A neighborhood rough set model with nominal metric embedding

Rough set theory is an essential tool for measuring uncertainty, which has been widely applied in attribute reduction algorithms. Most of the related researches focus on how to update the lower and the upper approximation operator to match data characteristics or how to improve the efficiency of the attribute reduction algorithm. However, in the nominal data environment, existing rough set models that use the Hamming metric and its variants to evaluate the relations between nominal objects can not capture the inherent ordered relationships and statistic information from nominal values due to the complexity of data. The missing information will affect the accuracy and validity of the data representation, thereby reducing the reliability of rough set models. To overcome this challenge, we propose a novel object dissimilarity measure, i.e., relative object dissimilarity metric(RODM) that learned from nominal data to replace the Hamming metric and then construct a ψ-neighborhood rough set model. It extends the classical rough set model to a robust, representative, and effective model which is close to the characteristics of nominal data. Based on the ψ-neighborhood rough set model, we propose a heuristic two-stage attribute reduction algorithm(HTSAR) to perform the feature selection task. Experiments show that the ψ-neighborhood rough set model can take advantage of more potential knowledge in nominal data and achieve better performance for attribute reduction than the existing rough set model.