A new fuzzy membership assignment and model selection approach based on dynamic class centers for fuzzy SVM family using the firefly algorithm

The support vector machine (SVM) is a powerful tool for classification problems. Unfortunately, the training phase of the SVM is highly sensitive to noises in the training set. Noises are inevitable in real-world applications. To overcome this problem, the SVM was extended to a fuzzy SVM by assigning an appropriate fuzzy membership to each data point. However, suitable choice of fuzzy memberships and an accurate model selection raise fundamental issues. In this paper, we propose a new method based on optimization methods to simultaneously generate appropriate fuzzy membership and solve the model selection problem for the SVM family in linear/nonlinear and separable/nonseparable classification problems. Both the SVM and least square SVM are included in the study. The fuzzy memberships are built based on dynamic class centers. The firefly algorithm (FA), a recently developed nature-inspired optimization algorithm, provides variation in the position of class centers by changing their attributes' values. Hence, adjusting the place of the class center can properly generate accurate fuzzy memberships to cope with both attribute and class noises. Furthermore, through the process of generating fuzzy memberships, the FA can choose the best parameters for the SVM family. A set of experiments is conducted on nine benchmarking data sets of the UCI data base. The experimental results show the effectiveness of the proposed method in comparison to the seven well-known methods of the SVM literature.