Advertisement

Modified Relational Mountain Clustering Method

  • Kristina P. Sinaga
  • June-Nan Hsieh
  • Josephine B. M. Benjamin
  • Miin-Shen YangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10841)

Abstract

The relational mountain clustering method (RMCM) is a simple and effective algorithm that can be used to obtain cluster centers and partitions for a relational data set. However, the performance of RMCM heavily depends on the choice of parameters of relational mountain function. In order to solve this problem, we propose a modified RMCM (M-RMCM) by using the correlation self-comparison method to estimate the parameters of the modified relational mountain function, and then applied a validity index to estimate the number of clusters. The proposed M-RMCM can provide good cluster centers, partitions and the number of clusters for most relational data sets in which the results will not be sensitive to parameters. The simulations and comparisons show the superiority and effectiveness of the proposed M-RMCM.

Keywords

Clustering algorithms Mountain method Relational data Relational mountain method 

References

  1. 1.
    Bezdek, J.C.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum, New York (1981)CrossRefGoogle Scholar
  2. 2.
    Chiu, S.L.: Fuzzy model identification based on cluster estimation. J. Intel. Fuzzy Syst. 2, 267–278 (1994)Google Scholar
  3. 3.
    Dave, R.N., Sen, S.: Robust fuzzy clustering of relational data. IEEE Trans. Fuzzy Syst. 10, 713–727 (2002)CrossRefGoogle Scholar
  4. 4.
    Hathaway, R.J., Bezdek, J.C.: NERF c-means: non-euclidean relational fuzzy clustering. Pattern Recogn. 27, 429–437 (1994)CrossRefGoogle Scholar
  5. 5.
    Hathaway, R.J., Davenport, J.W., Bezdek, J.C.: Relational duals of the c-means clustering. Pattern Recogn. 22, 205–212 (1989)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hwang, C.M., Yang, M.S., Hung, W.L., Lee, M.G.: A similarity measure of intuitionistic fuzzy sets based on Sugeno integral with its application to pattern recognition. Inf. Sci. 189, 93–109 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium, vol. 1, pp. 281–297 (1967)Google Scholar
  8. 8.
    Pal, N.R., Chakraborty, D.: Mountain and subtractive clustering method: improvements and generalizations. Int. J. Intell. Syst. 15, 329–341 (2000)CrossRefGoogle Scholar
  9. 9.
    Pal, K., Pal, N.R., Keller, J.M., Bezdek, J.C.: Relational mountain (density) clustering method and web log analysis. Int. J. Intell. Syst. 20, 375–392 (2005)CrossRefGoogle Scholar
  10. 10.
    Velthuizen, B.P., Hall, L.O., Clarke, L.P., Silbiger, M.L.: An investigation of mountain method clustering for large data sets. Pattern Recogn. 30, 1121–1135 (1997)CrossRefGoogle Scholar
  11. 11.
    Wu, K.L., Yang, M.S., Hsieh, J.N.: Mountain c-regressions method. Pattern Recogn. 43, 86–98 (2010)CrossRefGoogle Scholar
  12. 12.
    Yager, R.R., Filev, D.P.: Approximate clustering via the mountain method. IEEE Trans Syst. Man Cybern. 24, 1279–1284 (1994)CrossRefGoogle Scholar
  13. 13.
    Yager, R.R., Filev, D.P.: Generation of fuzzy rules by mountain clustering. J. Intell. Fuzzy Syst. 2, 209–219 (1994)Google Scholar
  14. 14.
    Yang, M.S., Shih, H.M.: Cluster analysis based on fuzzy relations. Fuzzy Sets Syst. 120, 197–212 (2001)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yang, M.S., Wu, K.L.: A modified mountain clustering algorithm. Pattern Anal. Appl. 8, 125–138 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yang, M.S., Tian, Y.C.: Bias-correction fuzzy clustering algorithms. Inf. Sci. 309, 138–162 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Kristina P. Sinaga
    • 1
  • June-Nan Hsieh
    • 1
  • Josephine B. M. Benjamin
    • 1
  • Miin-Shen Yang
    • 1
    Email author
  1. 1.Department of Applied MathematicsChung Yuan Christian UniversityChung-LiTaiwan

Personalised recommendations