A Fuzzy If-Then Rule-Based Nonlinear Classifier

• Autorzy: Łęski J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

classifier design; fuzzy if-then rules; generalization control; mixture of experts

PL

projekt klasyfikatora; sterowanie uogólnione; mieszanka ekspertów

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 2
• Strony: 215--223
• Opis fizyczny: Bibliogr. 36 poz., tab., wykr.

Twórcy

autor

Łęski J.

• Institute of Electronics Silesian University of Technology Akademicka 16, 44-100 Gliwice, Poland,

Bibliografia

• [1] 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.
• [2] Bellman R., Kalaba K. and Zadeh L.A. (1966): Abstraction and pattern classification. — J. Math. Anal. Appl., Vol. 13, No. 1, pp. 1–7.
• [3] Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. —New York: Plenum Press.
• [4] Bezdek J.C. and Pal S.K. (Eds.) (1992): Fuzzy Models for Pattern Recognition. — New York: IEEE Press.
• [5] 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.
• [6] Czogała E. and Łęski J.M. (2000): Fuzzy and Neuro-Fuzzy Intelligent Systems. — Heidelberg: Physica-Verlag.
• [7] Duda R.O. and Hart P.E. (1973): Pattern Classification and Scene Analysis. — New York: Wiley.
• [8] Herbrich R., Graepel T. and Campbell C. (2001): Bayes point machines. —J. Mach. Res., Vol. 1, No. 2, pp. 245–279.
• [9] Ho Y.-C. and Kashyap R.L. (1965): An algorithm for linear inequalities and its applications. — IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683–688.
• [10] 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.
• [11] 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.
• [12] Huber P.J. (1981): Robust Statistics.—New York: Wiley.
• [13] Keller J.M., Gray M.R. and Givens J.A. (1985): A fuzzy k-nearest neighbors algorithm. — IEEE Trans. Syst. Man Cybern., Vol. 15, No. 3, pp. 580–585.
• [14] Krishnapuram R. and Keller J.M. (1993): A possibilistic approach to clustering. — IEEE Trans. Fuzzy Syst., Vol. 1, No. 2, pp. 98–110.
• [15] 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.
• [16] 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.
• [17] 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.
• [18] Kuncheva L.I. (2000b): Fuzzy Classifier Design.—Heidelberg: Physica-Verlag.
• [19] 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.
• [20] 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.
• [21] 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.
• [22] Łęski J. (2002): Robust weighted averaging. — IEEE Trans. Biomed. Eng., Vol. 49, No. 8, pp. 796–804.
• [23] Malek J.E., Alimi A.M. and Tourki R. (2002): Problems in pattern classification in high dimensional spaces: Behavior of a class of combined neuro-fuzzy classifiers. — Fuzzy Sets Syst., Vol. 128, No. 1, pp. 15–33.
• [24] 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.
• [25] Marín-Blázquez J. and Shen Q. (2002): From approximative to descriptive fuzzy classifiers. — IEEE Trans. Fuzzy Syst., Vol. 10, No. 4, pp. 484–497.
• [26] 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.
• [27] 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.
• [28] Ripley B.D. (1996): Pattern Recognition and Neural Networks. —Cambridge: Cambridge University Press.
• [29] 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.
• [30] Rutkowska D. (2002): Neuro-Fuzzy Architectures and Hybrid Learning. — Heidelberg: Physica-Verlag.
• [31] Setnes M. and Babuška R. (1999): Fuzzy relational classifier trained by fuzzy clustering. — IEEE Trans. Syst. Man Cybern., Part B, Vol. 29, No. 5, pp. 619–625.
• [32] Tipping M.E. (2001): Sparse Bayesian learning and the relevance vector machine. — J. Mach. Res., Vol. 1, No. 2, pp. 211–244.
• [33] Tou J.T. and Gonzalez R.C. (1974): Pattern Recognition Principles. — London: Addison-Wesley.
• [34] Vapnik V. (1998): Statistical Learning Theory. — New York: Wiley.
• [35] Vapnik V. (1999): An overview of statistical learning theory. — IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 988–999.
• [36] Webb A. (1999): Statistical Pattern Recognition. — London: Arnold.