Abstract
Cluster analysis is a tool for data analysis. It is a method for finding clusters of a data set with most similarity in the same group and most dissimilarity between different groups. In general, there are two ways, mixture distributions and classification maximum likelihood method, to use probability models for cluster analysis. However, the corresponding probability distributions to most clustering algorithms such as fuzzy c-means, possibilistic c-means, mode-seeking methods, etc., have not yet been found. In this paper, we construct a multimodal probability distribution model and then present the relationships between many clustering algorithms and the proposed model via the maximum likelihood estimation.
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
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Bryant, P.G., Williamson, J.A.: Asymptotic behavior of classification maximum likelihood estimates. Biometrica 65, 273–438 (1978)
Celeux, G., Govaert, G.: Clustering criteria for discrete data and latent class models. Journal of classification 8, 157–176 (1991)
Fukunaga, K., Hostetler, L.D.: The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Trans. Information Theory 21, 32–40 (1975)
Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)
Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Systems 1, 98–110 (1993)
Lloyd, S.: Least squares quantization in pcm. Bell Telephone Laboratories Papers. Marray Hill (1957)
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proc. of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkley (1967)
McLachlan, G.J., Basford, K.E.: Mixture Models: Inference and Applications to clustering. Marcel Dekker, New York (1988)
Scott, A.J., Symons, M.J.: Clustering methods based on likelihood ration criteria. Biometrics 27, 387–397 (1971)
Bock, H.H.: Probability models and hypotheses testing in partitioning cluster analysis. In: Arabie, P., Hubert, L.J., Soete, G.D. (eds.) Clustering and Classification, pp. 377–453. World Scientific Publ., River Edge (1996)
Yang, M.S.: On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets and Systems 57, 365–375 (1993)
Yang, M.S., Wu, K.L.: A similarity-based robust clustering method. IEEE Trans. Pattern Anal. Machine Intelligence 26, 434–448 (2004)
Yu, J.: General C-means clustering model. IEEE Trans. Pattern Anal. Machine Intelligence 27(8), 1197–1211 (2005)
Windham, M.P.: Statistical models for cluster analysis. In: Diday, E., Lechevallier, Y. (eds.) Symbolic-numeric data analysis and learning, Commack, pp. 17–26. Nova Science, New York (1991)
Govaert, G.: Clustering model and metric with continuous data. In: Diday, E. (ed.) Learning symbolic and numeric knowledge, Commack, pp. 95–102. Nova Science, New York (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yu, J., Yang, MS., Hao, P. (2009). A Novel Multimodal Probability Model for Cluster Analysis. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_50
Download citation
DOI: https://doi.org/10.1007/978-3-642-02962-2_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02961-5
Online ISBN: 978-3-642-02962-2
eBook Packages: Computer ScienceComputer Science (R0)