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Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation

Author

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  • Branislav Panić

    (Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, 1000 Ljubljana, Slovenia)

  • Jernej Klemenc

    (Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, 1000 Ljubljana, Slovenia)

  • Marko Nagode

    (Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, 1000 Ljubljana, Slovenia)

Abstract

A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.

Suggested Citation

  • Branislav Panić & Jernej Klemenc & Marko Nagode, 2020. "Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:373-:d:329636
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    References listed on IDEAS

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    1. McLachlan, Geoffrey J. & Krishnan, Thriyambakam & Ng, See Ket, 2004. "The EM Algorithm," Papers 2004,24, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    2. Franko, Mitja & Nagode, Marko, 2015. "Probability density function of the equivalent stress amplitude using statistical transformation," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 118-125.
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    2. Nagode, Marko & Oman, Simon & Klemenc, Jernej & Panić, Branislav, 2023. "Gumbel mixture modelling for multiple failure data," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. Yingkui Jiao & Zhiwei Li & Junchao Zhu & Bin Xue & Baofeng Zhang, 2022. "ABIDE: A Novel Scheme for Ultrasonic Echo Estimation by Combining CEEMD-SSWT Method with EM Algorithm," Sustainability, MDPI, vol. 14(4), pages 1-21, February.
    4. Branislav Panić & Marko Nagode & Jernej Klemenc & Simon Oman, 2022. "On Methods for Merging Mixture Model Components Suitable for Unsupervised Image Segmentation Tasks," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    5. Ben Wu & Subhadip Pal & Jian Kang & Ying Guo, 2022. "Rejoinder to discussions of “distributional independent component analysis for diverse neuroimaging modalities”," Biometrics, The International Biometric Society, vol. 78(3), pages 1122-1126, September.
    6. Yinan Li & Kai-Tai Fang & Ping He & Heng Peng, 2022. "Representative Points from a Mixture of Two Normal Distributions," Mathematics, MDPI, vol. 10(21), pages 1-28, October.

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