A KERNEL-BASED SUPPORT TENSOR DATA DESCRIPTION FOR ONE-CLASS CLASSIFICATION

The issue of one-class classification has got a great deal of studies. However, the classical algorithms represented by Support Vector Data Description (SVDD) have restrictions when the input is not vector. Therefore, we present a nonlinear tensor-based data description that is named as Kernel-based Support Tensor Data Description (KSTDD). The basic thought of KSTDD is to seek for an enclosing hypersphere of smallest volume that contains most of target objects. KSTDD uses tensor as input, and it has the ability to keep more data topology. Meanwhile, the number of parameters that need to be estimated by KSTDD is reduced considerably, which makes KSTDD more fit for small-sample learning. KSTDD is iteratively solved, and the computation complexity and the convergence of the corresponding iterative algorithm are provided respectively. We prove that KSTDD is equivalent to One-Class Support Tensor Machine (OCSTM) for Gaussian-based kernel matrix. However, the two algorithms cannot be completely equivalent to each other since they are quite different for other kernel matrices. Therefore, we evaluate KSTDD with different kernel matrices including Gaussian-based kernel matrices and polynomial-based kernel matrices. Experiments have verified the efficiency of the KSTDD.