On Kernel Based Rough Intuitionistic Fuzzy C-means Algorithm and a Comparative Analysis

  • B. K. Tripathy
  • Anurag Tripathy
  • K. Govindarajulu
  • Rohan Bhargav
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 27)

Abstract

Clustering of real life data for analysis has gained popularity and imprecise methods or their hybrid approaches has attracted many researchers of late. Recently, rough intuitionistic fuzzy c-means algorithm was introduced and studied by Tripathy et al [3] and it was found to be superior to all other algorithms in this family. Kernel based counter part of these algorithms have been found to behave better than their corresponding Euclidean distance based algorithms. Very recently kernel based rough fuzzy algorithm was put forth by Bhargav et al [4]. A comparative analysis over standard datasets and images has established the superiority of this algorithm over its corresponding standard algorithm. In this paper we introduce the kernel based rough intuitionistic fuzzy c-means algorithm and show that it is superior to all the algorithms in the sequel; i.e. both normal and the kernel based algorithms. We establish it through experimental analysis by taking different type of inputs and using standard accuracy measures.

Keywords

clustering fuzzy sets rough sets intuitionistic fuzzy sets rough fuzzy sets rough intuitionistic fuzzy sets DB index D index 

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References

  1. 1.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20(1), 87–96 (1986)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers (1981)Google Scholar
  3. 3.
    Bhargav, R., Tripathy, B.K., Tripathy, A., Dhull, R., Verma, E., Swarnalatha, P.: Rough Intuitionistic Fuzzy C-Means Algorithm and a Comparative Analysis. In: ACM Conference, Compute 2013, pp. 978–971 (2013) 978-1-4503-2545-5/13/08Google Scholar
  4. 4.
    Bhargava, R., Tripathy, B.: Kernel Based Rough-Fuzzy C-Means. In: Maji, P., Ghosh, A., Murty, M.N., Ghosh, K., Pal, S.K. (eds.) PReMI 2013. LNCS, vol. 8251, pp. 148–155. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Chaira, T., Anand, S.: A Novel Intuitionistic Fuzzy Approach for Tumor/Hemorrhage Detection in Medical Images. Journal of Scientific and Industrial Research 70(6) (2011)Google Scholar
  6. 6.
    Davis, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-1(2), 224–227 (1979)CrossRefGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Rough fuzzy sets model. International Journal of General Systems 46(1), 191–208 (1990)CrossRefGoogle Scholar
  8. 8.
    Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, pp. 32–57 (1973)Google Scholar
  9. 9.
    Lingras, P., West, C.: Interval set clustering of web users with rough k-mean. Journal of Intelligent Information Systems 23(1), 5–16 (2004)CrossRefMATHGoogle Scholar
  10. 10.
    Macqueen, J.B.: Some Methods for classification and Analysis of Multivariate Observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297. University of California Press (1967)Google Scholar
  11. 11.
    Maji, P., Pal, S.K.: RFCM: A Hybrid Clustering Algorithm using rough and fuzzy set. Fundamenta Informaticae 80(4), 475–496 (2007)MATHMathSciNetGoogle Scholar
  12. 12.
    Mitra, S., Banka, H., Pedrycz, W.: Rough-Fuzzy Collaborative Clustering. IEEE Transactions on System, Man, and Cybernetics, Part B: Cybernetics 36(4), 795–805 (2006)CrossRefGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough sets. Int. Jour. of Computer and Information Sciences 11, 341–356 (1982)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Ruspini, E.H.: A new approach to clustering. Information and Control 15(1), 22–32 (1969)CrossRefMATHGoogle Scholar
  15. 15.
    Saleha, R., Haider, J.N., Danish, N.: Rough Intuitionistic Fuzzy Set. In: Proc. of 8th Int. Conf. on Fuzzy Theory and Technology (FT & T), Durham, North Carolina (USA), March 9-12 (2002)Google Scholar
  16. 16.
    Sugeno, M.: Fuzzy Measures and Fuzzy integrals-A survey. In: Gupta, M., Sardis, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 89–102 (1977)Google Scholar
  17. 17.
    Tripathy, B.K., Ghosh, A., Panda, G.K.: Kernel based K-means clustering using rough set. In: 2012 International IEEE Conference on Computer Communication and Informatics, ICCCI (2012)Google Scholar
  18. 18.
    Tripathy, B.K., Ghosh, A., Panda, G.K.: Adaptive K-Means Clustering to Handle Heterogeneous Data Using Basic Rough Set Theory. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds.) CCSIT 2012, Part I. LNICST, vol. 84, pp. 193–202. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8(11), 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Zhang, D., Chen, S.: Fuzzy Clustering Using Kernel Method. In: Proceedings of the International Conference on Control and Automation, Xiamen, China, pp. 123–127 (2002)Google Scholar
  21. 21.
    Zhou, T., Zhang, Y., Lu, H., Deng, F., Wang, F.: Rough Cluster Algorithm Based on Kernel Function. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 172–179. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • B. K. Tripathy
    • 1
  • Anurag Tripathy
    • 1
  • K. Govindarajulu
    • 2
  • Rohan Bhargav
    • 3
  1. 1.SCSEVIT UniversityVelloreIndia
  2. 2.Vignan Institute of Technology and ManagementOdishaIndia
  3. 3.SMR, Vinay GalaxyBangaloreIndia

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