Scalarization for Approximate Multiobjective Multiclass Support Vector Machine Using the Large-k Norm

DOI

10.2991/eusflat-19.2019.97How to use a DOI?

Keywords

Support vector machine Multiclass classification Multiobjective optimization Large-$k$ norm

Abstract

We study a multiclass extension of support vector machine (SVM) based on geometric margin maximization. Since there are different margins for different class-pairs, the maximum-margin SVM can be formulated as a multiobjective optimization problem. This multiobjective multiclass SVM (MMSVM) is difficult to be solved because not only it is multiobjective but also it is nonconvex. In order to solve the MMSVM, we approximate it by a convex multiobjective problem, and furthermore scalarize its objective functions. In this paper, we propose a new scalarization for MMSVM using the large-$k$ norm, which provides a spectrum between the $\ell_\infty$ and $\ell_1$ norms.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yoshifumi Kusunoki
AU  - Keiji Tatsumi
PY  - 2019/08
DA  - 2019/08
TI  - Scalarization for Approximate Multiobjective Multiclass Support Vector Machine Using the Large-k Norm
BT  - Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
PB  - Atlantis Press
SP  - 698
EP  - 705
SN  - 2589-6644
UR  - https://doi.org/10.2991/eusflat-19.2019.97
DO  - 10.2991/eusflat-19.2019.97
ID  - Kusunoki2019/08
ER  -