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

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.

Keywords

• Gustafson-Kessel Method
• Fuzzy Clustering Analysis
• Weighted Regression
• Forecasting

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