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Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation

Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, 1000 Ljubljana, Slovenia
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Mathematics 2020, 8(3), 373; https://doi.org/10.3390/math8030373 (registering DOI)
Received: 14 February 2020 / Revised: 2 March 2020 / Accepted: 3 March 2020 / Published: 7 March 2020
(This article belongs to the Section Mathematics and Computer Science)
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. View Full-Text
Keywords: mixture model; parameter estimation; EM algorithm; REBMIX algorithm; density estimation; clustering; image segmentation mixture model; parameter estimation; EM algorithm; REBMIX algorithm; density estimation; clustering; image segmentation
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Panić, B.; Klemenc, J.; Nagode, M. Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation. Mathematics 2020, 8, 373.

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