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A Probability for Classification Based on the Dirichlet Process Mixture Model

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Abstract

In this paper we provide an explicit probability distribution for classification purposes when observations are viewed on the real line and classifications are to be based on numerical orderings. The classification model is derived from a Bayesian nonparametric mixture of Dirichlet process model; with some modifications. The resulting approach then more closely resembles a classical hierarchical grouping rule in that it depends on sums of squares of neighboring values. The proposed probability model for classification relies on a numerical procedure based on a reversible Markov chain Monte Carlo (MCMC) algorithm for determining the probabilities. Some numerical illustrations comparing with alternative ideas for classification are provided.

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Authors and Affiliations

  1. Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Ruth Fuentes–García

  2. IIMAS, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Ramsés H. Mena

  3. University of Kent, Canterbury, Kent, CT2 7NZ, UK

    Stephen G. Walker

Authors
  1. Ruth Fuentes–García
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  2. Ramsés H. Mena
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  3. Stephen G. Walker
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Corresponding author

Correspondence to Stephen G. Walker.

Additional information

The first author gratefully acknowledges the Mexican Mathematical Society and the Sofia Kovalevskaia Fund, and the second author gratefully acknowledges CONACYT for Grant No. J50160-F, for allowing them to travel to the UK, where the work was completed during a visit to the University of Kent. The authors gratefully acknowledge the comments of three referees which have improved the paper.

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Fuentes–García, R., Mena, R.H. & Walker, S.G. A Probability for Classification Based on the Dirichlet Process Mixture Model. J Classif 27, 389–403 (2010). https://doi.org/10.1007/s00357-010-9061-9

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  • DOI: https://doi.org/10.1007/s00357-010-9061-9

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