Design of Reinforced Interval Type-2 Fuzzy C-Means-Based Fuzzy Classifier

Abstract

This paper is concerned with a new design methodology of a reinforced interval type-2 fuzzy c-means (FCM) based fuzzy classifier (FC). The key point of this study is to reduce the computational complexity of type-2 fuzzy set-based models and to alleviate the deterioration of its generalization abilities through the synergistic effect of two algorithms: First, interval type-2 FCM (IT2FCM) is used in the hidden layer of the network and connections (weights) are adjusted by invoking the least squares error estimation method. Second, an L2-norm regularization is considered in the cost function to avoid the construction of the network suffering from overfitting. In more detail, the hidden layer of the proposed FC is realized by interval type-2 FCM clustering to deal with the factor of uncertainty involved in the problem. This type of clustering is realized by using two values of the fuzzification coefficient resulting in the interval type-2 membership functions. Once completing type reduction, the membership grades of IT2FCM are used as the outputs of the hidden layer. Instead of the backpropagation training, least squares estimator based learning is applied to adjust the functional connection being regarded as linear functions mapping the hidden layer to the output layer. In order to reduce potential overfitting, L2-norm regularization is taken into account. The effectiveness of the proposed classifier is analyzed with the aid of a number of machine learning datasets as well as face image datasets. Thorough comparative studies are also included.