Hypersphere Neighborhood Rough Set for Rapid Attribute Reduction

Yu Fang, Xue-Mei Cao, Xin Wang, Fan Min

Abstract: Neighborhood rough set (NRS) has been successfully applied to attribute reduction for numeric data. Most existing algorithms have a time complexity of at least $$O(MN^2)$$ . In this paper, we propose a hypersphere neighborhood rough set (HNRS) algorithm with a time complexity of O(MN). HNRS adaptively generates the neighborhood radius without manual setting. First, a set of hyperspheres is built to accurately describe the decision boundary on the original data. Second, the hypersphere radius serves as the neighborhood radius to obtain the positive region. Therefore, we avoid the time-consuming grid searching of the NRS algorithm for radius optimization. Third, according to the change of objects within the positive region, the redundant attributes can be reduced efficiently. Experimental results show that HNRS outperforms state-of-the-art attribute reduction methods in terms of both efficiency and classification accuracy.