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Initializing the EM algorithm in Gaussian mixture models with an unknown number of components

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  • Melnykov, Volodymyr
  • Melnykov, Igor
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    Abstract

    An approach is proposed for initializing the expectation–maximization (EM) algorithm in multivariate Gaussian mixture models with an unknown number of components. As the EM algorithm is often sensitive to the choice of the initial parameter vector, efficient initialization is an important preliminary process for the future convergence of the algorithm to the best local maximum of the likelihood function. We propose a strategy initializing mean vectors by choosing points with higher concentrations of neighbors and using a truncated normal distribution for the preliminary estimation of dispersion matrices. The suggested approach is illustrated on examples and compared with several other initialization methods.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1381-1395

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1381-1395

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Gaussian mixture model; Initialization; EM algorithm; Eigenvalue decomposition; Truncated normal distribution;

    References

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    1. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    2. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    3. Li, Jia & Zha, Hongyuan, 2006. "Two-way Poisson mixture models for simultaneous document classification and word clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 163-180, January.
    4. Bouveyron, C. & Girard, S. & Schmid, C., 2007. "High-dimensional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 502-519, September.
    5. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-34, March.
    6. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    7. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    8. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer, vol. 2(1), pages 193-218, December.
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    Cited by:
    1. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    2. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    3. Xu, Wenjing & Pan, Qing & Gastwirth, Joseph L., 2014. "Cox proportional hazards models with frailty for negatively correlated employment processes," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 295-307.

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