Weighting factor for attributes based on reduct cardinality

Estimation of attribute importance can be obtained by a mechanism that allows to assign some weight to variables. Weighting attributes can lead to their ordering, which, in turn, can be exploited for feature selection and reduction. Decision reducts constitute an example of a mechanism aiming at dimensionality reduction, embedded in rough set approach to data mining. The paper presents research works, where the process of weighting was driven by the proposed factor based on reducts, with varying their sets, and the results were analysed through the perspective of reduct cardinality, since it is typically considered as the most significant indicator of reduct quality. Constructed rankings of variables were used for inferring sets of decision rules from gradually decreasing numbers of features, and then the performance of the rule classifiers was tested. The experiments show that for the weighting factor to be useful for feature reduction, not only reduct cardinalities, but also the numbers of reducts found need to be taken into account.