Regression parameters prediction in data set with outliers using neural network

Year 2019, , 1170 - 1184, 08.08.2019

Tahereh Razzaghnia

https://doi.org/10.15672/hujms.544496

Abstract

Popular regression techniques often suffer at the presence of data outliers. The different methods have proposed to make smaller the effect of the outlier on the parameter estimates. In this study, an algorithm has been addressed based on Adaptive network based fuzzy inference system to define the unknown parameters of regression model where dependent variable has outlier. So, three numerical examples are solved to test the activity of the proposed algorithm in regression model estimation. Also, the obtained results from the different methods, such as linear programming (LP) and fuzzy weights with linear programming (FWLP) are compared together. The results show that the proposed method is not to be affected the outliers in the solving process.

Keywords

Fuzzy regression, Outlier, Linear programming, Fuzzy least squares, Adaptive neural networks

References

• [1] A. Celmins. Multidimensional least-squares fitting of fuzzy models, Fuzzy sets and systems 22 ,1997.
• [2] Y. S. Chen. Outliers detection and confidence interval modification in fuzzy regression. Fuzzy sets and systems 119, 259-272, 2001.
• [3] C. -B. Cheng and E. S. Lee. Applying Fuzzy Adoptive Network to Fuzzy Regression Analysis. Computers and Mathematics with Applications 38, 123-140, 1999.
• [4] C. -B. Cheng and E. S. Lee. Nonparametric fuzzy regression k-NN and kernel smoothing techniques. Computers and Mathematics with Applications 38, 239-251,1999.
• [5] C. -B. Cheng and E. S. Lee. Fuzzy regression with radial basis function networks. Fuzzy Sets and Systems 119, 291-301 ,2001.
• [6] P. D’Urso and T. Gastaldi. A least-squares approach to fuzzy linear regression analysis. Computational Statistics and Data Analysis 34, 427-440 ,2000.
• [7] T. E. Dalkilic and T. Apaydin. A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution. Journal of Computational and Applied Mathematics 233, 36-45 ,2009.
• [8] T. E. Dalkilic and T. Apaydin. Parameter Estimation by ANFIS in Cases Where Outputs are Non-Symmetric Fuzzy Numbers. International Journal of Applied Science and Technology, 92-103 ,2014.
• [9] S. Danesh. Fuzzy Parameters Estimation via Hybrid Methods. Hacettepe Journal of Mathematics and Statistics, inpress, Doi: 10.15672/HJMS.201614621831.
• [10] S. Danesh, R. Farnoosh and T. Razzaghnia. Fuzzy nonparametric regression based on adaptive neuro fuzzy inference system, Neurocomputing, 173, 1450-1460, 2016.
• [11] P. Diamond. Fuzzy least squares. Information Sciences 46, 141-157,1988.
• [12] S. Donoso, N. Marin and M. Amparo Vila. Quadratic programming models for fuzzy regression. International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo, 2006.
• [13] R. Farnoosh, J. Ghasemian and O. Solaymani fard. A modification on ridge estimation for fuzzy nonparametric regression. Iranian Journal of Fuzzy System Vol. 9, No. 2, 75-88 (2012)
• [14] L. V. Fausett. Fundamentals of neural networks: architectures, algorithms, and applications. Prentice Hall (1994)
• [15] D. H. Hong, J. -K. Song and H. Young. Fuzzy least-squares linear regression analysis using shape preserving operations. Information Sciences 138, 185-193 (2001)
• [16] W. L. Hung and M. S. Yang. An omission approach for detecting outliers in fuzzy regression models. Fuzzy sets and systems 157, 3109-3122 (2006)
• [17] H. Ishibuchi, K. Kwon and H. Tanaka. A learning algorithm of fuzzy neural networks with triangular fuzzy weights. Fuzzy Sets and Systems 71, 277-293 (1995)
• [18] H. Ishibuchi and H. Tanaka. Fuzzy regression analysis using neural networks. Fuzzy Sets and Systems 50, 257-265 ,1992.
• [19] P. James and W. Donald. Fuzzy regression by fuzzy number neural networks, Journal Fuzzy Sets and Systems 112 Issue 3, 371-380 (2000)
• [20] J. S. R. Jang. Self-learning fuzzy controllers based on temporal back-propagation. IEEE Transactions on Neural Network 3, 714-723 (1992)
• [21] J. S. R. Jang. ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cyber 23(3) 665-685 (1993)
• [22] B. Kim and R. R. Bishu. Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets and Systems 100, 343-351 (1998)
• [23] A. Z. Lotfi. Fuzzy logic toolbox for use with MATLAB. Math Works 38, 109-12 ,1995.
• [24] A. Maleki, E. Pasha, G. H. Yari and T. Razzaghnia. Detecting outliers in fuzzy regression analysis wih asymmetric trapezoidal fuzzy data. SPIE 8349,221-226 (2012)
• [25] M. B. Menhaj. Fundamentals of neural networks. Tehran: Professor Hesabi Publications, 1998.
• [26] M. Ming, M. Friedman and A. Kandel. General fuzzy least squares. Fuzzy Sets and Systems 88, 107-118 ,1997.
• [27] M. Modarres, E. Nasrabadi and M. M. Nasrabadi. A mathematical-programming approach to fuzzy linear regression analysis. Applied Mathematics and Computation 163 (2), 977- 989,2005.
• [28] A. Mottaghi, A. Ezzat and R. E. Khorram. A New Method For Solving Fuzzy Linear Programming Problems Based on The Fuzzy Linear Complementary Problem (FLCP). International Journal of Fuzzy Systems, 2015.
• [29] M .M Nasrabadi and E. Nasrabadi. A mathematical-programming approach to fuzzy linear regression analysis. Applied Mathematics and Computation 155 (3), 873-881 ,2004.
• [30] E. Pasha, T. Razzaghnia, T. Allahviranloo, G. H. Yari and H. R. Mostafaei. A new mathematical programming approach in fuzzy linear regression models. Applied Mathematical Sciences 35, 2007.
• [31] T. Razzaghnia, S. Danesh and A. Maleki. Hybrid fuzzy regression with trapezoidal fuzzy data. Proc. SPIE 8349,211-216,2012.
• [32] T. Razzaghnia and S. Danesh. Nonparametric Regression with Trapezoidal Fuzzy Data. International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC), 3826-3831 ,2015.
• [33] T. Takagi and M. Sugeo. Fuzzy identification of system and its application to modeling and control. IEEE Trans. Syst. Man Cybern 15, 116-132 ,1985.
• [34] H. Tanaka, I. Hayashi and J. Watada. Possibilistic linear regression analysis for fuzzy data. European Journal of Operational Research 40, 389-396 ,1989.
• [35] H. Tanaka and H. Ishibushi. Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters. Fuzzy Sets and Systems 41, 145-160 ,1991.
• [36] H. Tanaka and H. Lee. Interval regression analysis by quadratic programming approach. IEEE Transactions on Fuzzy Systems 6, 473-481 ,1998.
• [37] H. Tanaka, S. Uejima and K. Asia. Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man and Cybernetics 12, 903-907,1982.
• [38] H. Tanaka. Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems 24, 363-375 ,1987.
• [39] N. Wang, W. X. Zhang and C. L. Mei. Fuzzy nonparametric regression based on local linear smoothing technique. Information Sciences 177, 3882-3900 ,2007.
• [40] L. A. Zadeh. Fuzzy sets. Information and Control 8, 338-353 ,1965.