JACIII Vol.11 No.1 pp. 35-39
doi: 10.20965/jaciii.2007.p0035


Quantification of Multivariate Categorical Data Considering Typicality of Item

Chi-Hyon Oh*, Katsuhiro Honda**, and Hidetomo Ichihashi**

*Faculty of Liberal Arts and Sciences, Osaka University of Economics and Law, 6-10 Gakuonji, Yao, Osaka 581-8511, Japan

**Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

October 31, 2005
March 31, 2006
January 20, 2007
fuzzy clustering, homogeneity analysis, multivariate categorical data

We propose simultaneously applying homogeneity analysis and fuzzy clustering that simultaneously partitions individuals and items in categorical multivariate datasets. This objective function includes two types of memberships. One is conventional membership representing the degree of membership of each individual in each cluster. The other is an additional parameter that represents typicality of item. A numerical experiment demonstrates that our proposal is useful in quantifying categorical data, taking the typicality of each item into account.

Cite this article as:
Chi-Hyon Oh, Katsuhiro Honda, and Hidetomo Ichihashi, “Quantification of Multivariate Categorical Data Considering Typicality of Item,” J. Adv. Comput. Intell. Intell. Inform., Vol.11, No.1, pp. 35-39, 2007.
Data files:
  1. [1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
  2. [2] J. C. Bezdek, C. Coray, R. Gunderson, and J. Watson, “Detection and characterization of cluster substructure 2. fuzzy c-varieties and convex combinations thereof,” SIAM J. Appl. Math., Vol.40, No.2, pp. 358-372, 1981.
  3. [3] F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, “Fuzzy Cluster Analysis,” John Wiley & Sons, 1999.
  4. [4] K. Honda, N. Sugiura, H. Ichihashi, and S. Araki, “Collaborative filtering using principal component analysis and fuzzy clustering,” Web Intelligence: Research and Development, Lecture Notes in Artificial Intelligence 2198, Springer, pp. 394-402, 2001.
  5. [5] K. Honda and H. Ichihashi, “Linear fuzzy clustering techniques with missing values and their application to local principal component analysis,” IEEE Trans. on Fuzzy Systems, Vol.12, No.2, pp. 183-193, 2004.
  6. [6] A. Gifi, “Nonlinear Multivariate Analysis,” Wiley, 1990.
  7. [7] J. Bond and G. Michailidis, “Homogeneity analysis in Lisp-Stat,” J. Statistical Software, Vol.1, Issue 2, 1996.
  8. [8] K. Honda, Y. Nakamura, and H. Ichihashi, “Simultaneous application of fuzzy clustering and quantification with incomplete categorical data,” J. Advanced Computational Intelligence and Intelligent Informatics, Vol.8, No.4, pp. 183-193, 2004.
  9. [9] S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” Proc. the 7th International Fuzzy Systems Association World Congress, Vol.2, pp. 86-92, 1997.
  10. [10] T. Tsuchiya, “A quantification method for classification of variables,” Japanese J. Behaviormetrics, Vol.22, No.2, pp. 95-109, 1995 (in Japanese).
  11. [11] N. R. Pal, K. Pal, and J. C. Bezdek, “A mixed c-means clustering model,” Proc. of 1997 IEEE Int. Conf. on Fuzzy Systems, pp. 11-21, 1997.
  12. [12] N. R. Pal, K. Pal, J. M. Keller, and J. C. Bezdek, “A possibilistic fuzzy c-means clustering algorithm,” IEEE Transactions on Fuzzy Systems, Vol.13, No.4, pp. 508-516, 2005.
  13. [13] R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Transactions on Fuzzy Systems, Vol.1, pp. 98-110, 1993.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Mar. 05, 2021