Geodesic
A note on supervised classification and Nash-equilibrium problems
Couellan, Nicolas1 
1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, UPS IMT, 31062 Toulouse cedex 9, France
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 329-341

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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.

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DOI : 10.1051/ro/2016024
Classification : 91A80, 68T05, 68Q32
Keywords: Supervised classification, support vector machine, multi-class SVM, Nash equilibrium, generalized Nash equilibrium, game theory

Couellan, Nicolas 1

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, UPS IMT, 31062 Toulouse cedex 9, France 
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     title = {A note on supervised classification and {Nash-equilibrium} problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {329--341},
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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

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