A unified reduction algorithm based on invariant matrices for decision tables

Attribute reduction is an important issue for decision analysis in databases. Absolute reduction, distributive reduction and positive region reduction are the most common types of attribute reduction discussed in the existing literature. This paper considers these three reduction types from the viewpoint of matrices and proposes the concept of reduction invariant matrices for each type in decision tables. Based on invariant matrices, we establish a unified algorithm for all three reduction types in decision tables. We also study the relationships among the three reduction types. Finally, experiments with UCI data sets are presented to verify the effectiveness of the proposed algorithm.