Parameter Estimation by Fuzzy Adaptive Networks and Comparison with Robust Regression Methods

Kamile Şanlı Kula, Türkan Erbay Dalkılıç
1.657 438


Fuzzy adaptive networks used for estimating the unknown parameters of a regression model are based on fuzzy if-then rules and a fuzzy inference system. In regression analysis, data analysis is very important, because, every observation may have a large influence on the parameters estimates in the regression model. When a data set has outliers, robust methods such as the M method (Huber, Hampel, Andrews and Tukey), Least Median of Squares (LMS) and Reweighed Least Squares Based on the LMS (RLS) are used for estimating parameters. In this study, a method and an algorithm have been suggested to define the parameters of a switching regression model. Adaptive networks have been used in constructing one model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, to define the optimal class number of independent variables, we aimed to use the suggested validity criterion. The proposed method has the properties of a robust method, because the process does not give permission to the intuitional and is not affected by the outliers, which exist in the independent variable. Consequently, another aim of this study is, to compare the proposed method with the robust methods that are mentioned above. For the comparison the cross-validation method is used.Keywords: Fuzzy adaptive network, robust regression, switching regression.


Fuzzy adaptive network, robust regression, switching regression

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L. Lung-Fei and H.P. Robert, Switching Regression Models Separation Information-With an Application on Cartel Stability, Econometrica 52 (1984) 391-418.

M. Michel, Fuzzy Clustering and Switching Regression Models Using Ambiguity and Distance Rejects, Fuzzy Sets and Systems 122 (2001) 363- 3

E.Q. Richard, A New Approach to Estimating Switching Regressions, Journal of the American Statistical Association, 67 (1972) 306-310.

X.L. Xie and G. Beni, A validity measure for fuzzy clustering, IEEE Trans Pattern Anal. Machine Intell. 13 (1991) 841-847.

C. Mu-Song. And S.W. Wang, Fuzzy Clustering Analysis for Optimizing Fuzzy Membership Functions, Fuzzy Sets and Systems, 103 (1999) 239-2

C.J. Bezdek, R. Ehrlich and W. Full, FCM: The Fuzzy c_Means Clustering Algorithm, Computer and Geoscience, 10 (1984) 191-203.

C.B. Cheng and E.S. Lee, Applying fuzzy adaptive network International Journal Computers & Mathematics with Applications 38 (1999) 123-140.

C.B. Cheng and E.S. Lee, Switching Regression Analysis by Fuzzy Adaptive Network, European Journal of Operational Research, 128 (2001) 647- 6

R.J. Jyh-Shing, ANFIS: Adaptive-Network-Based Fuzzy Inference System, IEEE Transaction on Systems, Man and Cybernetics, 23 (1993) 665-685

E. Nasrabadi and S.M. Hashemi, Robust Fuzzy Regression Analaysis Using Neural Networks, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16 (2008) 579-598

K.S. Kula and A. Apaydın, Fuzzy Robust Regression Analaysis Based on The Rankinf of Fuzzy Sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16 (2008)

F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics. (John-Willey & Sons, New-York 1986).

R.V. Hogg, Statistician robustness: One View of Its Use in Applications Today, The American Statistician, 33(1979) 108-115.

P.J. Huber, Robust statistics.( John Willey & Son 1981).

H. Huynh, A Comparison of For Approaches to Robust Regression, Psychological Bulletin, 92, (1982) 505-512.

P.J. Rousseeuw and A.M. Leroy, Robust regression and outlier detection. (John Willey & Son1987).

R.J. Hathaway and J.C. Bezdek, Switching Regression Models and Fuzzy Clustering, IEEE Transaction on Fuzzy Systems, 1 (1993)195-204.

F. Horia and S. Costel, A New Fuzzy Regression Algorithm, Anal. Chem. 68 (1996)771-778.

H. Ishibuchi and M. Nii, Fuzzy regression using asymmetric fuzzy coefficients and fuzzed neural networks, Fuzzy Sets and Systems 119 (2001) 273- 2

H. Ishibuchi and H. Tanaka, Fuzzy Regression Analysis Using Neural Networks, Fuzzy Sets and Systems, 50 (1992) 257-265.

T.E. Dalkılıç and A. Apaydın, A Fuzzy Adaptive Network Approach to Parameter Estimation in case Where Independent Variables Come From Exponential Computational 233,(2009) 26-45. Journal of Applied Mathematics,