Utilizing Ellipsoid on Support Vector Machines

In this paper we propose a modified framework for support vector machines, called ellipsoid support vector machines (ESVMs), to improve classification capability. The principle of ESVMs is to use a minimum ellipsoid to enclose the specific patterns. Utilizing an approximation algorithm for the minimum enclosing ellipsoid problem in computational geometry allow ESVMs provided better performance than existing SVMs models. With this method maximizing the margin of separation and minimizing the volume of ellipsoid are formulated as the regularized risk function. To simply implementation a smoothing technique is adopted to convert the constrained nonlinear programming problem into an unconstrained optimum problem. By adopting an efficient algorithm the proposed algorithm in this paper can be used with nonlinear kernels and has a time complexity that is linear in $N$. Experiments on large-scale data demonstrate that the ESVMs have comparable performance with existing SVM models.