A Method to Enhance the ‘Possibilistic C-Means with Repulsion’ Algorithm based on Cluster Validity Index (original) (raw)
Abstract
In this paper, we examine the performance of fuzzy clustering algorithms as the major technique in pattern recognition. Both possibilistic and probabilistic approaches are explored. While the Possibilistic C-Means (PCM) has been shown to be advantageous over Fuzzy C-Means (FCM) in noisy environments, it has been reported that the PCM has an undesirable tendency to produce coincident clusters. Recently, an extension of the PCM has been presented by Timm et al., by introducing a repulsion term. This approach combines the partitioning property of the FCM with the robust noise insensibility of the PCM. We illustrate the advantages of both the possibilistic and probabilistic families of algorithms with several examples and discuss the PCM with cluster repulsion. We provide a cluster valid-ity function evaluation algorithm to solve the problem of parameter optimization. The algorithm is especially useful for the unsupervised case, when labeled data is unavailable.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
- Jain, A. K. and Dubes, R. C. (1988), Algorithms for clustering data, Prentice Hall, New Jersey.
MATH Google Scholar - Zadeh, L. A. (1965), “Fuzzy Sets,” Information and Control, vol. 8, pp. 338–353.
Article MATH MathSciNet Google Scholar - Bezdek, J. C., (1982), Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York.
MATH Google Scholar - Krishnapuram, R. and Keller, J. (1993), “A possibilistic approach to clustering,” IEEE Trans. Fuzzy Systems, vol. 1, pp. 98–110.
Article Google Scholar - Timm, H., Borgelt, C. and Kruse, R. (2001), “Fuzzy cluster analysis with cluster repulsion,” In Proc. of the European Symp. on Intelligent Tech., Hybrid Syst. and their implementation on Smart Adapt. Syst., Tenerife, Spain.
Google Scholar - Krishnapuram, R. and Keller, J. (1996), “The Possibilistic C-Means algorithm: Insights and recommendations”, IEEE Trans. Fuzzy Systems, vol. 4, pp. 385–393.
Article Google Scholar - Barni, M., Cappellini V., and Mecocci, A. (1996), “Comments on ‘A Possibilistic Approach to Clustering’,” IEEE Trans. Fuzzy Systems, vol. 4, pp. 393–396.
Article Google Scholar - Bezdek, J. C. and Pal, N. R. (1998), “Some New Indexes of Cluster Validity,” IEEE Trans, on SMC, Part B, vol. 28, no.3, pp. 301–315.
Google Scholar - Dave, R. N. and Krishnapuram, R. (1997), “Robust clustering methods: a unified view,” IEEE Trans. Fuzzy Systems, vol. 5 no. 2, pp.270–293.
Article Google Scholar - Fisher, R. (1936), “The use of multiple measurements in taxonomic problems,” Annals of Eugenics, vol.7, no. 2, 179–188.
Google Scholar - Merz, C. J. and Murphy, P. M. (1996), UCI Repository of Machine Learning Databases, http://www.ics.uci.edu/\~mlearn/MLRepository.html, University of California, Department of Information and computer Science.
Google Scholar
Author information
Authors and Affiliations
- Department of Industrial Engineering and Management, Intelligent Systems Division, Ben-Gurion University of the Negev, Be’er-Sheeva, 84105, Israel
Juan Wachs, Oren Shapira & Helman Stern
Authors
- Juan Wachs
You can also search for this author inPubMed Google Scholar - Oren Shapira
You can also search for this author inPubMed Google Scholar - Helman Stern
You can also search for this author inPubMed Google Scholar
Editor information
Editors and Affiliations
- School of Computer Science and Engineering, Chung-Ang University, Heukseok-dong 221, 156-756, Seoul, Korea
Ajith Abraham - Department of Applied Mathematics Biometrics and Process Control, University Gent, Coupure Links 653, 9000 Gent, Belgium
Bernard de Baets - Dept. Automation Technologies, Fraunhofer IPK Berlin, Pascalstr. 8-9, 10587, Berlin, Germany
Mario Köppen - Dept. Automation Technologies, Fraunhofer IPK Berlin, Pascalstr. 8-9, 10587, Berlin, Germany
Bertram Nickolay
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Wachs, J., Shapira, O., Stern, H. (2006). A Method to Enhance the ‘Possibilistic C-Means with Repulsion’ Algorithm based on Cluster Validity Index. In: Abraham, A., de Baets, B., Köppen, M., Nickolay, B. (eds) Applied Soft Computing Technologies: The Challenge of Complexity. Advances in Soft Computing, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31662-0\_6
Download citation
- .RIS
- .ENW
- .BIB
- DOI: https://doi.org/10.1007/3-540-31662-0\_6
- Publisher Name: Springer, Berlin, Heidelberg
- Print ISBN: 978-3-540-31649-7
- Online ISBN: 978-3-540-31662-6
- eBook Packages: EngineeringEngineering (R0)