Abstract
Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β - spread transformation was proposed for such cases, which modified a given set of relational data or a given a kernel Gram matrix such that the modified β value is common to all objects.
In this paper, we propose a quadratic programming-based object-wise β -spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.
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
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Hathaway, R.J., Davenport, J.W., Bezdek, J.C.: Relational Duals of the c-Means Clustering Algorithms. Pattern Recognition 22(2), 205–212 (1989)
Hathaway, R.J., Bezdek, J.C.: NERF C-means: Non-Euclidean Relational Fuzzy Clustering. Pattern Recognition 27, 429–437 (1994)
Miyamoto, S., Suizu, D.: Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines. J. Advanced Computational Intelligence and Intelligent Informatics 7(1), 25–30 (2003)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
Miyamoto, S., Kawasaki, Y., Sawazaki, K.: An Explicit Mapping for Kernel Data Analysis and Application to Text Analysis. In: Proc. IFSA-EUSFLAT 2009, pp. 618–623 (2009)
Miyamoto, S., Sawazaki, K.: An Explicit Mapping for Kernel Data Analysis and Application to c-Means Clustering. In: Proc. NOLTA 2009, pp. 556–559 (2009)
Kanzawa, Y., Endo, Y., Miyamoto, S.: Indefinite Kernel Fuzzy c-Means Clustering Algorithms. In: Torra, V., Narukawa, Y., Daumas, M. (eds.) MDAI 2010. LNCS (LNAI), vol. 6408, pp. 116–128. Springer, Heidelberg (2010)
Tamura, S., Higuchi, S., Tanaka, K.: Pattern Classification Based on Fuzzy Relations. IEEE Trans. Syst. Man Cybern. 1(1), 61–66 (1971)
Scannell, J.W., Blakemore, C., Young, M.P.: Analysis of Connectivity in the Cat Cerebral Cortex. J. Neuroscience 15(2), 1463–1483 (1995)
Ghosh, G., Strehl, A., Merugu, S.: A Consensus Framework for Integrating Distributed Clusterings under Limited Knowledge Sharing. In: Proc. NSF Workshop on Next Generation Data Mining, pp. 99–108 (2002)
Bezdek, J.C., Keller, J., Krishnapuram, R., Pal, N.-R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishing, Boston (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Kanzawa, Y. (2014). Relational Fuzzy c-Means and Kernel Fuzzy c-Means Using a Quadratic Programming-Based Object-Wise β-Spread Transformation. In: Huynh, V., Denoeux, T., Tran, D., Le, A., Pham, S. (eds) Knowledge and Systems Engineering. Advances in Intelligent Systems and Computing, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-02821-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-02821-7_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02820-0
Online ISBN: 978-3-319-02821-7
eBook Packages: EngineeringEngineering (R0)