Fuzzy one-class support vector machines

In one-class classification, the problem is to distinguish one class of data from the rest of the feature space. It is important in many applications where one of the classes is characterized well, while no measurements are available for the other class. Scholkopf et al. first introduced a method of adapting the support vector machine (SVM) methodology to the one-class classification problem, called one-class SVM. In this paper, we incorporate the concept of fuzzy set theory into the one-class SVM. We apply a fuzzy membership to each input point and reformulate the one-class SVM such that different input points can make different contributions to the learning of decision surface. Besides, the parameters to be identified in one-class SVM, such as the components within the weight vector and the bias term, are fuzzy numbers. This integration preserves the benefits of SVM learning theory and fuzzy set theory, where the SVM learning theory characterizes the properties of learning machines which enable them to effectively generalize the unseen data and the fuzzy set theory might be very useful for finding a fuzzy structure in an evaluation system.