Fuzzy support vector machine for regression estimation

The theory of support vector machine (SVM), as a tool of pattern classification and regression estimation, draws much attention on this field. In this method, it maps the input data into a high dimensional characteristic space in which it constructs an optimal separating hyperplane. In many applications it has provided high generalization ability. In this paper we provide the fuzzy SVM for regression estimation problem. This method combines the fuzzy logic with the generalize SVM to construct multi-layer SVM. The first layer is the fuzzification process. We apply a fuzzy membership to each data point of SVM and reformulate the SVM such that different input points can make different contributions to the learning of regression function. The second layer is the generalize SVM which make the kernel function and may not satisfy the Mercer's condition. The proposed method enhances the SVM in reducing the effect of outliers and noises in the application of data fitting.

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