On Positive-Correlation-Promoting Reducts

We introduce a new rough-set-inspired binary feature selection framework, whereby it is preferred to choose attributes which let us distinguish between objects (cases, rows, examples) having different decision values according to the following mechanism: for objects u1 and u2 with decision values dec(u1)=0 and dec(u2)=1, it is preferred to select attributes a such that a(u1)=0 and a(u2)=1, with the secondary option – if the first one is impossible – to select a such that a(u1)=1 and a(u2)=0. We discuss the background for this approach, originally inspired by the needs of the genetic data analysis. We show how to derive the sets of such attributes – called positive-correlation-promoting reducts (PCP reducts in short) – using standard calculations over appropriately modified rough-set-based discernibility matrices. The proposed framework is implemented within the RoughSets R package which is widely used for the data exploration and knowledge discovery purposes.