Ellipsoidal Support Vector Machines

This paper proposes the ellipsoidal SVM (e-SVM) that uses an ellipsoid center, in the version space, to approximate the Bayes point. Since SVM approximates it by a sphere center, e-SVM provides an extension to SVM for better approximation of the Bayes point. Although the idea has been mentioned before (Ruján, 1997), no work has been done for formulating and kernelizing the method. Starting from the maximum volume ellipsoid problem, we successfully formulate and kernelize it by employing relaxations. The resulting e-SVM optimization framework has much similarity to SVM; it is naturally extendable to other loss functions and other problems. A variant of the sequential minimal optimization is provided for efficient batch implementation. Moreover, we provide an online version of linear, or primal, e-SVM to be applicable for large-scale datasets.