Abstract
When there are two classes whose mean vectors and covariance matrices are known, Lanckriet et al. [7] 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 |
|---|---|
| Pages (from-to) | 191-201 |
| Number of pages | 11 |
| Journal | Journal of the Operations Research Society of Japan |
| Volume | 51 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2008 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Quadratic and convex minimax classification problems
AU - Kitahara, Tomonari
AU - Mizuno, Shinji
AU - Nakata, Kazuhide
PY - 2008/6
Y1 - 2008/6
N2 - When there are two classes whose mean vectors and covariance matrices are known, Lanckriet et al. [7] 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.
AB - When there are two classes whose mean vectors and covariance matrices are known, Lanckriet et al. [7] 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.
UR - http://www.scopus.com/inward/record.url?scp=49349087498&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=49349087498&partnerID=8YFLogxK
U2 - 10.15807/jorsj.51.191
DO - 10.15807/jorsj.51.191
M3 - Article
AN - SCOPUS:49349087498
VL - 51
SP - 191
EP - 201
JO - Journal of the Operations Research Society of Japan
JF - Journal of the Operations Research Society of Japan
SN - 0453-4514
IS - 2
ER -