Game theoretical analysis of the simple one-vs.-all classifier

Authors:
Yuichi Shiraishi
Affiliations:
Department of Statistical Science, The Graduate University for Advanced Studies, The Institute of Statistical Mathematics, Minami-Azabu, Tokyo 106-8569, Japan
Venue:
Neurocomputing
Year:
2008

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Abstract

One of the popular multi-class classification methods is to combine binary classifiers. As well as the simplest approach, a variety of methods to derive a conclusion from the results of binary classifiers can be created in diverse ways. In this paper, however, we show that the simplest approach by calculating linear combinations of binary classifiers with equal weights has a certain advantage. After introducing the ECOC approach and its extensions, we analyze the problems from a game-theoretical point of view. We show that the simplest approach has the minimax property in the one-vs.-all case.