Support Vector Data Description with Fractional Order Kernel

Support Vector Data Description (SVDD) as a kernel-based method constructs a minimum hypersphere so as to enclose all the data of the target class in the kernel mapping space. In this paper, it is found that the kernel matrix G of SVDD can always have the Singular Value Decomposition (SVD) and the corresponding kernel mapping space can be made up of a set of base vectors generated by SVD. In order to make the kernel mapping more flexible, we induce a parameter λ into the set of base vectors and thus propose a novel SVDD with fractional order kernel (named λ-SVDD). In doing so, we can expand the solution space for the optimized dual problem of the SVDD. The experimental results on both synthetic data set and some real data sets show that the proposed method can bring more accurate description for all the tested target cases than the conventional SVDD.