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Classification based on Gaussian-kernel Support Vector Machine with Adaptive Fuzzy Inference System DOI:10.15199/48.2018.05.03

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Support Vector Machine (SVM) has been widely used as a technique for solving pattern classification and prediction problems. It can be viewed as an approximate implementation of what Vapnik has defined as Structure Risk Minimization (SRM), an inductive principle that aims to minimize the upper bound on the generalization error of a model, rather than minimizing the mean-square-error over the training data set. In the last two decades, Fuzzy methodology has been successfully applied in a variety of areas including control and system identification, signal and image processing, pattern classification, and information retrieval [1, 2, 3, 4]. In general, building a fuzzy system consists of three basic steps: structure identification (variable selection, partitioning input and output spaces, specifying the number of fuzzy rules, and choosing a parametric/nonparametric form of membership functions); parameter estimation (obtaining unknown parameters in fuzzy rules via optimizing a given criterion); and model validation (performance evaluation and model simplification). The design methodology for the construction of fuzzy models involves both rule extraction and parameter learning aspects. In spite of the popularity of both SVM and Fuzzy systems, there had been almost no work in the literature that relates both these methods. In this paper, we will focus on the rule extraction methods which have been formulated using neural networks, genetic algorithms, and a variety of clustering-based techniques in an effort to select only those rules that contribute to the inference consequence. We will investigate the connection between fuzzy rule-base systems and kernel machines. We then relate kernel function to fuzzy basis function and develop a new fuzzy rule-based inference system that fuses these two concepts thus; preserving the advantages of both these systems. The overall fuzzy inference system can be represented as series expansion[...]

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