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      Maximum likelihood estimation of Gaussian mixture models using stochastic search

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      Author
      Ar, C.
      Aksoy, S.
      Arıkan, Orhan
      Date
      2012
      Source Title
      Pattern Recognition
      Print ISSN
      0031-3203
      Publisher
      Elsevier BV
      Volume
      45
      Issue
      7
      Pages
      2804 - 2816
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Gaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectationmaximization (EM) algorithm for the maximum likelihood estimation of the parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have been popular alternatives for global optimization but their uses for GMM estimation have been limited to constrained models using identity or diagonal covariance matrices. Our major contributions in this paper are twofold. First, we present a novel parametrization for arbitrary covariance matrices that allow independent updating of individual parameters while retaining validity of the resultant matrices. Second, we propose an effective parameter matching technique to mitigate the issues related with the existence of multiple candidate solutions that are equivalent under permutations of the GMM components. Experiments on synthetic and real data sets show that the proposed framework has a robust performance and achieves significantly higher likelihood values than the EM algorithm. © 2012 Elsevier Ltd. All rights reserved.
      Keywords
      Covariance parametrization
      Expectation – maximization
      Gaussian mixture models
      Identifiability
      Maximum likelihood estimation
      Particle swarm optimization
      Stochastic search
      Identifiability
      Permalink
      http://hdl.handle.net/11693/21405
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.patcog.2011.12.023
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      • Department of Computer Engineering 1368
      • Department of Electrical and Electronics Engineering 3524
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