Abstract
This paper proposes an unsupervised algorithm for learning a finite Dirichlet mixture model. An important part of the unsupervised learning problem is determining the number of clusters which best describe the data. We consider here the application of the Minimum Message length (MML) principle to determine the number of clusters. The Model is compared with results obtained by other selection criteria (AIC, MDL, MMDL, PC and a Bayesian method). The proposed method is validated by synthetic data and summarization of texture image database.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jain, A.K., Duin, R.P.W., Mao, J.: Statistical Pattern Recognition: A Review. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(1), 4–37 (2000)
McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley, New York (2000)
Wallace, C.S., Boulton, D.M.: An Information Measure for Classification. Computer Journal 11(2), 195–209 (1968)
Akaike, H.: A New Look at the Statistical Model Identification. IEEE Transaction on Automatic Control AC-19(6), 716–723 (1974)
Rissanen, J.: Modeling by Shortest Data Description. Automatica 14, 465–471 (1987)
Frigueiredo, M.A.T., Leitao, J.M.N., Jain, A.K.: On Fitting Mixture Models. In: Hancock, E.R., Pelillo, M. (eds.) EMMCVPR 1999. LNCS, vol. 1654, pp. 54–69. Springer, Heidelberg (1999)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Roberts, S.J., Husmeier, D., Rezek, I., Penny, W.: Bayesian Approaches to Gaussian Mixture Modeling. IEEE Transactions on PAMI 20(11), 1133–1142 (1998)
Baxter, R.A.: Minimum Message Length Inference: Theory and Applications. Ph.D. Thesis, Monash University, Clayton, Victoria, Australia (1996)
Ziou, D., Bouguila, N.: Unsupervised Learning of a Gamma Finite Mixture Using MML: Application to SAR Image Analysis. In: 17th International Conference on Pattern Recognition, ICPR 2004, pp. 280–283 (2004)
Bouguila, N., Ziou, D., Vaillancourt, J.: Unsupervised Learning of a Finite Mixture Model Based on the Dirichlet Distribution and its Application. IEEE Transactions on Image Processing 13(11), 1533–1543 (2004)
Bouguila, N., Ziou, D., Vaillancourt, J.: Novel Mixtures Based on the Dirichlet Distribution: Application to Data and Image Classification. In: Perner, P., Rosenfeld, A. (eds.) MLDM 2003. LNCS, vol. 2734, pp. 172–181. Springer, Heidelberg (2003)
Dowe, D.L., Farr, G.: An Introduction to MML Inference. Technical report, Department of Computer Science, Monash University (1997)
Graybill, F.A.: Matrices with applications in Statistics. Wadsworth, California (1983)
Baxter, R.A., Olivier, J.J.: Finding Overlapping Components with MML. Statistics and Computing 10(1), 5–16 (2000)
Haralick, R.M., Shanmugan, K., Dinstein, I.: Texture features for image classification. IEEE Transactions on Systems, Man and Cybernetics 8, 610–621 (1973)
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
Bouguila, N., Ziou, D. (2005). MML-Based Approach for Finite Dirichlet Mixture Estimation and Selection. In: Perner, P., Imiya, A. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2005. Lecture Notes in Computer Science(), vol 3587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11510888_5
Download citation
DOI: https://doi.org/10.1007/11510888_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26923-6
Online ISBN: 978-3-540-31891-0
eBook Packages: Computer ScienceComputer Science (R0)