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A Particle Swarm Clustering Algorithm with Fuzzy Weighted Step Sizes

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Intelligent Data Engineering and Automated Learning – IDEAL 2015 (IDEAL 2015)

Abstract

This paper proposes a modification in the Fuzzy Particle Swarm Clustering (FPSC) algorithm such that membership degrees are used to weight the step size in the direction of the local and global best particles, and in its movement in the direction of the input data at every iteration. This results in the so-called Membership Weighted Fuzzy Particle Swarm Clustering (MWFPSC). The modified algorithm was applied to six benchmark datasets from the literature and its results compared to that of the standard FPSC and FCM algorithms. By introducing these modifications it could be observed a gain in accuracy, representativeness of the clusters found and the final Xie-Beni index, at the expense of a slight increase in the practical computational time of the algorithm.

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Notes

  1. 1.

    http://archive.ics.uci.edu/ml/datasets.html.

References

  1. Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)

    Article  Google Scholar 

  2. Carmichael, J.W., George, J.A., Julius, R.S.: Finding natural clusters. Syst. Zool. 17(2), 144–150 (1968)

    Article  Google Scholar 

  3. Nagy, G.: State of the art in pattern recognition. In: IEEE, vol. 56, pp. 836–863 (1968)

    Google Scholar 

  4. de Oliveira, J.V., Pedrycz, W.: Advances in Fuzzy Clustering and Applications. Wiley, New York (2007)

    Book  Google Scholar 

  5. Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)

    Book  MATH  Google Scholar 

  6. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)

    Google Scholar 

  7. Cui, X., Potok, T., Palathingal, P.: Document clustering using particle swarm optimization. In: Swarm Intelligence Symposium, SIS 2005, pp. 185–191. IEEE (2005)

    Google Scholar 

  8. Mehdizadeh, E., Tavakkoli-Moghaddam, R.: A hybrid fuzzy clustering PSO algorithm for a clustering supplier problem. In: International Conference on Industrial Engineering and Engineering Management, pp. 1466–1470 (2007)

    Google Scholar 

  9. de Castro, L.N., Von Zuben, F.J.: aiNet: an artificial immune network for data analysis, chapter XII. In: Abbass, H.A., Saker, R.A., Newton, C.S. (eds.) Data Mining: A Heuristic Approach, pp. 231–259. Idea Group Publishing, Hershey (2001)

    Google Scholar 

  10. da Cruz, D.P.F., Maia, R.D., Szabo, A., de Castro, L.N.: A bee-inspired algorithm for optimal data clustering. In: IEEE Congress on Evolutionary Computation (CEC), pp. 3140–3147 (2013)

    Google Scholar 

  11. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948, Perth, Australia (1995)

    Google Scholar 

  12. van der Merwe, D.W., Engelbrecht, A.P.: Data clustering using particle swarm optimization. In: IEEE Congress on Evolutionary Computation, pp. 215–220 (2003)

    Google Scholar 

  13. Omran, M.G.H., Salman, A., Engelbrecht, A.P.: Dynamic clustering using particle swarm optimization with application in image segmentation. Pat. Anal. Appl. 8, 332–344 (2006)

    Article  MathSciNet  Google Scholar 

  14. Cohen, S.C.M., de Castro, L.N.: Data clustering with particle swarms. In: IEEE World Congress on Computational Intelligence, pp. 6256–6262 (2006)

    Google Scholar 

  15. Szabo, A., de Castro, L.N., Delgado, M.R.: The proposal of a fuzzy clustering algorithm based on particle swarm. In: IEEE 3rd NABIC, pp. 459–465 (2011)

    Google Scholar 

  16. Pang, W., Wang, K-P, Zhou, C-G, Dong, L-J: Fuzzy discrete particle swarm optimization for solving traveling salesman problem. In: 4th International Conference on Computer and Information Technology, pp. 796–800 (2004)

    Google Scholar 

  17. Runkler, T.A., Katz, C.: Fuzzy Clustering by Particle Swarm Optimization. In: IEEE International Conference on Fuzzy Systems, pp. 601–608 (2006)

    Google Scholar 

  18. Izakian, H., Abraham, A.: Fuzzy C-means and fuzzy swarm for fuzzy clustering problem. Expert Syst. Appl. 38, 1835–1838 (2011)

    Article  Google Scholar 

  19. Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 8, 841–847 (1991)

    Article  Google Scholar 

  20. Massey, F.J.: The Kolmogorov-Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46(253), 68–78 (1951)

    Article  MATH  Google Scholar 

  21. Derrac, J., Garcia, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1, 3–18 (2011)

    Article  Google Scholar 

  22. Cox, E.: Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration. Morgan Kaufmann, San Francisco (2005)

    MATH  Google Scholar 

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Acknowledgment

The authors thank FAPESP, CNPq, and CAPES for their financial support.

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Correspondence to Alexandre Szabo .

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Szabo, A., Delgado, M.R., de Castro, L.N. (2015). A Particle Swarm Clustering Algorithm with Fuzzy Weighted Step Sizes. In: Jackowski, K., Burduk, R., Walkowiak, K., Wozniak, M., Yin, H. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2015. IDEAL 2015. Lecture Notes in Computer Science(), vol 9375. Springer, Cham. https://doi.org/10.1007/978-3-319-24834-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-24834-9_11

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  • Online ISBN: 978-3-319-24834-9

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