Stratégies de rejet en classification supervisée: une synthèse par opérateurs de De Morgan
Reject strategies for supervised classification with De Morgan operators : a review
OPEN ACCESS
In this article we review strategies used in the design of two-folded rejection-based classifiers. Beside the so-called classical “accept-first” strategy we have recently proposed very general families built on two different approaches, namely the “reject-first”[Fré98a, MF01b] and “mixture-first”[SFM02] reject schemes. These three approaches differ by the kind, as well as the order, of the tests leading to the classifier final output. While the first one starts by testing for distance rejection and, if necessary, finishes by testing for exclusive classification or ambiguity rejection respectively, the two others start respectively by testing for exclusive classification and ambiguity rejection, and then finish by the remaining alternatives. We unify the three schemes by defining fuzzy operators built on De Morgan operators (t-norms, t-conorms, complement). Behaviours of such different classifiers are illustrated on artificially generated examples.
Résumé
Dans cet article, nous proposons une synthèse des stratégies mises en œuvre pour la conception de discriminateurs avec options de rejet opérant en deux étapes séquentielles. Outre l'approche classique dite «accepte d'abord», nous avons récemment défini des classes générales qui suivent deux approches différentes dites «rejette d'abord» [Fré98a, MF01b] et «mélange d'abord» [SFM02]. Ces trois approches diffèrent par la nature, et l'ordre, des tests effectués pour produire la sortie du discriminateur. La première consiste à tester en premier lieu le rejet de distance, puis seulement si nécessaire à tester l'affectation exclusive contre le rejet d'ambiguïté, la deuxième et la troisième, quant à elles, débutent, respectivement, par un test pour le classement exclusif et un test pour le rejet d'ambiguïté à opposer aux alternatives correspondantes. Nous unifions ici ces trois familles de discriminateurs par l'utilisation d'opérateurs flous fondés sur des opérateurs de De Morgan (t-norme, t-conorme, complément). Les comportements des différentes approches sont illustrées sur des exemples synthétiques.
Classification, reject options, De Morgan operators
Mots clés
Classification supervisée, rejet, opérateurs de De Morgan
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