Ellipsoidal support vector data description in kernel PCA subspace

Support vector data description (SVDD) is a popular kernel method for novelty detection, which constructs a spherical boundary around the normal class with minimum volume. Sphere being a special case of ellipsoid, it thus will be more general to extend classical SVDD to ellipsoidal boundary and better description ability can be anticipated. In this paper, we propose an ellipsoidal SVDD (ESVDD) by incorporating the ellipsoid estimation into kernel principal component analysis (kernel PCA). A minimum volume enclosing ellipsoid (MVEE) is constructed around a dataset in the kernel PCA subspace which can be solved through convex optimization. The outlyingness for new object is measured by the Mahalanobis distance. Experiments on artificial dataset validate the effectiveness of our method.