Rough-Fuzzy Support Vector Domain Description for outlier detection

We present Rough-Fuzzy Support Vector Domain Description (RFSVDD), a novel data description algorithm that provides a rough-fuzzy characterization of a data set and shows its potential for outlier detection. Its resulting data structure is characterized by two components: a crisp lower-approximation and a fuzzy boundary. While the lower-approximation consists of those data points that lie inside the hypersphere, obtained by traditional Support Vector Domain Description (SVDD), the membership degree of each element in the fuzzy boundary is calculated based on its closeness to the support vectors that define the frontier of the lower-approximation. This implies a quite natural way of determining membership values without assuming any prior knowledge about the data. Our computational experiments emphasize the strength of the proposed approach underlining its potential for outlier detection.