Efficient algorithms for attributes reduction problem

The theory of rough set, proposed by Pawlak, provides a formal tool for knowledge discovery from imprecise and incomplete data. Attributes reduction is a crucial problem for rough set based data mining. Unfortunately, finding minimal reduct turns out to be a NP-hard problem. In this paper, we propose a heuristic reduction algorithm HeuriRed and a complete heuristic reduction algorithm HeuriComRed based on discernibility matrix. The time and space requirements of two proposed algorithms are both O(\textbackslash{}A\textbackslash{}{*}\textbackslash{}U\textbackslash{}( 2)). In our experiment, in order to investigate the robustness, efficiency and completeness of proposed algorithms, we execute our algorithms HeuriRed, HeuriComRed and genetic reduct on some problems from UCI repository. The experimental results not only indicate the robustness and efficiency of our algorithms, but also provide proofs for the completeness of our algorithm HeuriComRed