Abstract
Data clustering has found its usefulness in various fields. Algorithms are mostly developed using euclidean distance. But it has several drawbacks which maybe rectified by using kernel distance formula. In this paper, we propose a kernel based rough-fuzzy C-Means (KRFCM) algorithm and use modified version of the performance indexes (DB and D) obtained by replacing the distance function with kernel function. We provide a comparative analysis of RFCM with KRFCM by computing their DB and D index values. The analysis is based upon both numerical as well as image datasets. The results establish that the proposed algotihtm outperforms the existing one.
Chapter PDF
Similar content being viewed by others
References
MacQueen, J.B.: Some Methods for classification and Analysis of Multivariate Observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297. University of California Press (1967)
Ruspini, E.H.: A new approach to clustering. Information and Control 15(1), 22–32 (1969)
Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, 32–57 (1973)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers (1981)
Lingras, P., West, J.: Interval set clustering of web users with rough k-means. Journal of Intelligent Information Systems 23(1), 5–16 (2004)
Zhou, T., Zhang, Y., Lu, H., Deng, F., Wang, F.: Rough Cluster Algorithm Based on Kernel Function. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 172–179. Springer, Heidelberg (2008)
Tripathy, B.K., Ghosh, A., Panda, G.K.: Kernel based K-means clustering using rough set. In: IEEE 2012 International Conference on Computer Communication and Informatics, ICCCI (2012)
Tripathy, B.K., Ghosh, A., Panda, G.K.: Adaptive K-Means Clustering to Handle Heterogeneous Data Using Basic Rough Set Theory. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds.) CCSIT 2012, Part I. LNICST, vol. 84, pp. 193–202. Springer, Heidelberg (2012)
Yang, M.S., Tsai, H.S.: A Gaussian kernel-based fuzzy c-means algorithm with a spatial bias correction. Pattern Recognition Letters 29(12), 1713–1725 (2008)
Zhang, D.Q., Chen, S.C.: Kernel Based Fuzzy and Possibilistic C-means Clustering. In: Proc. the International Conference Artificial Neural Network, Turkey, pp. 122–125 (2003)
Dubois, D., Prade, H.: Rough Fuzzy sets model. International Journal of General Systems 46(1), 191–208 (1990)
Maji, P., Pal, S.K.: RFCM: A Hybrid Clustering Algorithm using rough and fuzzy sets. Fundamenta Informaticae 80(4), 475–496 (2007)
Phillips, J.M., Venkatasubramanian, S.: A gentle introduction to the kernel distance, arXiv preprint arXiv:1103.1625 (2011)
Mitra, S., Banka, H., Pedrycz, W.: Rough-Fuzzy Collaborative Clustering. IEEE Transactions on System, Man, and Cybernetics, Part B: Cybernetics 36(4), 795–805 (2006)
Bezdek, J.C., Pal, N.R.: Some new indexes for cluster validity. IEEE Transaction on System, Man and Cybernetics, Part B: Cybernetics 28, 301–315 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bhargava, R., Tripathy, B. (2013). Kernel Based Rough-Fuzzy C-Means. In: Maji, P., Ghosh, A., Murty, M.N., Ghosh, K., Pal, S.K. (eds) Pattern Recognition and Machine Intelligence. PReMI 2013. Lecture Notes in Computer Science, vol 8251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45062-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-45062-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45061-7
Online ISBN: 978-3-642-45062-4
eBook Packages: Computer ScienceComputer Science (R0)