6. Finite Mixture Densities as Models for Cluster Analysis

  1. Brian S. Everitt,
  2. Sabine Landau,
  3. Morven Leese and
  4. Daniel Stahl

Published Online: 25 JAN 2011

DOI: 10.1002/9780470977811.ch6

Cluster Analysis, 5th Edition

Cluster Analysis, 5th Edition

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

Author Information

  1. King's College London, UK

Publication History

  1. Published Online: 25 JAN 2011
  2. Published Print: 7 JAN 2011

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470749913

Online ISBN: 9780470977811

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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