Double-local rough sets for efficient data mining

Abstract As an important extension of classical rough sets, local rough set model is effective to handle large data sets with small amounts of labeled data, which has an obvious advantage in improving computational performance. However, the existing mining algorithms based on local rough sets are still computationally time-consuming in processing large-scale labeled data sets. To overcome this limitation, we propose an enhanced local rough set framework called double-local rough sets, by introducing the notion of local equivalence classes. Under this framework, we define the lower deletion matrix, the upper addition matrix, and the upper deletion matrix. Based on these matrices, we develop a fast iteration method for computing the approximations, which is vital for attribute reduction and knowledge discovery. Furthermore, a fast attribute reduction method is presented by accelerating the calculation of stop criteria and attribute significance measures, which can obtain the same attribute reduct as its original local rough set version. Theoretical analysis and experimental results indicate that the proposed algorithms in double-local rough sets significantly outperform their original counterparts in classical local rough sets.