Abstract
Gaussian mixture modelling is a powerful tool for data analysis. However, the selection of number of Gaussians in the mixture, i.e., the mixture model or scale selection, remains a difficult problem. In this paper, we propose a new kind of dynamic merge-or-split learning (DMOSL) algorithm on Gaussian mixture such that the number of Gaussians can be determined automatically with a dynamic merge-or-split operation among estimated Gaussians from the EM algorithm. It is demonstrated by the simulation experiments that the DMOSL algorithm can automatically determine the number of Gaussians in a sample data set, and also lead to a good estimation of the parameters in the original mixture. Moreover, the DMOSL algorithm is applied to the classification of Iris data.
This work was supported by the Natural Science Foundation of China for Project 60471054
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Mclachlan, G., Peel, D.: Finite Mixture Models. Wiley, New York (2000)
Render, R.A., Walker, H.F.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Review 26(2), 195–239 (1984)
Jain, A.K., Dubes, R.C.: Algorithm for Clustering Data. Prentice Hall, Englewood Cliffs (1988)
Hartigan, J.A.: Distribution problems in clustering. In: Van Ryzin, J. (ed.) Classification and clustering, pp. 45–72. Academic Press, New York (1977)
Akaike, H.: A New Look at the Statistical Model Identification. IEEE Trans. on Automatic Control AC-19, 716–723 (1974)
Ma, J., Wang, T., Xu, L.: A gradient BYY harmony learning rule on Gaussian mixture with automated model selection. Neurocomputing 56, 481–487 (2004)
Ma, J., Gao, B., Wang, Y., Cheng, Q.: Two further gradient BYY learning rules for Gaussian mixture with automated model selection. In: Yang, Z.R., Yin, H., Everson, R.M. (eds.) IDEAL 2004. LNCS, vol. 3177, pp. 690–695. Springer, Heidelberg (2004)
Ma, J., Wang, T.: Entropy penalized automated model selection on Gaussian mixture. International Journal of Pattern Recognition and Artificial Intelligence 18(8), 1501–1512 (2004)
Ueda, N., Nakano, R., Ghahramani, Y.Z., Hiton, G.E.: SMEM algorithm for mixture models. Neural Computation 12(10), 2109–2128 (2000)
Zhang, Z., Chen, C., Sun, J., Chan, K.L.: EM Algorithm for learning Gaussian mixture models with split-and-merge operation. Pattern Recognition 36(9), 1973–1983 (2003)
Vlassis, N., Likas, A.: A Greedy EM Algorithm for Gaussian Mixture Learning. Neural Processing Letters 15, 77–87 (2002)
Srivastava, M.S.: Methods of Multivariate Statistics. Wiley-Interscience, New York (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, J., He, Q. (2005). A Dynamic Merge-or-Split Learning Algorithm on Gaussian Mixture for Automated Model Selection. In: Gallagher, M., Hogan, J.P., Maire, F. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2005. IDEAL 2005. Lecture Notes in Computer Science, vol 3578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11508069_27
Download citation
DOI: https://doi.org/10.1007/11508069_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26972-4
Online ISBN: 978-3-540-31693-0
eBook Packages: Computer ScienceComputer Science (R0)