Fuzzy regression based on asymmetric support vector machines. (English) Zbl 1113.62084
Summary: A modified framework of support vector machines which is called asymmetric support vector machines (ASVMs) is given and is designed to evaluate the functional relationship for fuzzy linear and nonlinear regression models. In earlier works, in order to cope with different types of input-output patterns, strong assumptions were made regarding linear fuzzy regression models with symmetric and asymmetric triangular fuzzy coefficients. Excellent performance is achieved on some linear fuzzy regression models.
However, the nonlinear fuzzy regression model has received relatively little attention, because such nonlinear fuzzy regression models have certain limitations. This study modifies the framework of support vector machines in order to overcome these limitations. The principle of ASVMs is applying an orthogonal vector into the weight vector in order to rotate the support hyperplanes. The prime merits of the proposed model are in its simplicity, understandability and effectiveness. Consequently, experimental results and comparisons are given to demonstrate that the basic idea underlying ASVMs can be effectively used for parameter estimation.
However, the nonlinear fuzzy regression model has received relatively little attention, because such nonlinear fuzzy regression models have certain limitations. This study modifies the framework of support vector machines in order to overcome these limitations. The principle of ASVMs is applying an orthogonal vector into the weight vector in order to rotate the support hyperplanes. The prime merits of the proposed model are in its simplicity, understandability and effectiveness. Consequently, experimental results and comparisons are given to demonstrate that the basic idea underlying ASVMs can be effectively used for parameter estimation.
MSC:
| 62J02 | General nonlinear regression |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 62J99 | Linear inference, regression |
References:
| [1] | Bertsekas, D. P., Nonlinear Programming (1999), Athena Scientific: Athena Scientific Massachusetts · Zbl 0935.90037 |
| [2] | Buckley, J. J.; Feuring, T., Linear and non-linear fuzzy regression: evolutionary algorithm solution, Fuzzy Sets and Systems, 112, 3, 381-394 (2000) · Zbl 0948.62048 |
| [3] | Chapelle, O.; Haffner, P.; Vapnik, V. N., Support vector machines for histogram-based image classification, IEEE Transactions on Neural Network, 10, 5, 1055-1064 (1999) |
| [4] | Dubios, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049 |
| [5] | Dunyak, J. P.; Wunsch, D., Fuzzy regression by fuzzy number neural networks, Fuzzy Sets and Systems, 112, 3, 371-380 (2000) · Zbl 0948.62049 |
| [6] | S. Gunn, Support vector machines for classification and regression, ESIS Technical Report, University of Southampton, 1998.; S. Gunn, Support vector machines for classification and regression, ESIS Technical Report, University of Southampton, 1998. |
| [7] | Guo, G.; Li, S. Z.; Chan, K. L., Support vector machines for face recognition, Image and Vision Computing, 19, 631-638 (2001) |
| [8] | Heshmaty, B.; Kandel, A., Fuzzy linear regression and its applications to forecasting in uncertain environment, Fuzzy Sets and Systems, 15, 159-191 (1985) · Zbl 0566.62099 |
| [9] | Hong, D. H.; Hwang, C., Support vector fuzzy regression machines, Fuzzy Sets and Systems, 13, 2, 205-213 (2003) |
| [10] | Ishibuchi, H.; Nii, M., Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks, Fuzzy Sets and Systems, 11, 2, 273-290 (2001) · Zbl 0964.62051 |
| [11] | H. Ishibuchi, H. Tanaka, Several formulations of interval regression analysis, in: Proceedings of Sino-Japan Join Meeting on Fuzzy Sets and Systems, Bejjing, China, 1990, p. B2-2.; H. Ishibuchi, H. Tanaka, Several formulations of interval regression analysis, in: Proceedings of Sino-Japan Join Meeting on Fuzzy Sets and Systems, Bejjing, China, 1990, p. B2-2. |
| [12] | Kacprzyk, J.; Fedrizzi, M., Fuzzy Regression Analysis (1992), Omnitech Press: Omnitech Press Warsaw · Zbl 0758.00005 |
| [13] | Lee, H.; Tanaka, H., Fuzzy approximations with non-symmetric fuzzy parameters in fuzzy regression analysis, Journal of Operation Research, 4, 1, 98-112 (1999) · Zbl 1138.62335 |
| [14] | Nasrabadi, M. M.; Nasrabadi, E., A mathematical-programming approach to fuzzy linear regression analysis, Applied Mathematics and Computation, 15, 3, 873-881 (2004) · Zbl 1051.62061 |
| [15] | Modarres, M.; Nasrabadi, E.; Nasrabadi, M. M., Fuzzy linear regression models with least square errors, Applied Mathematics and Computation, 15, 3, 873-881 (2004) · Zbl 1051.62061 |
| [16] | Schölkopf, B.; Smola, A. J., Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (2002), MIT Press: MIT Press Cambridge, MA, London |
| [17] | Tanaka, H.; Ishibuchi, H.; Hwang, S. G., Fuzzy model of the number of staff in local government by fuzzy regression analysis with similarity relations, Journal of the Japan Industrial Management Assocication, 4, 2, 99-104 (1990), (in Japanese) |
| [18] | Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE Transactions Systems Man and Cybernetics, 1, 6, 903-907 (1982) · Zbl 0501.90060 |
| [19] | V.N. Vapnik, The nature of statistical learning theory, New York, 1995.; V.N. Vapnik, The nature of statistical learning theory, New York, 1995. · Zbl 0833.62008 |
| [20] | Vapnik, V. N., Statistical Learning Theory (1998), Wiley: Wiley New York · Zbl 0934.62009 |
| [21] | Wang, H.-F.; Tsaur, R.-C., Resolution of fuzzy regression model, European Journal of Operational Research, 26, 637-650 (2000) · Zbl 1009.62054 |
| [22] | Xiu, R.; Li, C., Multidimensional least-squares fitting with a fuzzy model, Fuzzy Sets and Systems, 11, 2, 215-223 (2001) · Zbl 0964.62057 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
