Support vector-based fuzzy classifier with adaptive kernel

Abstract

Fuzzy neural network (FNN) and support vector machine (SVM) are popular techniques for pattern classification. FNN has a good local representation power and human-like reasoning benefit. But the learning algorithms used in most FNN classifiers only focus on minimizing empirical risk. SVM has excellent generalization performance due to focusing on simultaneously minimizing both empirical and expected risks. But this performance is dependent on choosing an appropriate kernel function. To overcome these challenges some efforts have been made to combine SVM and FNN; however, the methods proposed so far are faced with some major problems such as significantly increasing number of fuzzy rules. In this paper a support vector-based fuzzy classifier with adaptive kernel (SVFC-AK) is proposed. SVFC-AK implements the mentioned combining idea and yet not have disadvantages of the previous methods. This is realized by leveraging an underlying relation between FNN and kernel SVM. More precisely, SVFC-AK is a TS-type FNN for which the parameters are tuned through a new adaptive fuzzy kernel SVM. Also, the proposed fuzzy kernel, which is calculated automatically, is inspired by the fuzzy rule-based representation of FNN. Moreover, the fuzzy rules of SVFC-AK are generated using a modified clustering method based on Gaussian mixture model, which determines the number of required rules automatically. The experimental results illustrate that the classification performance of SVFC-AK is competitive or even better than some related methods, while the number of its fuzzy rules or hyper-parameters is substantially smaller.