Conditional minimum volume ellipsoid with application to multiclass discrimination
type: Item
instance of: scholarly article
title: Conditional minimum volume ellipsoid with application to multiclass discrimination
zbMATH Open document ID: 1201.90156
author: Jun-Ya Gotoh
author: Akiko Takeda
published in: Computational Optimization and Applications
publication date: 2009-10-09T00:00:00Z
full work available at URL: https://tsukuba.repo.nii.ac.jp/
review text: 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.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C51
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 5612736
zbMATH Keywords: conditional value-at-risk
zbMATH Keywords: minimum volume covering ellipsoid
zbMATH Keywords: minimum volume ellipsoid estimator
zbMATH Keywords: multiclass discrimination
zbMATH Keywords: interior point method
reviewed by: Oliver Stein
describes a project that uses: SDPT3
describes a project that uses: MVE
describes a project that uses: UCI-ml
describes a project that uses: LIBSVM
MaRDI profile type: Publication
OpenAlex ID: W2150437261
cites work: An Algorithm for Separating Patterns by Ellipsoids
cites work: Lectures on modern convex optimization. Analysis, algorithms, and engineering applications
cites work: Q4821526
cites work: Q4851781
cites work: On the complexity of approximating the maximal inscribed ellipsoid for a polytope
cites work: Q4782159
cites work: Breast Cancer Diagnosis and Prognosis Via Linear Programming
cites work: Q3749928
cites work: Q4692741
cites work: Clustering via minimum volume ellipsoids
cites work: Computation of Minimum-Volume Covering Ellipsoids
cites work: Optimal design: Some geometrical aspects of D-optimality
cites work: SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
cites work: On Numerical Solution of the Maximum Volume Ellipsoid Problem
DOI: 10.1007/S10589-007-9097-X
description: scientific article; zbMATH DE number 5612736