A Modified Fuzzy C-Means Algorithm for Natural Data Exploration

In Data mining, Fuzzy clustering algorithms have demonstrated advantage over crisp clustering algorithms in dealing with the challenges posed by large collections of vague and uncertain natural data. This paper reviews concept of fuzzy logic and fuzzy clustering. The classical fuzzy c-means algorithm is presented and its limitations are highlighted. Based on the study of the fuzzy c-means algorithm and its extensions, we propose a modification to the cmeans algorithm to overcome the limitations of it in calculating the new cluster centers and in finding the membership values with natural data. The efficiency of the new modified method is demonstrated on real data collected for Bhutan-s Gross National Happiness (GNH) program.

Authors:

• Binu Thomas
• Raju G.
• Sonam Wangmo

Keywords:

• Adaptive fuzzy clustering
• clustering
• fuzzy logic
• fuzzy clustering
• c-means.

References:

[1] Sankar K. Pal, P. Mitra, "Data Mining in Soft Computing Framework: A
Survey", IEEE transactions on neural networks, vol. 13, no. 1, January
2002.
[2] R. Cruse, C. Borgelt, "Fuzzy Data Analysis Challenges and
Perspective". Available: http://citeseer.ist.psu.edu/ kruse99fuzzy.html
[3] Lei Jiang and Wenhui Yang, "A Modified Fuzzy C-Means Algorithm
for Segmentation of Magnetic Resonance Images" Proc. VIIth Digital
Image Computing: Techniques and Applications, pp. 225-231, 10-12
Dec. 2003, Sydney.
[4] Frank Klawonn and Annette Keller, "Fuzzy Clustering Based on
Modified Distance Measures", Available:
http://citeseer.istpsu.edu/fuzzy_clustering_62
[5] W. H. Inmon, "The data warehouse and data mining", Commn. ACM,
vol. 39, pp. 49-50, 1996.
[6] U. Fayyad and R. Uthurusamy, "Data mining and knowledge discovery
in databases", Commn. ACM, vol. 39, pp. 24-27, 1996.
[7] Pavel Berkhin, "Survey of Clustering Data Mining Techniques",
Available: http://citeseer.ist.psu.edu/berkhin02survey.html
[8] Chau, M., Cheng, R., and Kao, B, "Uncertain Data Mining: A New
Research Direction", Available: www.business.hku.hk
/~mchau/papers/UncertainDataMining_WSA.pdf
[9] Keith C.C, C. Wai-Ho Au, B. Choi, "Mining Fuzzy Rules in A Donor
Database for Direct Marketing by A Charitable Organization", Proc of
First IEEE International Conference on Cognitive Informatics, pp: 239 -
246, 2002
[10] E. Cox, Fuzzy Modeling And Genetic Algorithms For Data Mining And
Exploration, Elsevier, 2005
[11] G. J Klir, T A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice
Hall,1988
[12] J Han, M Kamber, Data Mining Concepts and Techniques, Elsevier,
2003
[13] J. C. Bezdek, Fuzzy Mathematics in Pattern Classification, Ph.D. thesis,
Center for Applied Mathematics, Cornell University, Ithica, N.Y., 1973.
[14] Carl G. Looney, "A Fuzzy Clustering and Fuzzy Merging Algorithm"
Available: http://citeseer.ist.psu.edu/399498.html
[15] G. Raju, A. Singh, Th. Shanta Kumar, Binu Thomas, " Integration of
Fuzzy Logic in Data Mining: A comparative Case Study", Proc. of
International Conf. on Mathematics and Computer Science, Loyola
College, Chennai, 128-136, 2008
[16] Sullen Donnelly, "How Bhutan Can Develop and Measure GNH",
Available: www.bhutanstudies.org.bt/seminar/ 0402-gnh/GNH-papers-
1st_18-20.pdf