Comparative Analysis of Fuzzy C Means and Fuzzy C Means++

Manika garg

doi:10.65301/iitm.2018.9.1.1074

Articles Volume 9 Issue 1 January-June 2018

DOI 10.65301/iitm.2018.9.1.1074

Comparative Analysis of Fuzzy C Means and Fuzzy C Means++

Authors

MA

Manika garg

Assistant Professor, Department of Computer Science, IITM Janakpuri, New Delhi, India.

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Published 2018-01-30

Pages 52-55

Abstract

Cluster analysis is one of the most useful means for identifying relations and patterns in the area of data mining. It can be defined as partitioning of large volumes of data into various clusters that share some property or attribute. The most common clustering algorithm is k means. The more improved version of k means that incorporates fuzzy feature is fuzzy c means. To overcome some of the limitations of fuzzy c means, fuzzy c means ++ was introduced which was based on effective seeding mechanism of k means++ algorithm. The latter algorithm showed remarkable results but with some more limitations of its own. In this paper, we discuss both the methods and their algorithms in detail. We discuss the advantages and limitations of each in various scenarios.

Keywords

Fuzzy C Data Mining K means++

References

1. Adrian Stetco⇑, Xiao-Jun Zeng, John Keane.Fuzzy C-means++: Fuzzy C-means with effective seeding initialization
2. Arthur, D., Arthur, D., Vassilvitskii, S., & Vassilvitskii, S..k-Means++:, (2007)The advantages of careful seeding. In Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, Vol. 8, pp. 1027–1035.
3. Asuncion, A., & Newman, D. J.,. (2007) UCI machine learning repository.University of California Irvine School of Information.
4. Celebi, M. E., Kingravi, H. A., & Vela, P. A.,.A , (2013)comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Systems with Applications, 40, 200–210. http://dx.doi.org/10.1016/j.eswa.2012.07.021.
5. Doring, C., Lesot, M.-J., & Kruse, R.,. , (2006) Data analysis with fuzzy clustering methods. Computational Statistics & Data Analysis, 51, 192–214.
6. Fukuyama, Y., & Sugeno, M., (1989) A new method of choosing the number of clusters for the fuzzy c- means method, Proc. 5th Fuzzy Syst. Symp., pp. 247–250.
7. Gath, I., &Geva, A. B., (1989) Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 773–780.
8. Kolen, J. F., & Hutcheson, (2002)T.,.Reducing the time complexity of the fuzzy C means algorithm. IEEE Transactions on Fuzzy Systems, 10, 263–267.
9. Mac Queen, J.B., (1967) Some methods for classification and analysis of multivariate.
10. observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 281–297.
11. Meyer, D.,( 2014), Dimitriadou, E., Hornik, K., Weingessel, A., &Leisch, F..Miscfunctions of the department of statistics,.
12. Pal, N. R., &Bezdek, J. C., (1995)On cluster validity for the fuzzy C-means model. IEEE Transactions on Fuzzy Systems, Vol. 3, pp. 370 379.
13. Peizhuang, W., (1983) Pattern recognition with fuzzy objective function algorithms.
14. R Development Core Team,: (2013),A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.URL http://www.R-project.org/.
15. Wang, X., Wang, Y., & Wang, L., (2004)Improving fuzzy C-means clustering based on feature-weight Recognition Letters, learning. 25, Pattern 1123 1132.http://dx.doi.org/10.1016/j.patrec.2004.03.0 08.
16. Xie, X. L., &Beni, G.,(1991).A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841–847. http://dx.doi.org/ 10.1109/34.85677.
17. Yang, Q., Zhang, D., &Tian, F., (2010).An initialization method for fuzzy C means algorithm using subtractive clustering .In 2010 third international conference on intelligent networks and intelligent systems pp. 393–396.
18. Zou, K., Wang, Z., & Hu, M, (2008) An new initialization method for fuzzy C-means algorithm. Fuzzy Optimization and Decision Making, Vol. 7, pp. 409–416.

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Manika garg . (2018). Comparative Analysis of Fuzzy C Means and Fuzzy C Means++. IITM Journal of Management and IT, 9(1), 52-55.

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[1] 1. Adrian Stetco⇑, Xiao-Jun Zeng, John Keane.Fuzzy C-means++: Fuzzy C-means with effective seeding initialization

[2] 2. Arthur, D., Arthur, D., Vassilvitskii, S., & Vassilvitskii, S..k-Means++:, (2007)The advantages of careful seeding. In Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, Vol. 8, pp. 1027–1035.

[3] 3. Asuncion, A., & Newman, D. J.,. (2007) UCI machine learning repository.University of California Irvine School of Information.

[4] 4. Celebi, M. E., Kingravi, H. A., & Vela, P. A.,.A , (2013)comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Systems with Applications, 40, 200–210. http://dx.doi.org/10.1016/j.eswa.2012.07.021.

[5] 5. Doring, C., Lesot, M.-J., & Kruse, R.,. , (2006) Data analysis with fuzzy clustering methods. Computational Statistics & Data Analysis, 51, 192–214.

[6] 6. Fukuyama, Y., & Sugeno, M., (1989) A new method of choosing the number of clusters for the fuzzy c- means method, Proc. 5th Fuzzy Syst. Symp., pp. 247–250.

[7] 7. Gath, I., &Geva, A. B., (1989) Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 773–780.

[8] 8. Kolen, J. F., & Hutcheson, (2002)T.,.Reducing the time complexity of the fuzzy C means algorithm. IEEE Transactions on Fuzzy Systems, 10, 263–267.

[9] 9. Mac Queen, J.B., (1967) Some methods for classification and analysis of multivariate.

[10] 10. observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 281–297.

[11] 11. Meyer, D.,( 2014), Dimitriadou, E., Hornik, K., Weingessel, A., &Leisch, F..Miscfunctions of the department of statistics,.

[12] 12. Pal, N. R., &Bezdek, J. C., (1995)On cluster validity for the fuzzy C-means model. IEEE Transactions on Fuzzy Systems, Vol. 3, pp. 370 379.

[13] 13. Peizhuang, W., (1983) Pattern recognition with fuzzy objective function algorithms.

[14] 14. R Development Core Team,: (2013),A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.URL http://www.R-project.org/.

[15] 15. Wang, X., Wang, Y., & Wang, L., (2004)Improving fuzzy C-means clustering based on feature-weight Recognition Letters, learning. 25, Pattern 1123 1132.http://dx.doi.org/10.1016/j.patrec.2004.03.0 08.

[16] 16. Xie, X. L., &Beni, G.,(1991).A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841–847. http://dx.doi.org/ 10.1109/34.85677.

[17] 17. Yang, Q., Zhang, D., &Tian, F., (2010).An initialization method for fuzzy C means algorithm using subtractive clustering .In 2010 third international conference on intelligent networks and intelligent systems pp. 393–396.

[18] 18. Zou, K., Wang, Z., & Hu, M, (2008) An new initialization method for fuzzy C-means algorithm. Fuzzy Optimization and Decision Making, Vol. 7, pp. 409–416.