# Quadratic and convex minimax classification problems

Tomonari Kitahara, Shinji Mizuno, Kazuhide Nakata

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

When there are two classes whose mean vectors and covariance matrices are known, Lanckriet et al.  consider the Linear Minimax Classification (LMC) problem and they propose a method for solving it. In this paper we first discuss the Quadratic Minimax Classification (QMC) problem, which is a generalization of LMC. We show that QMC is transformed to a parametric Semidefinite Programming (SDP) problem. We further define the Convex Minimax Classification (CMC) problem. Though the two problems are generalizations of LMC, we prove that solutions of these problems can be obtained by solving LMC.

Original language English 191-201 11 Journal of the Operations Research Society of Japan 51 2 https://doi.org/10.15807/jorsj.51.191 Published - Jun 2008 Yes

### Fingerprint

Minimax
Semidefinite programming
Covariance matrix

### All Science Journal Classification (ASJC) codes

• Decision Sciences(all)
• Management Science and Operations Research

### Cite this

Quadratic and convex minimax classification problems. / Kitahara, Tomonari; Mizuno, Shinji; Nakata, Kazuhide.

In: Journal of the Operations Research Society of Japan, Vol. 51, No. 2, 06.2008, p. 191-201.

Research output: Contribution to journalArticle

Kitahara, Tomonari ; Mizuno, Shinji ; Nakata, Kazuhide. / Quadratic and convex minimax classification problems. In: Journal of the Operations Research Society of Japan. 2008 ; Vol. 51, No. 2. pp. 191-201.
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