Fuzzy clustering can be helpful in finding natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in the data. The present paper introduces a new ε-insensitive Fuzzy C-Means (εFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED). The performance of the new clustering algorithm is experimentally compared with the Fuzzy C-Means (FCM) method using synthetic data with outliers and heavy-tailed, overlapped groups of the data.
@article{bwmeta1.element.bwnjournal-article-amcv11i4p993bwm, author = {\L \k eski, Jacek}, title = {An $\epsilon$-insensitive approach to fuzzy clustering}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {11}, year = {2001}, pages = {993-1007}, zbl = {1004.94043}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p993bwm} }
Łęski, Jacek. An ε-insensitive approach to fuzzy clustering. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 993-1007. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p993bwm/
[000] Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. — New York: Plenum Press. | Zbl 0503.68069
[001] Davé R.N. (1991): Characterization and detection of noise in clustering. — Pattern Recogn. Lett., Vol.12, No.11, pp.657–664.
[002] Davé R.N. and Krishnapuram R. (1997): Robust clustering methods: A unified view. — IEEE Trans. Fuzzy Syst., Vol.5, No.2, pp.270–293.
[003] Duda R.O. and Hart P.E. (1973): Pattern Classification and Scene Analysis. — New York: Wiley. | Zbl 0277.68056
[004] Dunn J.C. (1973): A fuzzy relative of the ISODATA process and its use in detecting compact well-separated cluster. — J. Cybern., Vol.3, No.3, pp.32–57. | Zbl 0291.68033
[005] Fukunaga K. (1990): Introduction to Statistical Pattern Recognition. — San Diego: Academic Press. | Zbl 0711.62052
[006] Hathaway R.J. and Bezdek J.C. (2000): Generalized fuzzy c-means clustering strategies using Lp norm distances. — IEEE Trans. Fuzzy Syst., Vol.8, No.5, pp.576–582.
[007] Huber P.J. (1981): Robust statistics. — New York: Wiley.
[008] Jajuga K. (1991): L1 -norm based fuzzy clustering. — Fuzzy Sets Syst., Vol.39, No.1, pp.43– 50. | Zbl 0714.62052
[009] Kersten P.R. (1999): Fuzzy order statistics and their application to fuzzy clustering. — IEEE Trans. Fuzzy Syst., Vol.7, No.6, pp.708–712.
[010] Krishnapuram R. and Keller J.M. (1993): A possibilistic approach to clustering. — IEEE Trans. Fuzzy Syst., Vol.1, No.1, pp.98–110.
[011] Pal N.R. and J.C. Bezdek (1995): On cluster validity for the fuzzy c-means model. — IEEE Trans. Fuzzy Syst., Vol.3, No.3, pp.370–379.
[012] Ruspini E.H. (1969): A new approach to clustering. — Inf. Contr., Vol.15, No.1, pp.22–32. | Zbl 0192.57101
[013] Tou J.T. and Gonzalez R.C. (1974): Pattern Recognition Principles. — London: Addison-Wesley. | Zbl 0299.68058
[014] Vapnik V. (1998): Statistical Learning Theory. — New York: Wiley. | Zbl 0935.62007
[015] Zadeh L.A. (1965): Fuzzy sets. — Inf. Contr., Vol.8, pp.338–353. | Zbl 0139.24606