Efficient hash-based approximate reduct generation

Approximate reduct relaxes the requirement for the discernibility preserving and it can be applied to generate approximate decision rules. To compute such reducts, discernibility matrix and sorting are commonly used and they take O(mn²) and O(m²n log n) respectively to generate a reduct where m is the total number of attributes and n is the total number of instances. Instead of applying these methods, this paper proposes a hash-based discerning algorithm and an approximate reduct can be generated in O(m²n) time. Empirical results of using four of ten most popular UCI datasets are presented and they are compared to the Rough Set Exploration System (RSES). Besides approximate reducts, the hash-based discerning algorithm can be extended to generate other reducts like possible reduct, dynamic reduct, and generalized reduct.