This paper introduces a new classifier design method that is based on a modification of the classical Ho-Kashyap procedure. The proposed method uses the absolute error, rather than the squared error, to design a linear classifier. Additionally, easy control of the generalization ability and robustness to outliers are obtained. Next, an extension to a nonlinear classifier by the mixture-of-experts technique is presented. Each expert is represented by a fuzzy if-then rule in the Takagi-Sugeno-Kang form. Finally, examples are given to demonstrate the validity of the introduced method.
@article{bwmeta1.element.bwnjournal-article-amcv13i2p215bwm,
author = {\L \k eski, Jacek},
title = {A fuzzy if-then rule-based nonlinear classifier},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {13},
year = {2003},
pages = {215-223},
zbl = {1048.93503},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p215bwm}
}
Łęski, Jacek. A fuzzy if-then rule-based nonlinear classifier. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 215-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p215bwm/
[000] Abe S. and Lan M.-S. (1995): A method for fuzzy rules extraction directly from numerical data and its application to pattern classification. - IEEE Trans. Fuzzy Syst., Vol. 3, No. 1, pp. 18-28.
[001] Bellman R., Kalaba K. and Zadeh L.A. (1966): Abstraction and pattern classification. - J. Math. Anal. Appl., Vol. 13, No. 1, pp. 1-7. | Zbl 0134.15305
[002] Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press. | Zbl 0503.68069
[003] Bezdek J.C. and Pal S.K. (Eds.) (1992): Fuzzy Models for Pattern Recognition. - New York: IEEE Press.
[004] Bezdek J.C., Reichherzer T.R., Lim G.S. and Attikiouzel Y.(1998): Multiple-prototype classifier design. - IEEE Trans.Syst. Man Cybern., Part C, Vol. 28, No. 1, pp. 67-78.
[005] Czogal a E. and L ęski J.M. (2000): Fuzzy and Neuro-Fuzzy Intelligent Systems. - Heidelberg: Physica-Verlag.
[006] Duda R.O. and Hart P.E. (1973): Pattern Classification and Scene Analysis. - New York: Wiley. | Zbl 0277.68056
[007] Herbrich R., Graepel T. and Campbell C. (2001): Bayes point machines. - J. Mach. Res., Vol. 1, No. 2, pp. 245-279. | Zbl 1008.68104
[008] Ho Y.-C. and Kashyap R.L. (1965): An algorithmfor linear inequalities and its applications. - IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683-688. | Zbl 0173.17902
[009] Ho Y.-C. and Kashyap R.L. (1966): A class of iterative procedures for linear inequalities. - J. SIAM Contr., Vol. 4, No. 2, pp. 112-115. | Zbl 0143.37503
[010] Ishibuchi H., Nakashima T. and Murata T. (1999): Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. - IEEE Trans. Syst. Man Cybern., Part B, Vol. 29, No. 5, pp. 601-618.
[011] Huber P.J. (1981): Robust Statistics. - New York: Wiley. | Zbl 0536.62025
[012] Keller J.M., Gray M.R. and Givens J.A. (1985): Afuzzy k-nearest neighbors algorithm. - IEEE Trans. Syst. Man Cybern., Vol. 15, No. 3, pp. 580-585.
[013] Krishnapuram R. and Keller J.M. (1993): A possibilistic approach to clustering. - IEEE Trans. Fuzzy Syst., Vol. 1, No. 2, pp. 98-110.
[014] Kim E., Park M., Ji S. and Park M. (1997): A new approach to fuzzy modeling. - IEEE Trans. Fuzzy Syst., Vol. 5, No. 3, pp. 328-337.
[015] Kuncheva L.I. and Bezdek J.C. (1999): Presupervised and postsupervised prototype classifier design. - IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 1142-1152.
[016] Kuncheva L.I. (2000a): How good are fuzzy if-then classifiers? - IEEE Trans. Syst. Man Cybern., Part B, Vol. 30, No. 4, pp. 501-509.
[017] Kuncheva L.I. (2000b): Fuzzy Classifier Design.- Heidelberg: Physica-Verlag. | Zbl 0992.68183
[018] Kuncheva L.I. (2001): Using measures of similarity and inclusion for multiple classifier fusion by decision templates. -Fuzzy Sets Syst., Vol. 122, No. 3, pp. 401-407. | Zbl 1006.68127
[019] Kuncheva L.I. (2002): Switching between selection and fusion in combining classifiers: An experiment. - IEEE Trans. Syst. Man Cybern.. Part B, Vol. 32, No. 2, pp. 146-156.
[020] Łęski J. and Henzel N. (2001): A neuro-fuzzy system based on logical interpretation of if-then rules, In: Fuzzy Learning and Applications (Russo M. and Jain L.C., Eds.). - New York: CRC Press, pp. 359-388. | Zbl 0972.68135
[021] Łęski J. (2002): Robust weighted averaging.- IEEE Trans. Biomed. Eng., Vol. 49, No. 8, pp. 796-804.
[022] Malek J.E., Alimi A.M. and Tourki R. (2002): Problems in pattern classification in high dimensional spaces: Behavior of aclass of combined neuro-fuzzy classifiers. - Fuzzy Sets Syst., Vol. 128, No. 1, pp. 15-33. | Zbl 1002.68550
[023] Mangasarian O.L. and Musicant D.R. (2000): Lagrangian support vector machines. - Technical Report 00-06, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, available at ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-06.ps | Zbl 0997.68108
[024] Marin-Blazquez J. and Shen Q. (2002): From approximative to descriptive fuzzy classifiers. - IEEE Trans. FuzzySyst., Vol. 10, No. 4, pp. 484-497.
[025] Miller D., Rao A.V., Rose K. and Gersho A. (1996): A global optimization technique for statistical classifier design.- IEEE Trans. Signal Process., Vol. 44, No. 12, pp. 3108-3121.
[026] Nath A.K. and Lee T.T. (1982): On the design of a classifier with linguistic variables as inputs. - Fuzzy Sets Syst., Vol. 11, No. 2, pp. 265-286. | Zbl 0538.68069
[027] Ripley B.D. (1996): Pattern Recognition and Neural Networks. - Cambridge: Cambridge University Press. | Zbl 0853.62046
[028] Runkler T.A. and Bezdek J.C. (1999): Alternating cluster estimation: A new tool for clustering and function approximation.- IEEE Trans. Fuzzy Syst., Vol. 7, No. 4, pp. 377-393.
[029] Rutkowska D. (2002): Neuro-Fuzzy Architectures and Hybrid Learning. - Heidelberg: Physica-Verlag. | Zbl 1005.68127
[030] Setnes M. and Babuvska R. (1999): Fuzzy relational classifier trained by fuzzy clustering. - IEEE Trans. Syst. Man Cybern., Part B, Vol. 29, No. 5, pp. 619-625.
[031] Tipping M.E. (2001): Sparse Bayesian learning andthe relevance vector machine. - J. Mach. Res., Vol. 1, No. 2, pp. 211-244. | Zbl 0997.68109
[032] Tou J.T. and Gonzalez R.C. (1974): Pattern Recognition Principles. - London: Addison-Wesley. | Zbl 0299.68058
[033] Vapnik V. (1998): Statistical Learning Theory. -New York: Wiley. | Zbl 0935.62007
[034] Vapnik V. (1999): An overview of statistical learning theory. - IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 988-999.
[035] Webb A. (1999): Statistical Pattern Recognition.- London: Arnold. | Zbl 0968.68540