An Efficient Global Optimization Approach for Rough Set Based Dimensionality Reduction

The theory of rough set, proposed by Pawlak, provides a formal tool for knowledge discovery from imprecise and incomplete data. Dimensionality reduction (RED) is a crucial problem for rough set based data mining. Unfortunately, it proves to be a NP-hard problem. Many reduction algorithms based on heuristic information have been developed, but they are all based on Boolean space {0,1}m. In this paper, we introduce the Universal RED problem model, or UniRED, which transforms the discrete attributes reduction problems on Boolean space {0,1}m into continuous global optimization problems on real space E. Based on this transformation, we develop coordinate gradient descent algorithm RED2.1, and coordinate direct descent algorithm RED3.1 for attributes reduction problems. In order to investigate the robustness and efficiency of proposed algorithms, we execute our algorithm RED3.1 on problems from UCI. Meanwhile, the comparison between algorithm RED3.1 and other famous reduct algorithms, such as dynamical reduct algorithm and genetic reduct algorithm, is presented. The experimental results indicate the robustness and efficiency of our algorithms.