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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

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.

Suggested Citation

  • Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1381-1395
    DOI: 10.1016/j.csda.2011.11.002
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    Cited by:

    1. 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.
    2. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    3. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    4. Yoichi Miyata & Takayuki Shiohama & Toshihiro Abe, 2020. "Estimation of finite mixture models of skew-symmetric circular distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 895-922, November.
    5. Luca Scrucca & Adrian Raftery, 2015. "Improved initialisation of model-based clustering using Gaussian hierarchical partitions," 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. 9(4), pages 447-460, December.
    6. Volodymyr Melnykov & Xuwen Zhu, 2019. "An extension of the K-means algorithm to clustering skewed data," Computational Statistics, Springer, vol. 34(1), pages 373-394, March.
    7. Wan-Lun Wang & Luis M. Castro & Wan-Chen Hsieh & Tsung-I Lin, 2021. "Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables," Statistical Papers, Springer, vol. 62(5), pages 2119-2145, October.
    8. Branislav Panić & Jernej Klemenc & Marko Nagode, 2020. "Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation," Mathematics, MDPI, vol. 8(7), pages 1-30, July.
    9. Ye Tian & Yasunari Yokota, 2019. "Estimating the Major Cluster by Mean-Shift with Updating Kernel," Mathematics, MDPI, vol. 7(9), pages 1-25, August.
    10. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    11. Semhar Michael & Volodymyr Melnykov, 2016. "An effective strategy for initializing the EM algorithm in finite mixture models," 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. 10(4), pages 563-583, December.
    12. 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.
    13. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    14. 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.
    15. Semhar Michael & Volodymyr Melnykov, 2016. "Finite Mixture Modeling of Gaussian Regression Time Series with Application to Dendrochronology," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 412-441, October.
    16. Shiow-Lan Gau & Jean Dieu Tapsoba & Shen-Ming Lee, 2014. "Bayesian approach for mixture models with grouped data," Computational Statistics, Springer, vol. 29(5), pages 1025-1043, October.
    17. Volodymyr Melnykov, 2013. "Finite mixture modelling in mass spectrometry analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 573-592, August.

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