the form of a Poisson process is described. An approximate Bayesian method for choosing the number of clusters is given.

The performance of the proposed methods is studied by simulation, with encouraging results. The methods are applied to the analysis of a data set arising in the study of diabetes, and the results seem better than those of previous analyses. A magnetic resonance image (MRI) of the brain is also analyzed, and the methods appear successful in extracting the main features of anatomical interest. The methods described here have been implemented in both Fortran and S-PLUS versions, and the software is freely available through StatLib.

##### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62F15 | Bayesian inference |