A PRACTICAL METHOD FOR SELF-ADAPTING GAUSSIAN EXPECTATION MAXIMIZATION

Nicola Greggio, Alexandre Bernardino, José Santos-Victor

2010

Abstract

Split-and-merge techniques have been demonstrated to be effective in overtaking the convergence problems in classical EM. In this paper we follow a split-and-merge approach and we propose a new EM algorithm that makes use of a on-line variable number of mixture Gaussians components. We introduce a measure of the similarities to decide when to merge components. A set of adaptive thresholds keeps the number of mixture components close to optimal values. For sake of computational burden, our algorithm starts with a low initial number of Gaussians, adjusting it in runtime, if necessary. We show the effectivity of the method in a series of simulated experiments. Additionally, we illustrate the convergence rates of of the proposed algorithms with respect to the classical EM.

References

  1. Dempster, A., Laird, N., and Rubin, D. (1977). Maximum likelihood estimation from incomplete data via the em algorithm. J. Royal Statistic Soc., 30(B):1-38.
  2. Figueiredo, A. and Jain, A. (2002). Unsupervised learning of finite mixture models. IEEE Trans. Patt. Anal. Mach. Intell., 24(3).
  3. Mahalanobis, P. C. (1936). On the generalized distance in statistics. Proceedings of the National Institute of Sciences of India, 2(1):39-45.
  4. McLachlan, G. and Peel, D. (2000). Finite mixture models. John Wiley and Sons.
  5. Pernkopf, F. and Bouchaffra, D. (2005). Genetic-based em algorithm for learning gaussian mixture models. IEEE Trans. Patt. Anal. Mach. Intell., 27(8):1344-1348.
  6. Rissanen, J. (1989). Stochastic complexity in statistical jnquiry. Wold Scientific Publishing Co. USA.
  7. Sakimoto, Y., Iahiguro, M., and Kitagawa, G. (1986). Akaike information criterion statistics. KTK Scientific Publisher, Tokio.
  8. Sun, H., Sun, M., and Wang, S. (19-22 August 2007). A measurement of overlap rate between gaussian components. Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong,.
  9. Ueda, N., Nakano, R., Ghahramani, Y., and Hiton, G. (2000). Smem algorithm for mixture models. Neural Comput, 12(10):2109-2128.
  10. Zhang, Z., Chen, C., Sun, J., and Chan, K. (2003). Em algorithms for gaussian mixtures with split-and-merge operation. Pattern Recognition, 36:1973 - 1983.
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Paper Citation


in Harvard Style

Greggio N., Bernardino A. and Santos-Victor J. (2010). A PRACTICAL METHOD FOR SELF-ADAPTING GAUSSIAN EXPECTATION MAXIMIZATION . In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8425-00-3, pages 36-44. DOI: 10.5220/0002894600360044


in Bibtex Style

@conference{icinco10,
author={Nicola Greggio and Alexandre Bernardino and José Santos-Victor},
title={A PRACTICAL METHOD FOR SELF-ADAPTING GAUSSIAN EXPECTATION MAXIMIZATION},
booktitle={Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2010},
pages={36-44},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002894600360044},
isbn={978-989-8425-00-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - A PRACTICAL METHOD FOR SELF-ADAPTING GAUSSIAN EXPECTATION MAXIMIZATION
SN - 978-989-8425-00-3
AU - Greggio N.
AU - Bernardino A.
AU - Santos-Victor J.
PY - 2010
SP - 36
EP - 44
DO - 10.5220/0002894600360044