Research Article
BibTex RIS Cite
Year 2020, Volume: 04 Issue: 2, 16 - 25, 31.12.2020
https://doi.org/10.34110/forecasting.778616

Abstract

References

  • Bellman R.E., Kalaba R., Zadeh L.A. (1966). Abstraction and pattern classification. J. Math. Anal. Appl., 1-7.
  • Bezdek, J.C. (1974a). Cluster validity with fuzzy sets. Journal of Cybernetics, 3, 58–73.
  • Bezdek, J.C. (1974b). Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1, 57–71.
  • Carroll, R.J., Ruppert D. (1988). Transformation and Weighting in Regression, Chapman and Hall, New York.
  • Erilli, N.A., Yolcu, U., Egrioglu, E., Aladag, C.H., Oner, Y. (2011). Determining the Most Proper Number of Cluster in Fuzzy Clustering by Artificial Neural Networks, Expert Systems with Applications, 38: 2248-2252.
  • [6] Gath I. and Geva A. B. (1989). Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.11 n.7, p.773-780.
  • Gujarati D.N. (2002). Basic Econometrics. 4th ed. McGraw Hill pub., USA.
  • Gustafson, D.E., Kessel, W.C. (1979). Fuzzy clustering with fuzzy covariance matrix. In Proceedings of the IEEE CDC, San Diego, pp. 761–766.
  • Hathaway R.J., Bezdek J.C. (1993), Switching Regression Models and Fuzzy Clustering, IEEE Transactions fuzzy Systems, Vol. 1, No. 3, pp. 195-204.
  • Hu X., Sun F. (2009). Fuzzy Clustering Based Multi-model Support Vector Regression State of Charge Estimator for Lithium-ion Battery of Electric Vehicle. IEEE Xplore.
  • Oliveira J.V., Pedrycz W. (2007). Advances In Fuzzy Clustering and Its Applications, John Wiley &Sons Inc. Pub., West Sussex, England.
  • Ryan, T.P. (1997) Modern Regression Methods, Wiley, New York.
  • Sato-Ilic M., Matsuoka T. (2002). On an Application of Fuzzy Clustering for Weighted Regression Analysis, Proceedings of the 4th ARS Conference of the IASC, pp. 55-58.
  • Sato-Ilic M. (2004). On Fuzzy Clustering based Regression Models, NAI-ITS 2004 International Conference, pp. 216-221.
  • Xie L., Beni G., (1991). A Validity Measure For Fuzzy Clustering, IEEE Trans. On Pattern Analysis and Machine Int. 13(4),pp 841-846.
  • Wooldridge J. M. (2012). Introductory Econometrics: A Modern Approach. 5th ed., South Western Cengage Learning, USA.

Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm

Year 2020, Volume: 04 Issue: 2, 16 - 25, 31.12.2020
https://doi.org/10.34110/forecasting.778616

Abstract

Regression analysis is one of the well-known methods of multivariate analysis and it is efficiently used in many research fields, especially forecasting problems. In order for the results of regression analysis to be effective, some assumptions must be valid. One of these assumptions is the heterogeneity problem. One of the methods used to solve this problem is the weighted regression method. Weighted regression is a method that you can use when the least squares assumption of constant variance in the residuals is violated (heteroscedasticity). With the correct weight, this procedure minimizes the sum of weighted squared residuals to produce residuals with a constant variance (homoscedasticity). In this study, Gustafson-Kessel(GK) method is used to determine weights for weighted regression analysis. GK method is based on the minimization of the sum of weighted squared distances between the data points and the cluster centers. With the fuzzy clustering method, each observation value is bound to the specified clusters in a specific order of membership. These membership degrees will be calculated as weights in the weighted regression analysis and estimation work will be done. In application, 5 simulated and 1 real time data was estimated by the proposed method. The results were interpreted by comparing with Robust Methods (M and S estimator) and Weighted with FCM Regression analysis.

References

  • Bellman R.E., Kalaba R., Zadeh L.A. (1966). Abstraction and pattern classification. J. Math. Anal. Appl., 1-7.
  • Bezdek, J.C. (1974a). Cluster validity with fuzzy sets. Journal of Cybernetics, 3, 58–73.
  • Bezdek, J.C. (1974b). Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1, 57–71.
  • Carroll, R.J., Ruppert D. (1988). Transformation and Weighting in Regression, Chapman and Hall, New York.
  • Erilli, N.A., Yolcu, U., Egrioglu, E., Aladag, C.H., Oner, Y. (2011). Determining the Most Proper Number of Cluster in Fuzzy Clustering by Artificial Neural Networks, Expert Systems with Applications, 38: 2248-2252.
  • [6] Gath I. and Geva A. B. (1989). Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.11 n.7, p.773-780.
  • Gujarati D.N. (2002). Basic Econometrics. 4th ed. McGraw Hill pub., USA.
  • Gustafson, D.E., Kessel, W.C. (1979). Fuzzy clustering with fuzzy covariance matrix. In Proceedings of the IEEE CDC, San Diego, pp. 761–766.
  • Hathaway R.J., Bezdek J.C. (1993), Switching Regression Models and Fuzzy Clustering, IEEE Transactions fuzzy Systems, Vol. 1, No. 3, pp. 195-204.
  • Hu X., Sun F. (2009). Fuzzy Clustering Based Multi-model Support Vector Regression State of Charge Estimator for Lithium-ion Battery of Electric Vehicle. IEEE Xplore.
  • Oliveira J.V., Pedrycz W. (2007). Advances In Fuzzy Clustering and Its Applications, John Wiley &Sons Inc. Pub., West Sussex, England.
  • Ryan, T.P. (1997) Modern Regression Methods, Wiley, New York.
  • Sato-Ilic M., Matsuoka T. (2002). On an Application of Fuzzy Clustering for Weighted Regression Analysis, Proceedings of the 4th ARS Conference of the IASC, pp. 55-58.
  • Sato-Ilic M. (2004). On Fuzzy Clustering based Regression Models, NAI-ITS 2004 International Conference, pp. 216-221.
  • Xie L., Beni G., (1991). A Validity Measure For Fuzzy Clustering, IEEE Trans. On Pattern Analysis and Machine Int. 13(4),pp 841-846.
  • Wooldridge J. M. (2012). Introductory Econometrics: A Modern Approach. 5th ed., South Western Cengage Learning, USA.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Necati Erilli 0000-0001-6948-0880

Publication Date December 31, 2020
Submission Date August 10, 2020
Acceptance Date December 16, 2020
Published in Issue Year 2020 Volume: 04 Issue: 2

Cite

APA Erilli, N. (2020). Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. Turkish Journal of Forecasting, 04(2), 16-25. https://doi.org/10.34110/forecasting.778616
AMA Erilli N. Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. TJF. December 2020;04(2):16-25. doi:10.34110/forecasting.778616
Chicago Erilli, Necati. “Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm”. Turkish Journal of Forecasting 04, no. 2 (December 2020): 16-25. https://doi.org/10.34110/forecasting.778616.
EndNote Erilli N (December 1, 2020) Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. Turkish Journal of Forecasting 04 2 16–25.
IEEE N. Erilli, “Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm”, TJF, vol. 04, no. 2, pp. 16–25, 2020, doi: 10.34110/forecasting.778616.
ISNAD Erilli, Necati. “Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm”. Turkish Journal of Forecasting 04/2 (December 2020), 16-25. https://doi.org/10.34110/forecasting.778616.
JAMA Erilli N. Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. TJF. 2020;04:16–25.
MLA Erilli, Necati. “Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm”. Turkish Journal of Forecasting, vol. 04, no. 2, 2020, pp. 16-25, doi:10.34110/forecasting.778616.
Vancouver Erilli N. Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. TJF. 2020;04(2):16-25.

INDEXING

   16153                        16126   

  16127                       16128                       16129