# 6. Finite Mixture Densities as Models for Cluster Analysis

Published Online: 25 JAN 2011

DOI: 10.1002/9780470977811.ch6

Copyright © 2011 John Wiley & Sons, Ltd

Book Title

## Cluster Analysis, 5th Edition

Additional Information

#### How to Cite

Everitt, B. S., Landau, S., Leese, M. and Stahl, D. (2011) Finite Mixture Densities as Models for Cluster Analysis, in Cluster Analysis, 5th Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470977811.ch6

#### Publication History

- Published Online: 25 JAN 2011
- Published Print: 7 JAN 2011

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780470749913

Online ISBN: 9780470977811

- Summary
- Chapter

### Keywords:

- Bayesian inference;
- cluster analysis;
- finite mixture densities;
- Gaussian process;
- multivariate Gaussian components;
- normal distribution

### Summary

This chapter introduces an alternative approach to clustering which postulates a formal statistical model for the population from which the data are sampled, a model that assumes that this population consists of a number of subpopulations in each of which the variables have a different multivariate probability density function, resulting in what is known as a finite mixture density for the population as a whole. It introduces the concept of model-based cluster analysis using finite mixture models, and gives details of estimation, model selection and the use of a Bayesian approach. An obvious extension of the finite mixture model is a mixture of generalized linear models (GLMs) by estimating a generalized linear model for each component. The chapter gives a number of examples of how finite mixture densities are used in practice, beginning with those involving Gaussian components, the first univariate and the second multivariate.

#### Controlled Vocabulary Terms

Bayesian inference; cluster analysis; Gaussian process; normal distribution