Generation of rough sets reducts and constructs based on inter-class and intra-class information

The reduct, originating from the Classic Rough Set Approach (CRSA), is an inclusion minimal subset of attributes that provides discernibility between objects from different classes in at least the same degree as the set of all attributes. It can be thus referred to as being consistent and minimal, which are the two important characteristics of filter-based feature selection. These two characteristics have been also utilized to define reducts within the Dominance-based Rough Set Approach (DRSA). Further, the classic reduct, here referred to as an inter-class reduct, has evolved into what is known as intra-class reduct and construct in CRSA. The idea is that while inter-class reducts utilize only one part of information generated from all pairs of objects, intra-class reducts utilize the remaining part, while constructs utilize both. The paper delivers a final unification of inter-class reducts, intra-class reducts and constructs across CRSA and DRSA, showing how they can be both defined and computed uniformly, i.e. using basically the same concepts and algorithms. It also presents an exact algorithm, capable of generating all exact reduced subsets, but of considerable complexity, as well as a simple and fast heuristic, designed to generate a single reduced subset. Finally, it illustrates the computation process with examples and some experimental evaluation of CRSA constructs, which show how the use of both the inter-class and the intra-class information can assist the attribute reduction process and help obtaining useful insights into the analyzed data set.