Abstract
This paper describes an extension of the standard k-modes method (SKM) to cluster categorical objects under uncertain framework. Our proposed approach combines the SKM with possibility theory in order to obtain the so-called k-modes method based on possibilistic membership (KM-PM). This latter makes it possible to deal with uncertainty in the assignment of the objects to different clusters using possibilistic membership degrees. Besides, it facilitates the detection of boundary objects by taking into account of the similarity of each object to all clusters. The KM-PM also overcomes the numeric limitation of the existing possibilistic clustering approaches (i.e. the dealing only with numeric values) and easily handles the extreme cases of knowledge, namely the complete knowledge and the total ignorance. Simulations on real-world databases show that the proposed KM-PM algorithm gives more meaningful results.
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
Ammar, A., Elouedi, Z.: A New Possibilistic Clustering Method: The Possibilistic K-Modes. In: Pirrone, R., Sorbello, F. (eds.) AI*IA 2011. LNCS (LNAI), vol. 6934, pp. 413–419. Springer, Heidelberg (2011)
Anderberg, M.R.: Cluster Analysis for Applications. Probability and Mathematical Statistics. Academic Press, New York (1973)
Ben Hariz, S., Elouedi, Z., Mellouli, K.: Selection Initial modes for Belief K-modes Method. International Journal of Applied Science, Engineering and Technology 4, 233–242 (2007)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers (1981)
Dubois, D., Prade, H.: Possibility theory: An approach to computerized processing of uncertainty. Plenium Press, New York (1988)
Dubois, D., Prade, H.: Possibility theory and data fusion in poorly informed environments. Control Engineering Practice 25, 811–823 (1994)
Dubois, D., Prade, H.: Possibility theory: Qualitative and quantitative aspects. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. I, pp. 169–226. Kluwer Academic Publishers, Netherlands (1998)
Huang, Z.: Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Mining Knowl. Discov. 2, 283–304 (1998)
Huang, Z., Ng, M.K.: A Fuzzy k-Modes Algorithm for Clustering Categorical Data. IEEE Transactions on Fuzzy Systems 7, 446–452 (1999)
Huang, Z., Ng, M.K.: A note on k-modes clustering. Journal of Classification 20, 257–261 (2003)
Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy System 1, 98–110 (1993)
MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: The 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
Masson, M.H., Denoeux, T.: ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition 41, 1384–1397 (2008)
Murphy, M.P., Aha, D.W.: Uci repository databases (1996), http://www.ics.uci.edu/mlearn
Pal, N.R., Pal, K., Keller, J.M., Bezdek, J.C.: A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy Systems, 517–530 (2005)
Yang, M.S., Wu, K.L.: Unsupervised possibilistic clustering. Pattern Recognition 39, 5–21 (2006)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)
Zhang, J.S., Leung, Y.W.: Improved possibilistic c-means clustering algorithms. IEEE Transactions on Fuzzy Systems 23 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ammar, A., Elouedi, Z., Lingras, P. (2012). K-Modes Clustering Using Possibilistic Membership. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_61
Download citation
DOI: https://doi.org/10.1007/978-3-642-31718-7_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31717-0
Online ISBN: 978-3-642-31718-7
eBook Packages: Computer ScienceComputer Science (R0)