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How many data clusters are in the Galaxy data set?

Author

Listed:
  • Bettina Grün

    (Wirtschaftsuniversität Wien)

  • Gertraud Malsiner-Walli

    (Wirtschaftsuniversität Wien)

  • Sylvia Frühwirth-Schnatter

    (Wirtschaftsuniversität Wien)

Abstract

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (Stat Model 1:287–304) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn. The aim of the paper is to address Aitkin’s concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations. A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.

Suggested Citation

  • Bettina Grün & Gertraud Malsiner-Walli & Sylvia Frühwirth-Schnatter, 2022. "How many data clusters are in the Galaxy data set?," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 325-349, June.
  • Handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00461-8
    DOI: 10.1007/s11634-021-00461-8
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
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    3. Jeffrey W. Miller & Matthew T. Harrison, 2018. "Mixture Models With a Prior on the Number of Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 340-356, January.
    4. G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
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