Counting and enumerating aggregate classifiers

Authors:
Jan Adem;Yves Crama;Willy Gochet;Frits C. R. Spieksma
Affiliations:
Financial Markets, ING, Avenue Marnix 24, B-1000 Brussels, Belgium;HEC Management School, University of Liège, Boulevard du Rectorat 7 (B31), 4000 Liège, Belgium;Operations Research Group, FETEW, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000, Leuven, Belgium;Operations Research Group, FETEW, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000, Leuven, Belgium
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We propose a generic model for the ''weighted voting'' aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to enumerate the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions.