Ensembles of bireducts: Towards robust classification and simple representation

Abstract

We introduce the notion of a bireduct, which is an extension of the notion of a reduct developed within the theory of rough sets. For a decision system double-struck A = (U, A ∪ {d}), a bireduct is a pair (B,X), where B ⊆ A is a subset of attributes that discerns all pairs of objects in X ⊆ U with different values of the decision attribute d, and where B and X cannot be, respectively, reduced and extended without losing this property. We investigate the ability of ensembles of bireducts (B,X) characterized by significant diversity with respect to both B and X to represent knowledge hidden in data and to serve as the means for learning robust classification systems. We show fundamental properties of bireducts and provide algorithms aimed at searching for ensembles of bireducts in data. We also report results obtained for some benchmark data sets. © 2011 Springer-Verlag.