Conditional minimum volume ellipsoid with application to multiclass discrimination
The paper presents a new formulation for constructing an \(n\)-dimensional ellipsoid by generalizing the computation of the minimum volume covering ellipsoid, based on the CVaR technique proposed by Rockafellar and Uryasev. The resulting convex optimization problem is solved using an interior point method based on an algorithm proposed by Sun and Freund. The maximization of the normal likelihood function can be characterized as well as generalized in the context of the proposed ellipsoid construction. Motivated by this fact, the proposed ellipsoid construction is examined through a multiclass discrimination problem. Numerical results show the computational performance of the interior point method and the capabilities of the proposed generalization.
scientific article; zbMATH DE number 5612736