Learning of Class Membership Values by Ellipsoidal Decision Regions
A novel method of learning complex fuzzy decision regions in the n-dimensional feature space is proposed. Through the fuzzy decision regions, a given pattern's class membership value of every class is determined instead of the conventional crisp class the pattern belongs to. The n-dimensional fuzzy decision region is approximated by union of hyperellipsoids. By explicitly parameterizing these hyperellipsoids, the decision regions are determined by estimating the parameters of each hyperellipsoid.Genetic Algorithm is applied to estimate the parameters of each region component. With the global optimization ability of GA, the learned decision region can be arbitrarily complex.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082867Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1089
 J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum Press, 1981.
 J. C. Bezdek, S. K. Pal, eds., Fuzzy Models for Pattern Recognition, New York: IEEE Press, 1992
 J. C. Bezdek, '' Computing with uncertainty, '' IEEE Commun. Mag., vol.30, Sept. 1992, pp. 24-37
 S. K. Pal, D. K. Dutta Majumber, Fuzzy Mathematical Approach to Pattern Recognition, New York: John Wiley, 1986.
 S. K. Pal, S. Mitra, Multilayer perception, fuzzy sets and classification, IEEE Trans. Neural Networks, vol. 3, May 1992, pp. 683-697
 W. Pedrycz, ''Fuzzy sets in pattern recognition: methodology and methods,'' Pattern Recognition, vol. 23, 1990, pp. 121-146
 W. Pedrycz, ''Fuzzy neural networks with reference neurons as pattern classifiers,'' IEEE Trans. Neural Networks, vol. 3, May 1992, pp.770-775
 S. T. Bow, Pattern Recognition Application to Large Dataset Problems,New York: Marcel Dekker, 1980.
 R. S.chalkoff, Pattern Recognition: Statistical, Structural and Neural Approaches, New York: John Wiley & Sons, 1992.
 J. C. Bezdek, J. M. Keller, R. Krishnapuram, N. R. Pal, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, Norwell, MA: Kluwer, 1999.
 R. J. Hathaway, J. C. Bezdek, Y. Hu, "Generalized fuzzy c-means clustering strategies using Lp norm distances," IEEE Trans. Fuzzy Syst., vol. 8, May 2000, pp. 576-582
 R. Krishnapuram, J. M. Keller, "A possibility approach to clustering," IEEE Trans. Fuzzy Syst., vol. 1, Mar. 1993, pp. 98-110
 L. Zhao, Y. Tsujimura, M. Gen, "Genetic algorithm for fuzzy clustering," Proceeding of IEEE International Conference on Evolutionary Computation," 1996, pp. 716-719.
 B. P. Buckles, F. E. Petry, D. Prabhu, R. George and R. Srikanth, " Fuzzy clustering with genetic search," Proceeding of IEEE World Congress on Coimputational Intelligence, 1994, pp. 46-50.
 R. P. Lippmann, "An introduction to computing with neural nets," IEEE ASSP Mag., April 1987, pp. 4-22.
 T. Khanna, Foundations of Neural Networks, MA: Addison-Wesley, 1990.
 H. I. Avi-Itzhak, J. A. Van Mieghem, L. Rub, "Multiple subclass pattern recognition: a maximum correlation approach," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, April 1995, pp. 418-431.
 Q. Zhu, Y. Cai, "A subclass model for nonlinear pattern classification," Pattern Recognition Lett., vol. 19, Feb. 1998, pp. 19-29.
 Q. Zhu, Y. Cai, L. Liu, "A multiple hyper-ellipsoidal subclass model for an evolutionary classifier," Pattern Recognition, vol. 34, March 2001, pp. 547-560.
 L. Yao, "Nonparametric learning of decision regions via the genetic algorithm," IEEE Trans. System, Man, and Cybernetics, vol. 26, Feb. 1996, pp. 313-321.