A Fitness-Based Adaptive Differential Evolution Approach to Data Clustering

  • G. R. Patra
  • T. Singha
  • S. S. Choudhury
  • S. Das
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 199)


Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy c-means (FCM) is one of the most popular clustering methods based on minimization of a criterion function as it works fast in most scenarios. However, it is sensitive to initialization and is easily trapped in local optima. In this work, a fuzzy clustering (FC) algorithm based on Differential Evolution (DE) is proposed. Here we use a DE with Fitness Based Adaptive Technique (FBADE) for the adaptation of DE parameters. 3 well-known data sets viz. Iris, Wine, Motorcycle and 2 synthetic datasets are used to demonstrate the effectiveness of the algorithm. The resulting algorithm is compared with conventional Fuzzy C-Means (FCM) algorithm, FCM with DE (FCM-DE), FCM with Self Adaptive DE (FCM-SADE).


Differential Evolution Fuzzy Clustering Global Optimization Evolutionary Algorithm 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bezdek, J.C.: Fuzzy Mathematics in Pattern Classification, Ph. D. thesis, Center for Applied Mathematics, Cornell University (1973)Google Scholar
  2. 2.
    Kuncheva, L.I., Bezdek, J.C.: Selection of cluster prototypes from data by a genetic algorithm. In: Proc. 5th European Congress on Intelligent Techniques and Soft Computing (EUFIT), Aachen, Germany, vol. 18, pp. 1683–1688 (1997)Google Scholar
  3. 3.
    Sun, L.X., Danzer, K.: Fuzzy cluster analysis by simulate annealing. Journal of Chemometrics 10, 325–342 (1996)CrossRefGoogle Scholar
  4. 4.
    Hall, L.O., Ozyurt, I.B., Bezdek, J.C.: Clustering with a genetically optimized approach. IEEE Transactions on Evolutionary Computation 3, 103–112 (1999)CrossRefGoogle Scholar
  5. 5.
    Al-Sultan, K.S., Fedjki, C.A.: A tabu search-based algorithm for the fuzzy clustering problem. Pattern Recognition 30, 2023–2030 (1997)CrossRefGoogle Scholar
  6. 6.
    Runkler, T.A., Katz, C.: Fuzzy Clustering by Particle Swarm Optimization. In: IEEE International Conference on Fuzzy Systems, pp. 601–608 (2006)Google Scholar
  7. 7.
    Das, S., Sil, S.: Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm. Information Sciences 180(8), 1237–1256 (2010)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Kao, Y., Lin, J., Huang, S.: Fuzzy Clustering by Differential Evolution. Intelligent Systems Design and Application (1), 246–250 (2008)Google Scholar
  9. 9.
    Storn, R., Price, K.: Differential evolution a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Zhang, J., Sanderson, A.C.: JADE: Adaptive Differential Evolution with Optional External Archive. IEEE Transactions on Evolutionary Computation 13(5), 945–958 (2009)CrossRefGoogle Scholar
  11. 11.
    Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation 10(6), 646–657 (2006)CrossRefGoogle Scholar
  12. 12.
    Das, S., Suganthan, P.N.: Differential Evolution: A Survey of the State-of-the-Art. IEEE Transactions on Evolutionary Computation 15(1), 4–31 (2011)CrossRefGoogle Scholar
  13. 13.
    Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential Evolution Algorithm with strategy adaptation for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation 13(2) (2009)Google Scholar
  14. 14.
    Salman, A., Engelbrecht, A.P., Omran, M.G.H.: Empirical analysis of self-adaptive differential evolution. European Journal of Operational Research 183, 785–804 (2007)CrossRefMATHGoogle Scholar
  15. 15.
    Ravi, V., Aggarwal, N., Chauhan, N.: Differential Evolution Based Fuzzy Clustering. In: Panigrahi, B.K., Das, S., Suganthan, P.N., Dash, S.S. (eds.) SEMCCO 2010. LNCS, vol. 6466, pp. 38–45. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Srinivas, M., Patnaik, L.M.: Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 24(4), 656–667 (1994)CrossRefGoogle Scholar
  17. 17.
    Blake, C.L., Merz, C.J.: UCI repository of machine learning databases. University of California, Department of Information and Computer Science, Irvine (1998),

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • G. R. Patra
    • 1
  • T. Singha
    • 1
  • S. S. Choudhury
    • 1
  • S. Das
    • 2
  1. 1.Department of Electronics and Telecommunication EngineeringJadavpur UniversityKolkataIndia
  2. 2.Engineering and Communication Sciences UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations