Hybrid Fuzzy Least Squares Support Vector Machine Regression for Crisp Input and Fuzzy Output Shim, Joo-Yong; Seok, Kyung-Ha; Hwang, Chang-Ha;
Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.
Fuzzy regression;hybrid regression;least squares support vector machine;nonlinear;weighted fuzzy arithmetic;
Chang, Y. -H. O. (2001). Hybrid fuzzy least-squares regression analysis and its reliability measures, Fuzzy Sets and Systems, 119, 225-246.
Chao, R. and Ayyub, B. M. (1996). Structural analysis with fuzzy variables, Microcomputers in Civil Engineering, 11, 47-58.
Gunn, S. (1998). Support vector machines for classification and regression, ISIS Technical Report, University of Southampton.
Hong, D. H. and Hwang, C. (2003). Support vector fuzzy regression machines, Fuzzy Sets and Systems, 138, 271-281.
Hong, D. H. and Hwang, C. (2005). Interval regression analysis using quadratic loss support vector machine, IEEE Transactions on Fuzzy Systems, 13, 229-237.
Hwang, C., Hong, D. H., Na, E., Park, H. and Shim, J. (2005). Interval regressing analysis using support vector machine and quantile regression, Lecture Notes in Computer Science, 3613, 100-109.
Hwang, C., Hong, D. H. and Seok, K. H. (2006). Support vector interval regression machine for crisp input and out data, Fuzzy Sets and Systems, 157, 1114-1125.
Shim, J., Hwang, C. and Hong, D. H. (2009), Fuzzy semiparametric support vector regression for seasonal time series analysis, Communications of the Korean Statistical Society, 16, 335-348.
Smola, A. J. and Schoelkopf, B. (1998). A tutorial on support vector regression, Neuro-COLT2 Technical Report, NeuroCOLT.
Suykens, J. A. K. (2001). Nonlinear modelling and support vector machines, Proceeding of the IEEE International Conference on Instrumentation and Measurement Technology, Budapest, Hungary, 287-294.
Tanaka, H. (1987). Fuzzy data anlysis by possigbilistic linear models, Fuzzy Sets and Systems, 24, 363-375.
Tanaka, H., Uejima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Transactions and Systems, Man, and Cybernetics, 12, 903-907.
Tanaka, H. and Watada, J. (1988). Possibilistics linear systems, and their applications to linear regression mode, Fuzzy Sets and Systems, 27, 275-289.
Vapnik, V. N. (1998). Statistical Learning Theory, John Wiley & Sons, New York.