Granular maximum decision entropy-based monotonic uncertainty measure for attribute reduction

Abstract Attribute reduction is considered an important preprocessing step in machine learning, pattern recognition, and data mining, and several attribute reduction measures based on rough set theory have been introduced to deal with vague, imprecise, or uncertain data. However, some of the measures inherently suffer from nonmonotonicity and redundancy. In this paper, a monotonic uncertainty measure, called granular maximum decision entropy (GMDE), is proposed. Specifically, we first develop a notion of maximum decision entropy. By integrating the uncertainty of the maximum decision entropy with the granulation of knowledge, a novel uncertainty measure is then presented, and its monotonicity is theoretically proved. We also provide a forward heuristic attribute reduction algorithm based on the proposed uncertainty measure, which could simultaneously select the informative attributes and remove the unnecessary attributes in the procedure of attribute reduction, thus resulting in high efficiency. The experiments conducted on several UCI data sets demonstrate that the proposed measure and algorithm are effective and computationally inexpensive and are superior to the representatives in terms of classification performance and efficiency.