A New Fuzzy Support Vector Data Description Machine

Abstract

Data domain description or one-class classification concerns the characterization of a data set. A good description covers all target data but includes no superfluous space. The boundary of a dataset can be used to detect novel data or outliers. One-class classification is important in many applications where one of the classes is characterized well, while no measurements are available for the other class. Tax et al. first introduced a method of adapting the support vector machine (SVM) methodology to the one-class classification problem, called support vector data description (SVDD). In this paper, we incorporate the concept of fuzzy set theory into the SVDD. We apply a fuzzy membership to each input point and reformulate the SVDD such that different input points can make different contributions to the learning of decision surface. Besides, the parameters to be identified in SVDD, such as the components within the spherical center vector and the radius, 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.