In this note, we investigate connections between supervised classification and (Generalized) Nash equilibrium problems (NEP & GNEP). For the specific case of support vector machines (SVM), we exploit the geometric properties of class separation in the dual space to formulate a non-cooperative game. NEP and Generalized NEP formulations are proposed for both binary and multi-class SVM problems.
Accepté le :
DOI : 10.1051/ro/2016024
Mots clés : Supervised classification, support vector machine, multi-class SVM, Nash equilibrium, generalized Nash equilibrium, game theory
@article{RO_2017__51_2_329_0,
author = {Couellan, Nicolas},
title = {A note on supervised classification and {Nash-equilibrium} problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {329--341},
publisher = {EDP-Sciences},
volume = {51},
number = {2},
year = {2017},
doi = {10.1051/ro/2016024},
mrnumber = {3619707},
zbl = {1364.68321},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2016024/}
}
TY - JOUR AU - Couellan, Nicolas TI - A note on supervised classification and Nash-equilibrium problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 329 EP - 341 VL - 51 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016024/ DO - 10.1051/ro/2016024 LA - en ID - RO_2017__51_2_329_0 ER -
%0 Journal Article %A Couellan, Nicolas %T A note on supervised classification and Nash-equilibrium problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 329-341 %V 51 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016024/ %R 10.1051/ro/2016024 %G en %F RO_2017__51_2_329_0
Couellan, Nicolas. A note on supervised classification and Nash-equilibrium problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 329-341. doi : 10.1051/ro/2016024. http://www.numdam.org/articles/10.1051/ro/2016024/
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