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A merging algorithm for Gaussian mixture components


  • Andrea Pastore

    () (Department of Economics, University Of Venice C� Foscari)

  • Stefano Tonellato

    (Department of Economics, University Of Venice C� Foscari)


In finite mixture model clustering, each component of the fitted mixture is usually associated with a cluster. In other words, each component of the mixture is interpreted as the probability distribution of the variables of interest conditionally on the membership to a given cluster. The Gaussian mixture model (GMM) is very popular in this context for its simplicity and flexibility. It may happen, however, that the components of the fitted model are not well separated. In such a circumstance, the number of clusters is often overestimated and a better clustering could be obtained by joining some subsets of the partition based on the fitted GMM. Some methods for the aggregation of mixture components have been recently proposed in the literature. In this work, we propose a hierarchical aggregation algorithm based on a generalisation of the definition of silhouette-width taking into account the Mahalanobis distances induced by the precison matrices of the components of the fitted GMM. The algorithm chooses the number of groups corresponding to the hierarchy level giving rise to the highest average-silhouette-width. Some simulation experiments and real data applications indicate that its performance is at least as good as the one of other existing methods.

Suggested Citation

  • Andrea Pastore & Stefano Tonellato, 2013. "A merging algorithm for Gaussian mixture components," Working Papers 2013:04, Department of Economics, University of Venice "Ca' Foscari".
  • Handle: RePEc:ven:wpaper:2013:04

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    References listed on IDEAS

    1. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    2. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    3. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    4. Zacharias Psaradakis & Nicola Spagnolo, 2003. "On The Determination Of The Number Of Regimes In Markov-Switching Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 237-252, March.
    5. Zacharias Psaradakis & Nicola Spagnolo, 2006. "Joint Determination of the State Dimension and Autoregressive Order for Models with Markov Regime Switching," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 753-766, September.
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    More about this item


    similarity indices; Rand index; mixture models; bootstrap.;

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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