Support Vector Data Description by using hyper-ellipse instead of hyper-sphere

Support Vector Data Description (SVDD) describes data by using a hyper-sphere. In this paper, we propose an extended SVDD (ESVDD) which describes data by using a hyper-ellipse. Clearly, ESVDD can describe data better than SVDD in the input space. Both hyper-sphere and hyper-ellipse are very rigid for data description. The kernel ESVDD which will be proposed in this paper and the kernel SVDD enhance the ability of ESVDD and SVDD for data description, respectively. The formulation of SVDD/ESVDD contains a penalty term C which controls the tradeoff between the volume of hyper-sphere/hyper-ellipse and the training errors. We show that the ESVDD can control this tradeoff better than the SVDD.