Abstract
This paper presents an extension to the genetic fuzzy clustering algorithm proposed by the authors. The original algorithm, which combines the powerful search technique of genetic algorithms with the fuzzy c-means (FCM) algorithm, is extended such that the FCM algorithm was totally embedded in the genetic operators design. Two objective functions are applied as fitness functions: the performance index of a P fuzzy c-partition J m (P), used on the FCM algorithm, and the partition coefficient F C (P), a function commonly used as a measure of cluster validity.
The fuzzy c-means and the new proposal for the genetic fuzzy clustering algorithm were compared on generating multiple prototypes. The experimental results show that the use of genetic search improves the quality of the clustering solutions and that the partition coefficient F c (P) is a better measure for clustering than the performance index J m (P).
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
E. Anderson. The irises of the gaspe peninsula. Bull. Amer. IRIS Soc., 59:2–5, 1935.
J. C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, 1981.
J. C. Bezdek and R. J. Hathaway. Optimization of fuzzy clustering criteria using genetic algorithms. In First IEEE Conference on Evolutionary Computation (EC-IEEE'94), pages 46–50, Orlando, June 1994.
J. C. Bezdek and T. R. Reichherzer. Multiple prototype classifier design. In NATO-Advanced Study Institute on Soft Computing and its Applications, pages 1–24, Manavgat, Antalya, Turkey, Aug. 1996.
J. N. Bhuyan, V. Raghavan, and V. Elayavalli. Genetic algorithm for clustering with an ordered representation. In K. B. Richard and B. Lashon, editors, Fourth International Conference on Genetic Algorithms), pages 408–415, University of California, San Diego, 1991. Morgan Kaufmann Publishers, San Mateo, CA.
L. Bobrowski and J. C. Bezdek. c-means clustering with 11 and 1 norms. IEEE Trans, on Syst. Man and Cyb. Journal, 21(3):545–553, 1991.
B.P.Buckles, F. Petry, D. Prabhu, R. George, and R. Srikanth. Fuzzy clustering with genetic search. In First IEEE Conference on Evolutionary Computation (EC-IEEE'94), pages 46–50, Orlando, June 1994.
L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York, 1991.
D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989.
J. H. Holland. Adaptation in Natural and Artificial Systems. MIT Press, 1993.
A. Hunter. SUGAL Programming Manual. University of Sunderland, England, 1995.
K. Krishna and M. N. Murty. Genetic k-mean algorithm. Communicated to IEEE Transactions on SMC, 1995.
J. Liu and W. Xie. A genetics-based approach to fuzzy clustering. In W. V. Oz and M. Yannakakis, editors, Fourth IEEE International Conference on Fuzzy Systems (FUZZY-IEEE '95), pages 2233–2240, Yokohama, Mar. 1995.
C. J. Merz and O. Murphy. Uci repository of machine learning databases, 1996.
S. Nascimento and F. Moura-Pires. A genetic fuzzy c-means algoritm. In Information Processing and Managment of Uncertainty in Knowledge-Based Systems (IPMU'96), number 2, pages 745–750, Granada Spain, July 1996.
B. Yuan, G. J. Klir, and J. F. Swan-Stone. Evolutionary fuzzy c-means clustering algorithm. In Fourth IEEE International Conference on Fuzzy Systems (FUZZY-IEEE '95), pages 2221–2226, Yokohama, Mar. 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this paper
Cite this paper
Nascimento, S., Moura-Pires, F. (1997). A genetic approach to fuzzy clustering with a validity measure fitness function. In: Liu, X., Cohen, P., Berthold, M. (eds) Advances in Intelligent Data Analysis Reasoning about Data. IDA 1997. Lecture Notes in Computer Science, vol 1280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052851
Download citation
DOI: https://doi.org/10.1007/BFb0052851
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63346-4
Online ISBN: 978-3-540-69520-2
eBook Packages: Springer Book Archive