Fast Computation of the EM Algorithm for Mixture Models

Mixture models become increasingly popular due to their modeling flexibility and are applied to the clustering and classification of heterogeneous data. The EM algorithm is largely used for the maximum likelihood estimation of mixture models because the algorithm is stable in convergence and simple in implementation. Despite such advantages, it is pointed out that the EM algorithm is local and has slow convergence as the main drawback. To avoid the local convergence of the EM algorithm, multiple runs from several different initial values are usually used. Then the algorithm may take a large number of iterations and long computation time to find the maximum likelihood estimates. The speedup of computation of the EM algorithm is available for these problems. We give the algorithms to accelerate the convergence of the EM algorithm and apply them to mixture model estimation. Numerical experiments examine the performance of the acceleration algorithms in terms of the number of iterations and computation time.

• Publication year

  2021

• Venue

  Computational Statistics [Working Title]

• Publication date

  2021-12-08

• Fields of study

  Not labeled

• Identifiers
  DOI 10.5772/intechopen.101249
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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• R: A language and environment for statistical computing.

  2014cited by this paper
• MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms

  2012influential reference
• Simulating Data to Study Performance of Finite Mixture Modeling and Clustering Algorithms

  2010influential reference
• Acceleration of the EM algorithm using the vector epsilon algorithm

  2008cited by this paper
• Accelerating the convergence of the EM algorithm using the vector algorithm

  2006cited by this paper
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  2006cited by this paper
• Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models

  2003influential reference
• Finite Mixture Models

  2000cited by this paper
• Acceleration of the EM Algorithm by using Quasi‐Newton Methods

  1997cited by this paper
• Extrapolation methods: theory and practice

  1993cited by this paper
• Conjugate Gradient Acceleration of the EM Algorithm

  1993cited by this paper
• Extrapolation methods for vector sequences

  1987cited by this paper
• Finding the Observed Information Matrix When Using the EM Algorithm

  1982cited by this paper
• Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper

  1977cited by this paper
• Acceleration techniques for iterated vector and matrix problems : (mathematics of computation, _1_6(1962), nr 79, p 301-322)

  1962cited by this paper

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  2022cites this paper