DYNAMIC REDUCTS GENERATION USING CASCADING HASHES

Abstract

Reducts preserve original classification properties using minimal number of attributes in a table. Dynamic reducts are the most stable reducts in the process of random sampling of original decision table, and they are proposed to classify unseen cases. Classical reduct generation methods can be applied to compute dynamic reducts but the time complexity of computing dynamic reducts are rarely discussed. This paper proposes a cascading hash function, and dynamic reduct can be derived in O(m2n) time with O(mn) space where m and n are total number of attributes and total number of instances of the table. Core of dynamic reducts is also discussed, and the computation of core of dynamic reducts takes O(mn) time with O(mn) space. Sixteen UCI datasets are applied to compute (F, ε)-dynamic reducts for ε = 1, and results are compared to Rough Set Exploration System (RSES). Results show the execution time on generating dynamic reducts using cascading hash tables is faster than RSES up to 1700 times. Besides the efficiency issue of the algorithms, our algorithms are also very easy to implement and applicable to any system.