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Alternative Fuzzy Switching Regression

paper present an alternative method for fuzzy switching regression analysis. The traditional fuzzy c-regression (FCR) is a method by embedding the fuzzy c-means (FCM) into switching regression. By defining an alternative residual measurement, we modified the fuzzy c-regression (FCR) and proposed an alternative fuzzy c-regression (AFCR). The proposed method is more robust to noise and outlier than the EM and FCR algorithms. Numerical examples show the robustness and superiority of our proposed method. I. INTRODUCTION Regression analysis is used to model the function relation between the independent and dependent variables. Usually, a single regression model is used for fitting a data set. However, the data set may contain more than one regression model, say c regression models. This kind of model fitting is called switching regressions. Quandt [1,2] and Chow [3] initiated the studies of switching regressions. Subsequently, Quandt [4], Quandt and Ramsey [5] and De Veaux [6] considered the mixture of regressions approach to estimating switching regressions that is widely studied and applied in psychology, economics, social science and music perception [7-10]. Hathaway and Bezdek [11] first combined switching regressions with FCM and referred to them as fuzzy c-regressions (FCR). To increase the speed of FCR, Wang et al. [12] combined the concept of Newton's law of gravity with FCR. However, these FCRs are sensitive to noise and outliers. To improve the robustness against noise and outliers, Leski