| | | |

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

#### Necati ERİLLİ [1]

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.
Gustafson-Kessel Method, Fuzzy Clustering Analysis, Weighted Regression, Forecasting
• 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.
Birincil Dil en Matematik Articles Orcid: 0000-0001-6948-0880Yazar: Necati ERİLLİ (Sorumlu Yazar)Kurum: SİVAS CUMHURİYET ÜNİVERSİTESİÜlke: Turkey Yayımlanma Tarihi : 31 Aralık 2020
 Bibtex @araştırma makalesi { forecasting778616, journal = {Turkish Journal of Forecasting}, issn = {}, eissn = {2618-6594}, address = {Giresun Üniversitesi Fen Edebiyat Fakültesi İstatistik Bölümü, Güre Yerleşkesi, 28100 Merkez, Giresun}, publisher = {Giresun Üniversitesi}, year = {2020}, volume = {04}, pages = {16 - 25}, doi = {10.34110/forecasting.778616}, title = {Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm}, key = {cite}, author = {Erilli, Necati} } APA Erilli, N . (2020). Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm . Turkish Journal of Forecasting , 04 (2) , 16-25 . DOI: 10.34110/forecasting.778616 MLA Erilli, N . "Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm" . Turkish Journal of Forecasting 04 (2020 ): 16-25 Chicago Erilli, N . "Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm". Turkish Journal of Forecasting 04 (2020 ): 16-25 RIS TY - JOUR T1 - Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm AU - Necati Erilli Y1 - 2020 PY - 2020 N1 - doi: 10.34110/forecasting.778616 DO - 10.34110/forecasting.778616 T2 - Turkish Journal of Forecasting JF - Journal JO - JOR SP - 16 EP - 25 VL - 04 IS - 2 SN - -2618-6594 M3 - doi: 10.34110/forecasting.778616 UR - https://doi.org/10.34110/forecasting.778616 Y2 - 2020 ER - EndNote %0 Turkish Journal of Forecasting Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm %A Necati Erilli %T Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm %D 2020 %J Turkish Journal of Forecasting %P -2618-6594 %V 04 %N 2 %R doi: 10.34110/forecasting.778616 %U 10.34110/forecasting.778616 ISNAD Erilli, Necati . "Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm". Turkish Journal of Forecasting 04 / 2 (Aralık 2020): 16-25 . https://doi.org/10.34110/forecasting.778616 AMA Erilli N . Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. TJF. 2020; 04(2): 16-25. Vancouver Erilli N . Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm. Turkish Journal of Forecasting. 2020; 04(2): 16-25. IEEE N. Erilli , "Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm", Turkish Journal of Forecasting, c. 04, sayı. 2, ss. 16-25, Ara. 2021, doi:10.34110/forecasting.778616

Makalenin Yazarları