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An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers

Listed author(s):
  • Wan-Lun Wang
  • Tsung-I Lin


Mixture of t factor analyzers (MtFA) have been shown to be a sound model-based tool for robust clustering of high-dimensional data. This approach, which is deemed to be one of natural parametric extensions with respect to normal-theory models, allows for accommodation of potential noise components, atypical observations or data with longer-than-normal tails. In this paper, we propose an efficient expectation conditional maximization (ECM) algorithm for fast maximum likelihood estimation of MtFA. The proposed algorithm inherits all appealing properties of the ordinary EM algorithm such as its stability and monotonicity, but has a faster convergence rate since its CM steps are governed by a much smaller fraction of missing information. Numerical experiments based on simulated and real data show that the new procedure outperforms the commonly used EM and AECM algorithms substantially in most of the situations, regardless of how the convergence speed is assessed by the computing time or number of iterations. Copyright Springer-Verlag 2013

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Article provided by Springer in its journal Computational Statistics.

Volume (Year): 28 (2013)
Issue (Month): 2 (April)
Pages: 751-769

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Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:751-769
DOI: 10.1007/s00180-012-0327-z
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  1. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
  2. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
  3. Tzy-Chy Lin & Tsung-I Lin, 2010. "Supervised learning of multivariate skew normal mixture models with missing information," Computational Statistics, Springer, vol. 25(2), pages 183-201, June.
  4. Tsung-I Lin & Hsiu Ho & Pao Shen, 2009. "Computationally efficient learning of multivariate t mixture models with missing information," Computational Statistics, Springer, vol. 24(3), pages 375-392, August.
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